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A Review of High Gain and High Efficiency Reflectarrays for 5G Communications <s> A. DIFFERENT ELEMENTS WITH HIGH GAIN REFLECTARRAY OPERATION <s> A novel structure using a variable microstrip ring with a slot ring on part of the ground plane is proposed as an auxiliary unit cell in a reflectarray. A progressive phase r... | The design of a unit cell reflectarray element plays an important role when it comes to the performance improvement. A notable work based on unit cell with a slot in ground plane was presented in BIB001 for the performance improvement of reflectarray antenna. A ring element was used with a same type of slot in the grou... |
A Review of High Gain and High Efficiency Reflectarrays for 5G Communications <s> B. FULL REFLECTARRAY BASED TECHNIQUES <s> Benzocyclobutene (BCB) polymer is proposed in this study as an innovative and versatile substrate material for millimetre-wave reflectarrays. The excellent material features in terms of low loss, ... | The gain of reflectarray antenna is actually governed and analyzed by the operation of a full reflectarray antenna. The combine effects of patch elements, substrate, feeding strategy and type of reflectarray can significantly control its gain behavior. The effects of unit cell patch element on the gain performance of r... |
A Review of High Gain and High Efficiency Reflectarrays for 5G Communications <s> 1) REFLECTARRAY WITH A SUB-REFLECTOR <s> The design, construction and measured performance is described of an offset parabolic reflector antenna which employs a reflectarray subreflector to tilt the focused beam from the boresight directi... | As earlier explained before the sub-reflector with a main reflectarray is used mainly to compensate the losses generated from conventional feed horn antenna during the illumination. These losses have an immense impact on the gain performance of the reflectarray antenna while controlling its cross polarization and side ... |
A Review of High Gain and High Efficiency Reflectarrays for 5G Communications <s> 2) FEEDING MECHANISM <s> A new cell element is introduced for broadband reflectarray applications. The presented unit cell exhibits linear phase response which makes it a suitable candidate for broadband X-Ku band applications. This cell ... | The effect of feed movement has been already analyzed for bandwidth improvement. The same technique was also used for the optimization of the gain performance of reflectarrays BIB001 . A unit cell with three rectangular loops was proposed for the construction of a full reflectarray. Three feed positions of 33 cm, 40 cm... |
A Review of High Gain and High Efficiency Reflectarrays for 5G Communications <s> 3) TYPE OF REFLECTARRAY <s> Dielectric reflectarray antennas are studied in this paper as a possible low-loss and low-cost solution for high gain THz antennas. Variable height dielectric slabs are proposed for the reflectarray elements wh... | The gain of a reflectarray can also be optimized based on its type. In this sub-section some types of reflectarray antenna other than the conventional microstrip reflectarray have been discussed for the gain enhancement purpose. Dielectric reflectarrays and metallic reflectarrays are two common types that are mostly us... |
A Review of High Gain and High Efficiency Reflectarrays for 5G Communications <s> A. DIFFERENT ELEMENTS WITH HIGH EFFICIENCY REFLECTARRAY OPERATION <s> The microstrip reflectarray is rapidly becoming an attractive alternative solution to the traditional parabolic reflector antenna due to its various advantages, such as... | The progressive phase distribution of the unit cell element of a reflectarray antenna is responsible for the optimized gain and efficiency performance. Some resonant elements have inability to acquire a full 360 • phase swing, which increases the amount of phase errors while designing a full reflectarray antenna. An en... |
A Review of High Gain and High Efficiency Reflectarrays for 5G Communications <s> FIGURE 12. <s> The objective of this paper is to carry out analysis and design for X/Ka dual-band, frequency selective surface (FSS)-backed reflectarrays. In this design, a novel ring structure has been developed as the cell element for b... | Dual layer reflectarray with Ka/X-band of operation BIB001 . compared to conventional design. The same approach for cross polarization reduction was also applied to a dual band design BIB003 where a circular element with cross slot and two phase tuning stubs was proposed for X-band and K-band operation as depicted in F... |
A Review of High Gain and High Efficiency Reflectarrays for 5G Communications <s> FIGURE 13. <s> In this article, a novel method is introduced to design a high efficiency and broadband reflectarray.Several techniques will be introduced for designing wideband reflectarray. First, by using fractal ring unit cell with 700... | Gain and efficiency with respect to frequency of the reflectarray with λ/2 element size BIB001 . As it has been mentioned earlier, the feed mechanism can also affect the gain and hence the efficiency performance of reflectarray antenna. In a proposed design of a reflectarray antenna feed distance from reflectarray was ... |
Survey on Reversible Watermarking <s> Higher embedding capacity : <s> An undesirable side effect of many watermarking and data-hiding schemes is that the host signal into which auxiliary data is embedded is distorted. Finding an optimal balance between the amount of information embedded and the induced distortion is th... | Capacity property of digital watermarks refers to amount of information that can be embedded within the media. The embedding capacity of the reversible watermarking is much more than the conventional watermarking scheme. The embedding capacity should not be low as it affects the accuracy of extracted watermark and the ... |
Survey on Reversible Watermarking <s> II. REVERSIBLE WATERMARKING SCHEME BY APPLYING DATA COMPRESSION <s> The need for reversible or lossless watermarking methods has been highlighted to associate information with losslessly processed media or to enable their authentication. The paper first analyzes the specificity and... | To extract the original image from the watermarked image, the recovery information is embedded into the original image. With the recovery information, we also have to embed the watermark data into the original image. That's why the capacity required to embed the information is more. So, to embed more data, a solution i... |
The State-of-the-Art of Knowledge-Intensive Agriculture: A Review on Applied Sensing Systems and Data Analytics <s> Introduction <s> Computer vision technology is a sophisticated inspection technology that is in common use in various industries. However, it is not as widely used in aquaculture. Application of computer ... | The Food and Agriculture Organization of the UN (FAO) predicts that the global population will reach 9.2 billion by 2050, and food production must increase by 70 percent to keep the pace . The income distribution in the world is uneven and hugely divided. In one part of the world, prosperity exists, and there is alway... |
The State-of-the-Art of Knowledge-Intensive Agriculture: A Review on Applied Sensing Systems and Data Analytics <s> Sensors and Data Analytics in Agriculture <s> Abstract This paper proposed an agricultural application of wirless sensor network. The main work is to implement two types of nodes and building sensor netwo... | 3.1. Agronomy/Crop Farming. The general use of wireless sensor networks in crop monitoring and data acquisition can be found in various research and review articles BIB001 BIB008 . Modern agronomical research and practice are becoming more and more data intensive. Data are continually collected, analyzed, and simulate... |
The State-of-the-Art of Knowledge-Intensive Agriculture: A Review on Applied Sensing Systems and Data Analytics <s> Journal of Sensors <s> Computer vision technology is a sophisticated inspection technology that is in common use in various industries. However, it is not as widely used in aquaculture. Application of com... | Markov process (CTMP) in order to model the random movement pattern (stochastic process) as shown in Here, P ij is the total probability that the cow moves from the location i to j. P n ij represents the probability P ij after the cow has taken n steps. p 1 , p 2 , p 3 , and p 4 represent the probability the cow is in ... |
The State-of-the-Art of Knowledge-Intensive Agriculture: A Review on Applied Sensing Systems and Data Analytics <s> Korean Scenario <s> The concept of "Plant factory" could realize the multiple targets of high yield, high quality, high efficiency and security. It had become the trend of agricultural development. It sol... | South Korea is a highly industrialized country and hosts some of the world's huge leading tech-giants like Samsung, LG, and Hyundai. The Korean government has initiated steps in transferring the technology used in the industrial sector for the development of the agricultural sector as well. A report published by the Ko... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> C. Why Is Data Link Important in UAVs? <s> Unmanned Aircraft System networks are a ::: special type of networks where high speeds of the nodes, long distances and ::: radio spectrum scarcity pose a number of challenges. In these network... | UASs come with many challenges, including the need for reliable data links and autonomous controls. Although this is not a general assumption, in case of collision, the kinetic energy stored in a 25 kg UAV would instigate severe damage. That means even the small UAVs need a reliable data link to guarantee safe flights.... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> A. Spectrum Considerations <s> This paper presents a summary of a measurement campaign on radio propagation channels in air-to-ground (A2G) links based on a usage scenario of unmanned aircraft services (UASs). In order to reveal their p... | The most commonly used frequency bands in UASs' data links are K, Ku, X, C, S, and L bands. We discuss each of these briefly next. K (18 to 27 GHz) band is a wide-range band that can carry a large amount of data, but it consumes a lot of power for transmission and is highly affected by environmental interferences. K, K... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> C. SWaP and Resource Allocation Considerations <s> The proven value of DOD Unmanned Aerial Vehicles (UAVs) will ultimately transition to National and Homeland Security missions that require real-time aerial surveillance, situation aware... | Size, weight and power (SWaP) of the aircraft are other design considerations to help determine which data link should be used in the system. The data link technologies that provide high range and reliability without increasing the size, weight or power consumption of the system are always preferable. The SWaP consider... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> D. Signal Propagation Considerations <s> The key challenges in the design of datalinks for UAS systems compared to other wireless links is the long range of distances and speeds that need to be covered. The amount of spectrum available ... | Due to the mobile nature of the UASs, several challenges arise with the signal propagation, including the Doppler frequency shift, dynamic connectivity, antenna power, losses due to signal attenuation, multi-path fading, interference, and jamming. The Doppler frequency shift is one of the important challenges in design... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> E. Routing <s> We consider a single Unmanned Aerial Vehicle (UAV) routing problem where there are multiple depots and the vehicle is allowed to refuel at any depot. The objective of the problem is to find a path for the UAV such that ea... | Route-planning is a critical step in every applications of UAVs. The scheduled route must be low risk and low cost, while maintaining the mission goals. In a multi-UAV network, this consideration becomes even more complicated. For instance, these concepts must be studied carefully: avoiding any conflict among the UAVs,... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> B. Disadvantages <s> The integration of unmanned aircraft systems (UAS) into the National Airspace System (NAS) presents many challenges including airworthiness certification. As an alternative to the time consuming process of modifying... | Despite all the great benefits of the satellite communication, this technology is an expensive data link, and it becomes cost effective only for high-altitude or at most for medium-altitude UAVs. Hence, SATCOM has not been used for small UASs so far. One of the main challenges with all satellite communications is laten... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> D. Available SATCOM Services <s> UAVs have been proposed as a platform for providing theater communications for the warfighter. UAVs have the advantage of being rapidly deployable and the potential to provide high capacity over-the-hori... | An increasing number of companies are providing satellite communication and are trying to test their services for the UAVs. Unlike the land-based or terrestrial communication, which has been provided by just a few companies offering relatively the same services, there are many different types of SATCOM services. Pickin... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> E. Related Research <s> Rapidly increasing growth and demand in various Unmanned Aircraft Systems (UAS) have pushed governmental regulation development and numerous technology research activities toward integrating unmanned and manned a... | Finding a proper solution to the problem of sharing the same spectrum with FSS in Ku/Ka band have been studied in BIB007 , BIB006 . In these works, the primary focus is to achieve an efficient BLOS satellite data link for the UAVs. However, as concluded, a specific regulation for SATCOM is still needed. From another pe... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> C. Cellular Aviation, 4G, and 5G <s> This letter studies a wireless system consisting of distributed ground terminals (GTs) communicating with an unmanned aerial vehicle (UAV) that serves as a mobile base station (BS). The UAV flies cyc... | As the mobile communication evolved to the fourth generation (4G), data rate, latency, throughput, and interference management improved significantly. Also, 4G or LTE enabled data links are dynamic and can be configured based on UAV requirements. Thus, they are considered a potential candidate for several UAS applicati... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> D. UAVs for Cellular Services <s> This paper presents an overview of unmanned aircraft systems developed at the University of Colorado and the development of a new software defined radio sensor that will be integrated into the existing ... | UAVs can also be very useful for cellular services (e.g., in case of emergency or disaster) to perform as a flying base stations (BS). In cellular communications, a wireless connection to the public telephone network is established through the local cell tower. During a disaster, these towers may lose their functionali... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> 1) UAVs as Users: <s> Recent advances in interference cancellation and signal processing techniques can enable full-duplex radios and multi-packet reception (MPR) capability, which will have significant impacts on the medium access cont... | The applicability of using 3G and 4G mobile communications for UAVs' data link has been studied in BIB003 . The results of the paper show that the Long-Term Evolution (LTE) and UMTS network provide secure, low latency, and high throughput data exchange. These features are critical in the UAV applications. On the other ... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> Aeronautical <s> The potential benefits and challenges of applications of IEEE 802.16j-based relays in AeroMACS networks are discussed at the outset. Perhaps the most important advantage of application of multihop relays in AeroMACS net... | Mobile Airport Communications System (AeroMACS) is based on WiMAX standard, IEEE 802. BIB005 . This standard is defined for the physical layer and the MAC layer of the ground-to-aircraft and aircraft-to-aircraft communications at airports . AeroMACS was developed by the Radio Technical Commission for Aeronautics (RTCA... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> B. L-DACS <s> The demand for air transportation is continuously growing. Likewise, unmanned aircraft systems (UAS) are proliferating at a tremendous pace. Both current and future air-to-ground (AG) communications systems will be deploye... | Several research papers exist on L-DACS1 such as BIB001 - BIB002 . A new multicarrier communication system operating in L band based on filter-bank multicarrier (FBMC) was investigated in these papers to enhance the advantages of L-DACS1. Of the two versions, only L-DACS1 is now active. It is being considered to be a p... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> C. ADS-B <s> Air traffic is continuously increasing worldwide, with both manned and unmanned aircraft looking to coexist in the same airspace in the future. Next generation air traffic management systems are crucial in successfully hand... | Automatic Dependent Surveillance-Broadcast (ADS-B) is a standard developed by the FAA. Current ADS-B systems will evolve to a next generation, called "ADS-B Next." The current systems work on 978/1090 MHz, but the next generation will be centered initially at 1030 MHz for more robustness and better efficiency. Complete... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> D. IEEE 802.11 <s> Advances in control engineering and material science made it possible to develop small-scale unmanned aerial vehicles (UAVs) equipped with cameras and sensors. These UAVs enable us to obtain a bird's eye view of the e... | Wireless local area networks (WLAN) are the most popular data links used in small UAVs so far. The reasons for its popularity include easy setup, mobility support, and low cost. IEEE 802.11, commonly known as Wi-Fi, is a set of standards for implementing WLAN in 2.4, 3.6, 5 and 60 GHz bands BIB004 . The 802.11 and 802.... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> F. CPDLC <s> This paper presents an analysis of the use of Controller-Pilot Data Link Communication (CPDLC) application for Unmanned Aerial System (UAS). A fault model for injecting different types of faults in the communication applica... | Controller pilot data link communication (CPDLC) is a message-based service for manned aviation communications between the pilot and the ATC. CPDLC usually uses satellite communication and VDL2 data links for ATC communications. InmarSAT was trying to get the certification to be allowed to tunnel CPDLC over their satel... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> G. SWIM <s> The NextGen National Airspace System (NAS) has begun to take shape with the functional emergence of En Route Automation Modernization (ERAM) and the Terminal Automation Modernization and Replacement (TAMR). NextGen Programs ... | As mentioned before, FAA is focusing on its future global plan for aviation standardization, NextGen, planning to roll out by 2025. System Wide Information Management (SWIM) is the main part of this plan. FAA is focusing on using SWIM to provide a secure platform for cooperation among the national and international avi... |
Potential Data Link Candidates for Civilian Unmanned Aircraft Systems: A Survey <s> H. Preliminary Study <s> Aeronautical Mobile Airport Communications System (AeroMACS) is based on the IEEE 802.16e mobile wireless standard commonly known as WiMAX. It is expected to be the main part of the next-generation aviation comm... | We have done a preliminary study BIB001 . In this work, we have investigated the limitations that AeroMACS imposes on the UAV communications in theory, when it comes to integrating the UAVs into the NAS, using AeroMACS. Signal to inter carrier interference (ICI) ratio and channel coherence time are the two channel mode... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> I. INTRODUCTION <s> Presents serial and parallel algorithms for solving a system of equations that arises from the discretization of the Hamilton-Jacobi equation associated to a trajectory optimization problem of the following type. A vehicle starts at a pr... | The Fast Marching Method (FMM) has been extensively applied since it was first proposed in 1995 BIB001 as a solution to isotropic control problems using first-order semi-Langragian discretizations on Cartesian grids. The first approach was introduced by Tsitsiklis BIB001 , but the most popular solution was given a few ... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> OTHER ALGORITHMS NOT INCLUDED IN THE SURVEY <s> Recently, fast marching methods (FMM) beyond first order have been developed for producing rapid solutions to the eikonal equation. In this paper, we present imaging results for 3‐D prestack Kirchhoff migratio... | There are some variations of these approaches which focus on improving some of the characteristics of the solution given by the fast methods. For example, in order to enhance the computation time, parallel approaches have been proposed of both the Fast Marching and Fast Sweeping BIB003 methods. In the Heat Method, us... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> A. N-DIMENSIONAL DISCRETE EIKONAL EQUATION <s> We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front also can be passive... | In this section the most common first-order discretization of the Eikonal equation is detailed. It is first derived in 2D for better understanding and then an n-dimensional approach is explained. The most common first-order discretization is given in BIB001 , which uses an upwind-difference scheme to approximate partia... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> III. FAST MARCHING METHODS <s> Abstract ::: A fast marching level set method is presented for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing ... | The Fast Marching Method (FMM) BIB001 is the most common Eikonal solver. It can be classified as a label-setting, Dijkstralike algorithm . It uses a first-order upwind finite difference scheme, which is described in detail in Section II, to simulate an isotropic front propagation computing the solution following Bellm... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> 8: <s> Unmanned surface vehicles (USVs) have been deployed over the past decade. Current USV platforms are generally of small size with low payload capacity and short endurance times. To improve effectiveness there is a trend to deploy multiple USVs as a fo... | end for Propagation: 9: while Narrow = ∅ do 10: x min ← arg min x i ∈Narrow {T i } Narrow top operation. BIB001 : For all neighbors not in Frozen. BIB002 : T i ← T i Narrow increase operation if x i ∈ Narrow. Narrow ← Narrow ∪ {x i } |
Fast Methods for Eikonal Equations: An Experimental Survey <s> 15: <s> We present a variational framework that integrates the statistical boundary shape models into a Level Set system that is capable of both segmenting and recognizing objects. Since we aim to recognize objects, we trace the active contour and stop it n... | end if BIB001 : Narrow push operation. end if 16: end for 17: Narrow ← Narrow\{x min } Narrow pop operation. BIB003 : end if 20: end while 21: return T 22: end procedure FIGURE 2. Untidy priority queue representation. Top: first iteration, the four neighbors of the initial point are pushed. Middle: the first bucket bec... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> 23: <s> The average number of levels that a new element moves up when inserted into a heap is investigated. Two probabilistic models under which such an average might be computed are proposed. A `Lemma of Conservation of Ignorance' is formulated and used in... | end while 24: return T 25: end procedure TABLE 1. Summary of amortized time complexities for common heaps used in FMM (n is the number of elements in the heap). Among all the existing heaps, FMM is usually implemented with a binary heap BIB001 . However, the Fibonacci Heap BIB002 has a better amortized time for Increas... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> C. UNTIDY FAST MARCHING METHOD <s> In this paper a fast sweeping method for computing the numerical solution of Eikonal equations on a rectangular grid is presented. The method is an iterative method which uses upwind difference for discretization and uses ... | The Untidy Fast Marching Method (UFMM) BIB002 , BIB003 follows exactly the same procedure as FMM. However, a special heap structure, which reduces the computational complexity of the method to O(n), is used: the untidy priority queue. This untidy priority queue is closer to a look-up table than to a tree. It assumes th... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> IV. FAST SWEEPING METHODS <s> We derive a Godunov-type numerical flux for the class of strictly convex, homogeneous Hamiltonians that includes $H(p,q)=\sqrt{ap^{2}+bq^{2}-2cpq},$ $c^{2}<ab.$ We combine our Godunov numerical fluxes with simple Gauss--Seidel-... | The Fast Sweeping Method (FSM) BIB002 , BIB001 is an iterative algorithm which computes the time-of-arrival map by successively sweeping (traversing) the whole grid following a specific order. FSM performs Gauss-Seidel iterations in alternating directions. These directions are chosen so that all the possible characteri... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> 13: <s> We present a variational framework that integrates the statistical boundary shape models into a Level Set system that is capable of both segmenting and recognizing objects. Since we aim to recognize objects, we trace the active contour and stop it n... | end if 14: end for 15: end if 16: return stop 17: end procedure The LSM procedure is detailed in Algorithm 8. During the initialization, all the cells are labeled as Frozen (the meaning of locked and Frozen is the same). Then, the starting cells X s are assigned a 0 value and all their neighbors are labeled as Narrow (... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> B. DYNAMIC DOUBLE QUEUE METHOD <s> In this paper, we outline two improvements to the fast sweeping method to improve the speed of the method in general and more specifically in cases where the speed is changing rapidly. The conventional wisdom is that fast ... | The Dynamic Double Queue Method (DDQM) BIB001 is inspired by LSM but resembles GMM. DDQM is 39012 VOLUME 7, 2019 Algorithm 10 Group Marching Method 1: procedure GMM(X , T , F, X s ) Initialization: 2: Unknown ← X , Narrow ← ∅, Frozen ← ∅ 3: for x i ∈ X s do 6: Adding neighbors of starting points to Narrow. BIB002 : end... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> 16: <s> Recently, fast marching methods (FMM) beyond first order have been developed for producing rapid solutions to the eikonal equation. In this paper, we present imaging results for 3‐D prestack Kirchhoff migration using traveltimes computed using the f... | end for 17: end for Propagation: 18: while Narrow = ∅ do BIB002 : for x i ∈ (Narrow ≤ T m ) REVERSE do Reverse traversal. BIB003 : end if 26: end for 27: end for 28: for x i ∈ (Narrow ≤ T m ) FORWARD do Forward tranversal. 29: for x j ∈ (N (x i ) ∩ X \Frozen) do : end if BIB001 : Unknown ← Unknown\{x i } |
Fast Methods for Eikonal Equations: An Experimental Survey <s> 40: <s> Abstract ::: A fast marching level set method is presented for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propaga... | Frozen ← Frozen ∪ {x i } 41: end for 42: end while 43: return T 44: end procedure conceptually simple: the Narrow set is divided into two nonsorted FIFO queues: one with cells to be evaluated sooner and the other one with cells to be evaluated later. Every iteration, an element from the first queue is evaluated. If its... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> C. FAST ITERATIVE METHOD <s> We present a variational framework that integrates the statistical boundary shape models into a Level Set system that is capable of both segmenting and recognizing objects. Since we aim to recognize objects, we trace the active ... | The Fast Iterative Method (FIM) BIB002 is based on the iterative method proposed by but inspired by FMM. It also resembles DDQM (concretely, its single queue variant). It iteratively evaluates every point in Narrow until it converges. Once a node has converged its neighbors are inserted into Narrow and the process con... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> 1) EMPTY MAP <s> In this paper we propose a novel computational technique to solve the Eikonal equation efficiently on parallel architectures. The proposed method manages the list of active nodes and iteratively updates the solutions on those nodes until th... | This experiment is designed to show the performance of the methods in the most basic situation, where most of the algorithms perform best. An empty map with constant speed represents the simplest possible case for the Fast Methods. In fact, analytical methods could be implemented by computing the Euclidean distance fro... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> 5) PATH PLANNING <s> Being able to build a map of the environment and to simultaneously localize within this map is an essential skill for mobile robots navigating in unknown environments in absence of external referencing systems such as GPS. This so-calle... | Fast Methods are commonly used for low-dimensional path planning problems, given that they produce deterministic results, are complete (will find a solution if there is any), and it is possible to easily influence some properties of the paths, such as their smoothness or obstacle clearance . Fast Methods are applied f... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> 6) VESSEL SEGMENTATION <s> Presents serial and parallel algorithms for solving a system of equations that arises from the discretization of the Hamilton-Jacobi equation associated to a trajectory optimization problem of the following type. A vehicle starts ... | Another of the main uses of Fast Methods is computer vision for medical applications, as intermediary steps in more complex algorithms. For example, in BIB004 , FMM is used for 2D vessel segmentation in retina images based on the assumption that vessels usually follow a smooth path. Flórez-Valencia et al. perform a ce... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> VII. DISCUSSION <s> We derive a Godunov-type numerical flux for the class of strictly convex, homogeneous Hamiltonians that includes $H(p,q)=\sqrt{ap^{2}+bq^{2}-2cpq},$ $c^{2}<ab.$ We combine our Godunov numerical fluxes with simple Gauss--Seidel-type itera... | Two different sets of experiments have been carried out. The first set contains canonical problems previously included in the literature that cover the best and worst case scenarios for all the methods. This set consists of: empty map, alternating barriers, random speed function and checkerboard experiment. The main hy... |
Fast Methods for Eikonal Equations: An Experimental Survey <s> VIII. CONCLUSIONS <s> A computational study of the fast marching and the fast sweeping methods for the eikonal equation is given. It is stressed that both algorithms should be considered as "direct" (as opposed to iterative) methods. On realistic grids, fas... | In this paper we have introduced the main Fast Methods in a common mathematical framework, adopting a practical point of view. Besides, an exhaustive comparison of the methods has been performed, which allows the users to choose among them depending on the application. The code is publicly available, BIB001 as are the ... |
Control Allocation- A Survey <s> Introduction <s> The performanceand computational requirements ofoptimization methodsfor control allocation areevaluated. Two control allocation problems are formulated: a direct allocation method that preserves the directionality of the moment and a mixed optimization method that minim... | The objective of this survey is to give an overview of control allocation methods. It is not the objective of this paper to give a complete bibliography, but rather provide a subjective survey with an emphasis on recent developments within a common framework that is independent of the application domains where control ... |
Control Allocation- A Survey <s> Over-actuated mechanical systems <s> A demonstration that feedback control of systems with redundant controls can be reduced to feedback control of systems without redundant controls and control allocation is presented. It is shown that control allocation can introduce unstable zero dyn... | Motion control systems are used to control the motion of mechanical systems such as vehicles and machines. Effectors are mechanical devices that can be used in order to generate time-varying mechanical forces and moments on the mechanical system, such as rudders, fins, propellers, jets, thrusters, and tires. Actuators ... |
Control Allocation- A Survey <s> Perspectives <s> Abstract We refer to Model Predictive Control (MPC) as that family of controllers in which there is a direct use of an explicit and separately identifiable model. Control design methods based on the MPC concept have found wide acceptance in industrial applications and h... | This survey focuses on motion control for over-actuated mechanical systems, which is the conventional application area of control allocation. However, the principles of control allocation are general and not limited to motion control systems. Consequently, one does not need to restrict the virtual control input τ to be... |
Control Allocation- A Survey <s> Unconstrained linear control allocation <s> Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canon... | The main challenge of inverting the model (11) is that B is not a square matrix. Usually, for an over-actuated system, B will have full row rank (equal to m < p) and we will in general assume it has a non-trivial null space. This means there is an infinite number of vectors u ∈ R p that satisfies (11) for any given τ ∈... |
Control Allocation- A Survey <s> Redistributed pseudo-inverse and Daisy chaining <s> A demonstration that feedback control of systems with redundant controls can be reduced to feedback control of systems without redundant controls and control allocation is presented. It is shown that control allocation can introduce un... | The first step of the redistributed pseudo-inverse method (see e.g. BIB003 ) is to solve the unconstrained control allocation problem, such as (12) (or a simpler version). If the solution satisfies the constraints, no further steps are needed. Otherwise, the unconstrained optimal vector u is projected onto the admissi... |
Control Allocation- A Survey <s> Direct allocation <s> This paper addresses the problem of the allocation of several airplane flight controls to the generation of specified body-axis moments. The number of controls is greater than the number of moments being controlled, and the ranges of the controls are constrained to... | Some constrained control allocation methods are based on some scaling of the unconstrained optimal control allocation, such that the resulting control allocation is projected onto the boundary of the set of attainable generalized forces. In aerospace applications this is commonly referred to as the attainable moment se... |
Control Allocation- A Survey <s> Error minimization using linear programming <s> An actuator selection procedure is presented that uses linear programming to optimally specify bounded aerosurface deflections and jet firings in response to differential torque and/or force commands. This method creates a highly adaptable... | A powerful approach is to explicitly minimize the weighted error between the allocated virtual control input and the desired one. Extending the unconstrained optimization problem formulation (12) with input constraints leads to formulations such as (8). The constraint set U is usually polyhedral, i.e. for some appropri... |
Control Allocation- A Survey <s> Error minimization using quadratic programming <s> Preface Table of Notation Part 1: Unconstrained Optimization Introduction Structure of Methods Newton-like Methods Conjugate Direction Methods Restricted Step Methods Sums of Squares and Nonlinear Equations Part 2: Constrained Optimizat... | With the common choice of 2-norm, the control allocation problems leads to a quadratic program (QP) that can be solved using numerical QP methods, e.g. BIB003 BIB004 BIB005 . As an example for such a formulation, consider the control allocation formulation It can be transformed into a standard QP form without additiona... |
Control Allocation- A Survey <s> 2 <s> In aircraft control, control allocation can be used to distribute the total control effort among the actuators when the number of actuators exceeds the number of controlled variables. The control allocation problem is often posed as a constrained least squares problem to incorpora... | Interior-point methods, on the other hand, replaces the inequality constraints with a barrier function that prevents the solution for going into the infeasible region, ). Newton's method is then applied to search towards the optimum of the unconstrained optimization problem resulting from this reformulation. For each ... |
Control Allocation- A Survey <s> Dynamics and fault tolerance <s> To enable autonomous operation of future reusable launch vehicles, reconfiguration technologies will be needed to facilitate mission recovery following a major anomalous event. The Air Force’s Integrated Adaptive Guidance and Control program developed su... | An optimization-based control allocation method that is integrated with a parameter estimation scheme is described in BIB008 . It leads to an adaptive solution that can accommodate an unknown time-varying B-matrix due to losses and faults. Control allocation is an effective approach to implement fault tolerant control.... |
Control Allocation- A Survey <s> Mixed-integer programming methods <s> This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as mixed logical dynamical (MLD) systems. These are described by linear dynamic equations... | One particular model class leading to control allocation problem formulations that can be solved using mixed-integer linear programming (MILP) are piecewise linear functions ). Generally, a control allocation problem based on a piecewise linear effector model, piecewise linear cost function, and a constraint set that ... |
Control Allocation- A Survey <s> Dynamic optimum-seeking methods <s> Control allocation is commonly utilized in overactuated mechanical systems in order to optimally generate a requested generalized force using a redundant set of actuators. Using a control-Lyapunov approach, we develop an optimizing control allocation ... | In BIB001 it was proposed to re-formulate the static nonlinear optimization formulations of control allocation, i.e. (5), (7), or (8), as a control Lyapunov-function and use constructive Lyapunov-design methods. In particular, it was assumed that the cost function J (x, u,t) = J(x, u,t) + ρ(u) was augmented with a barr... |
Control Allocation- A Survey <s> Direct nonlinear allocation <s> Control allocation techniques for inversion-based control laws have evolved that ensure that commands to the control effectors do not violate rate or position limits of the individual effectors. These allocation techniques typically assume that all effect... | An extension of the method of attainable moment set computations and direct allocation for nonlinear effector models can be found in BIB003 . The methods rely of nonlinear programming and the ideas in this paper can be traced back to BIB002 BIB001 . |
Control Allocation- A Survey <s> Aircraft <s> This paper addresses the problem of the allocation of several airplane flight controls to the generation of specified body-axis moments. The number of controls is greater than the number of moments being controlled, and the ranges of the controls are constrained to certain ... | In flight control applications the virtual control input τ is usually the moments about the roll, pitch and yaw axes. Conventional fixed-wing aircraft design and flight control systems are based on a relatively small number of control surfaces (effectors) that are dedicated to control each axis of the aircraft, like • ... |
Control Allocation- A Survey <s> Spacecraft <s> To enable autonomous operation of future reusable launch vehicles, reconfiguration technologies will be needed to facilitate mission recovery following a major anomalous event. The Air Force’s Integrated Adaptive Guidance and Control program developed such a system for Bo... | Spacecraft have other actuators and effectors, either instead of, or in addition to control surfaces. These include reaction control jets, and reaction wheels. In addition, the energy consumption for control is generally a high priority objective of the control system design of spacecraft and will often need to be stro... |
Control Allocation- A Survey <s> Station-keeping and low-speed maneuvering <s> Abstract This paper presents a new thrust-allocation scheme which significantly reduces the fuel consumption for dynamic positioning of ships when rotatable azimuth thrusters are used. Thrust allocation is the problem of determining the thru... | Several types of ships and specialized vessels, such as semisubmersible platforms used in the petroleum industry, depend on thrust allocation control systems during certain modes of operation. This is in particular the case during dynamic positioning operations that include station keeping and low-speed maneuvering usi... |
Control Allocation- A Survey <s> High-speed maneuvering and ship autopilots <s> In this work, a control strategy for ship parametric roll resonance is developed by changing the frequency of the parametric excitation. This is achieved by varying the ship’s forward speed. This changes the perceived frequency of the waves... | Ship autopilots conventionally use rudders to meet heading control objectives, while they may also use additional control surfaces such as fins and azimuth propellers (azipods) which calls for control allocation solutions. It is also possible to use rudders for roll damping alone or in combinations with controllable fi... |
Control Allocation- A Survey <s> Multi vessel operations <s> In this paper we present a strategy that allows a swarm of autonomous tugboats to cooperatively move a large object on the water. The two main challenges are: (1) the actuators are unidirectional and experience saturation; (2) the hydrodynamics of the system ... | Control allocation strategies have also been proposed for multi-vessel operations, where several tug-boats cooperatively generate forces and moments in order to tow a floating structure. This is formulated in a straightforward manner in the control allocation framework by incorporating the constraints on the tug-boats ... |
Control Allocation- A Survey <s> Maneuvering of underwater vehicles <s> The problem of controlling underwater mobile robots in 6 degrees of freedom (DOF) is addressed. Underwater mobile robots where the number of thrusters and control surfaces exceeds the number of controllable DOF are considered in detail. Unlike robo... | Highly maneuverable underwater vehicles, either ROVs (Remotely Operated Vehicles) or AUVs (Autonomous Underwater Vehicles), are often controlled using compact electrically driven thrusters and fins. The thrust allocation problem is similar to a dynamically positioned surface vessel, including cases when also vertical f... |
Control Allocation- A Survey <s> Yaw stability control <s> Currently, advanced control systems implemented on production ground vehicles have the goal of promoting maneuverability and stability. With proper coordination of steering and braking action, these goals may be achieved even when road conditions are severe. Th... | Active safety systems like the electronic stability control (ESC) are now common in production cars, and shown to have tremendous life-saving effect when skids may occur due to evasive maneuvers, slippery surface, or too high speed in curves, e.g. BIB008 ). The ESC detects deviation between the actual lateral motion o... |
Control Allocation- A Survey <s> Electrical propulsion <s> The majority of current mechanical systems used in machinery and especially those which are controlled by microprocessors can be described as equal-actuated. This means that the number of actuators (drives, controls) is equal to the number of degrees-of-freedom... | Electrically powered ground vehicles may have in-wheel electric motors that combine drive and regenerative brake functions, possibly in combination with friction brakes, and the trend is towards highly over-actuated vehicles, BIB001 , with extended stability, BIB002 . Control allocation can be used to coordinate the el... |
Control Allocation- A Survey <s> Rollover prevention <s> This paper uses Model Predictive Control theory to develop a framework for automobile stability control. The framework is then demonstrated with a roll mode controller which seeks to actively limit the peak roll angle of the vehicle while simultaneously tracking ... | Although yaw-stabilizing ESC does not explicitly consider the risk of roll-over, it is widely acknowledged that an ESC function will reduce the risk of rollover since it tends to reduce lateral accelerations that is a main cause of rollover accidents. Further enhancements can be achieved if rollover prevention function... |
Control Allocation- A Survey <s> Mobile robots <s> Active degrees of freedom provide a robotic vehicle the ability to enhance its performance in all terrain conditions. While active suspension systems are now commonplace in on-road vehicles, their application to off-road terrains has been little investigated. A fundame... | Traction control for mobile robots that operate off-road is considered in BIB001 . Based on the geometry of the problem, several simple (unconstrained) closed-form computationally efficient control allocation strategies for wheeled and legged mobile robots with active suspension are derived and compared in BIB001 , wh... |
Control Allocation- A Survey <s> Other application areas <s> Mechanisms interacting with their environments that possess complete contact force controllability such as multifingered hands and walking vehicles 2 are considered in this article. In these systems, the redundancy in actuation can be used to optimize the for... | Legged walking robots require coordination of the dynamic or periodic motion of each leg. The force distributing control allocation algorithm should take into account energyefficiency and contact friction between the leg and ground which is non-zero only for a fraction of a cycle, e.g. BIB001 . A nonlinear programming... |
Good fences make for good neighbors but bad science: a review of what improves Bayesian reasoning and why <s> Bayesian Reasoning as a Serious, Real World Problem <s> AS both the number and cost of clinical laboratory tests continue to increase at an accelerating rate,1 physicians are faced with the task of comprehendin... | Traditional research on people's abilities to engage in Bayesian reasoning uses the following protocol: a person is presented with a description of a situation in which Bayesian reasoning is relevant, the necessary numerical information for Bayesian calculations, and then a request that the participant calculate the po... |
Good fences make for good neighbors but bad science: a review of what improves Bayesian reasoning and why <s> Natural Sampling and Frequencies in Bayesian Reasoning <s> Contributions to Mathematical Psychology, Psycho-metrics and Methodology presents the most esteemed research findings of the 22nd European Mathematical... | A seminal paper in terms of improving Bayesian reasoning and the current issues revolving around those improvements is BIB002 . This paper described a structure for presenting information in such a way that it greatly helped people reach correct Bayesian conclusions. This structure is one of whole-number frequencies in... |
Good fences make for good neighbors but bad science: a review of what improves Bayesian reasoning and why <s> Using Pictures to Aid Bayesian Reasoning <s> Abstract Professional probabilists have long argued over what probability means, with, for example, Bayesians arguing that probabilities refer to subjective degrees ... | Generally speaking, pictures help Bayesian reasoning. Like the research on frequencies and natural sampling, however, there is disagreement on how and why they help. The ecological rationality account BIB001 considers pictorial representations as helping because they help to tap into the frequency-tracking cognitive m... |
Good fences make for good neighbors but bad science: a review of what improves Bayesian reasoning and why <s> Individual Differences in Bayesian Reasoning <s> Abstract Professional probabilists have long argued over what probability means, with, for example, Bayesians arguing that probabilities refer to subjective degr... | There have been various claims that certain individual differences may moderate the often-observed frequency effect in Bayesian reasoning. BIB006 demonstrated that numerical literacy (or numeracy)-an applicable understanding of probability, risk, and basic mathematics-moderated many classic judgment and decision making... |
Good fences make for good neighbors but bad science: a review of what improves Bayesian reasoning and why <s> Conclusion <s> Is the mind, by design, predisposed against performing Bayesian inference? Previous research on base rate neglect suggests that the mind lacks the appropriate cognitive algorithms. However, any c... | Overall, the literature on Bayesian reasoning is clear and straightforward in terms of what works for improving performance: natural sampling, frequencies, icon-based pictures, and more general development of the prerequisite skills for these tasks (i.e., numerical literacy, visual ability, and motivation to reach the ... |
Overview of Digital Television Development Worldwide <s> B. Analog TV Enhancement Projects <s> Statistics and reality are often in conflict, and nowhere is the contrast more marked than in the world of robotics in Japan. In the 1970s, statistics showed that Japan was using robots at a prodigious pace, yet visitors had ... | On the evolutionary path to fully digital TV systems, there were several projects to enhance and improve analog television using advanced analog and hybrid analog-digital technologies. Some of the projects worth mentioning are the Japan Broadcasting Corporation (NHK) HDTV BIB001 project in Japan, the Eureka EU 95 Proje... |
Overview of Digital Television Development Worldwide <s> 1) NHK HDTV Projects: <s> The status of high-definition television (HDTV) in Japan, Europe, and the US is examined. Japan has begun experimental broadcasts, and Europe plans experimental HDTV broadcasts in 1991, while the US is mired in disputes over just how imp... | In 1964, the NHK Science and Technical Research Laboratories (STRL) started a research project on future television systems. This work began right after the successful live broadcasting of the 1964 Tokyo Summer Olympic Games to audiences around the world using satellite video transmission techniques developed by NHK. A... |
Overview of Digital Television Development Worldwide <s> 1) ACATS: <s> The advanced compatible television (ACTV) system is a proposal for the single-channel transmission of widescreen enhanced-definition television (EDTV) images. A widescreen high-definition source is encoded into a signal that is NTSC-compatible. Exis... | On 21 February 1987 a "Petition for Notice of Inquiry" was filed with the U.S. FCC by 58 broadcasting organizations and companies requesting that the commission initiate a proceeding to explore issues arising from the introduction of advanced television technologies and their possible impact on the television broadcast... |
Overview of Digital Television Development Worldwide <s> B. DVB Process 1) DVB History and Organization: <s> This paper presents an overview of the fields of technology addressed by technical specifications created by the DVB Project (DVB). It serves as an introduction to the section of the special issue of the Proceed... | The DVB Project is the focal point of the development of DTV for many countries around the world BIB001 (Figs. 5 and 6 ). It was founded in 1993 and, as of late 2005, has about 270 member organizations from 32 countries. The DVB Project was preceded by the European Launching Group (ELG). The start of DVB, as it is usua... |
Service-Oriented Architecture in Industrial Automation Systems - The case of IEC 61499: A Review <s> I. INTRODUCTION Authors in the first issue of IEEE Transactions on Industrial <s> This paper outlines opportunities and challenges in the development of next-generation embedded devices, applications, and services, resu... | Informatics, ten years ago, described opportunities and challenges in using the service oriented architecture in manufacturing BIB001 . Since then several research articles published in the same journal reporting successful or promising results regarding the exploitation of the SOA paradigm in the industrial automation... |
Service-Oriented Architecture in Industrial Automation Systems - The case of IEC 61499: A Review <s> II. SOA IN INDUSTRIAL AUTOMATION SYSTEMS <s> This paper outlines opportunities and challenges in the development of next-generation embedded devices, applications, and services, resulting from their increasing intellige... | SOA was considered for several years as one of the hottest subjects in the IT community. This has been changed the last few years when IoT has replaced this buzzword. As expected, SOA has attracted the attention of researchers in the industrial automation domain. Several research groups presented their work towards the... |
Service-Oriented Architecture in Industrial Automation Systems - The case of IEC 61499: A Review <s> III. THE FORMAL SOA IEC 61499 FUNCTION BLOCK MODEL <s> Service-oriented computing promotes the idea of assembling application components into a network of services that can be loosely coupled to create flexible, dynamic... | SOA was introduced as an approach to design a software system to provide services either to end-user applications or other services distributed in a network, via published and discoverable interfaces BIB001 . Authors in [7, Sec. 1] admit that SOA has been introduced to facilitate the creation of distributed networked c... |
Service-Oriented Architecture in Industrial Automation Systems - The case of IEC 61499: A Review <s> A. The Execution Environment <s> The function block (FB) construct has been adopted by recent IEC standards for the design of reusable, interoperable, distributed control applications. In this paper, an approach to expl... | Authors in [7, Sec. V] describe an execution environment for IEC 61499 based on the formal model defined in the same paper. They present the key constructs of the execution environment using a class diagram [7, Fig.2] or [7, Fig.3 ] based on text BIB003 Sec IV] . From this diagram and Definition 1 that is utilized by a... |
Service-Oriented Architecture in Industrial Automation Systems - The case of IEC 61499: A Review <s> B. Run-time reconfiguration <s> Model-driven engineering (MDE) is proposed as the next revolution in embedded-system development. It is a promising paradigm that provides the developer the abstraction level required to ... | Run-time reconfiguration at the device level, which is considered as one benefit of the proposed architecture, imposes string real time constraints and complex algorithms not shown in BIB002 . The described case study even though considers the deletion and creation of FB types includes actions for deleting and creating... |
Literature survey on low rank approximation of matrices <s> Introduction <s> Let A be a given m×n real matrix with m≧n and of rank n and b a given vector. We wish to determine a vector x such that ::: ::: $$\parallel b - A\hat x\parallel = \min .$$ ::: ::: where ∥ … ∥ indicates the euclidean norm. Since the euclidean n... | The low rank matrix approximation is approximating a matrix by one whose rank is less than that of the original matrix. The goal of this is to obtain more compact representations of the data with limited loss of information. Let A be m × n matrix, then the low rank approximation (rank k) of A is given by A m×n ≈ B m×k ... |
Literature survey on low rank approximation of matrices <s> Algorithms and computational complexity <s> A partial reorthogonalization procedure (BPRO) for maintaining semi-orthogonality among the left and right Lanczos vectors in the Lanczos bidiagonalization (LBD) is presented. The resulting algorithm is mathematicall... | The SVD of a matrix A is typically computed numerically by a two-step procedure. In the first step, the matrix is reduced to a bidiagonal matrix. This takes O(mn 2 ) floating-point operations (flops), and the second step is to compute the SVD of the bidiagonal matrix. The second step takes O(n) iterations, each costing... |
Literature survey on low rank approximation of matrices <s> Pivoted QR decomposition <s> Let A be a given m×n real matrix with m≧n and of rank n and b a given vector. We wish to determine a vector x such that ::: ::: $$\parallel b - A\hat x\parallel = \min .$$ ::: ::: where ∥ … ∥ indicates the euclidean norm. Since the... | Let A m×n be a rank deficient matrix (m > n) with rank γ. A pivoted QR decomposition with column pivoting has the form AP = QR where P is a permutation matrix, Q is orthonormal and R is upper triangular matrix. In exact arithmetic, where R 11 is γ × γ upper triangular matrix with rank γ, Q ∈ R m×n and P ∈ R n×n . In fl... |
Literature survey on low rank approximation of matrices <s> Definition (RRQR): <s> Abstract The most widely used stable methods for numerical determination of the rank of a matrix A are the singular value decomposition and the QR algorithm with column interchanges. Here two algorithms are presented which determine rank... | Given a matrix A m×n (m ≥ n) and an integer k(k ≤ n), assume partial QR factorizations of the form where Q ∈ R m×n is an orthonormal matrix, R ∈ R n×n is block upper triangular, R 11 ∈ R k×k , R 12 ∈ R k×n−k , R 22 ∈ R n−k×n−k and P ∈ R n×n is a permutation matrix. The above factorization is call RRQR factorization if ... |
Literature survey on low rank approximation of matrices <s> Interpolative decomposition <s> A procedure is reported for the compression of rank-deficient matrices. A matrix A of rank k is represented in the form $A = U \circ B \circ V$, where B is a $k\times k$ submatrix of A, and U, V are well-conditioned matrices tha... | Interpolative decompositions (ID's) (also called as CX decomposition) are closely related to pivoted QR factorizations and are useful for representing low rank matrices in terms of linear combinations of their columns BIB001 BIB002 BIB003 . Interpolative decomposition of a matrix completely rely on the column subset se... |
Literature survey on low rank approximation of matrices <s> Subset selection problem <s> This paper is concerned with least squares problems when the least squares matrix A is near a matrix that is not of full rank. A definition of numerical rank is given. It is shown that under certain conditions when A has numerical ... | Subset selection is a method for selecting a subset of columns from a real matrix, so that the subset represents the entire matrix well and is far from being rank deficient. Given a m × n matrix A and an integer k, subset selection attempts to find the k most linearly independent columns that best represents the inform... |
Literature survey on low rank approximation of matrices <s> Definition (ID): <s> Given anm n matrixM withm > n, it is shown that there exists a permutation FI and an integer k such that the QR factorization MYI= Q(Ak ckBk) reveals the numerical rank of M: the k k upper-triangular matrix Ak is well conditioned, IlCkll2 ... | Let A m×n be a matrix of rank k. There exists an m × k matrix B whose columns constitute a subset of the columns of A, and k × n matrix P, such that 1. some subset of the columns of P makes up k × k identity matrix, 2. P is not too large (no entry of P has an absolute value greater than 1), and 3. A m×n = B m×k P k×n .... |
Literature survey on low rank approximation of matrices <s> Column subset selection problem (CSSP) <s> In many applications, the data consist of (or may be naturally formulated as) an $m \times n$ matrix $A$. It is often of interest to find a low-rank approximation to $A$, i.e., an approximation $D$ to the matrix $A$ o... | We have seen the mathematical formulation of the subset selection problem in section 2.3. There is an equivalent definition to the subset selection problem in the literature. Here we define the column subset selection problem. Definition (CSSP): Given a matrix A m×n and a positive integer k as the number of columns of ... |
Literature survey on low rank approximation of matrices <s> Randomised CUR <s> In many applications, the data consist of (or may be naturally formulated as) an $m \times n$ matrix $A$ which may be stored on disk but which is too large to be read into random access memory (RAM) or to practically perform superlinear poly... | As described in section 2.3, CU R decomposition gives low rank approximation explicitly expressed in terms of a small number of columns and rows of the matrix A. CU R decomposition problem has been widely studied in the literature. This problem has a close connection with the column subset selection problem. One can ob... |
Literature survey on low rank approximation of matrices <s> (II). Random projection based methods <s> Latent semantic indexing (LSI) is an information retrieval technique based on the spectral analysis of the term-document matrix, whose empirical success had heretofore been without rigorous prediction and explanation. ... | The random projection method for low rank approximation of a matrix is based on the idea of random projection. In random projection, the original d dimensional data is projected to a k dimensional (k << d) subspace by post-multiplying a k × d random matrix Ω (a matrix whose entries are independent random variables of s... |
Literature survey on low rank approximation of matrices <s> Set U = QŨ . <s> The main contribution of this paper is to demonstrate that a new randomized SVD algorithm, proposed by Drineas et. al. in [4], is not only of theoretical interest but also a viable and fast alternative to traditional SVD algorithms in applicat... | This approximates the SVD with the same rank as the basis matrix Q. The efficient implementation and approximation error of this procedure can be found in section 5 of BIB002 . This scheme is well suited for sparse and structured matrices. If the singular values of A decay slowly then power iterations (with q = 1 or 2)... |
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