Author: Henning Alexander ZörleinPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Channel Coding Inspired Contributions to Compressed Sensing
Author: Henning Alexander ZörleinPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Source and Channel Coding for Compressed Sensing and Control
Author: Handbook of Mathematical Methods in Imaging
Author: Otmar ScherzerPublisher: Springer Science & Business Media
ISBN: 0387929193
Category : Mathematics
Languages : en
Pages : 1626
Book Description
The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
Source-channel Mappings with Applications to Compressed Sensing
Author: Ahmad Abou SalehPublisher:
ISBN:
Category :
Languages : en
Pages : 180
Book Description
Tandem source-channel coding is proven to be optimal by Shannon given unlimited delay and complexity in the coders. Under low delay and low complexity constraints, joint source-channel coding may achieve better performance. Although digital joint source-channel coding has shown a noticeable gain in terms of reconstructed signal quality, coding delay, and complexity, it suffers from the leveling-off effect. However, analog systems do not suffer from the leveling-off effect. In this thesis, we investigate the advantage of analog systems based on the Shannon-Kotel'nikov approach and hybrid digital-analog coding systems, which combine digital and analog schemes to achieve a graceful degradation/improvement over a wide range of channel conditions. First, we propose a low delay and low complexity hybrid digital-analog coding that is able to achieve high (integer) expansion ratios (>3). This is achieved by combining the spiral mapping with multiple stage quantizers. The system is simulated for a 1 : 3 bandwidth expansion and the behavior for a 1 : M (with M an integer>3) system is studied in the low noise level regime. Next, we propose an analog joint source-channel coding system that is able to achieve a low (fractional) expansion ratio between 1 and 2. More precisely, this is an N : M bandwidth expansion system based on combining uncoded transmission and a 1 : 2 bandwidth expansion system (with N
Channel coding LP decoding and compressed sensing LP decoding
Author: Alexandros G. DimakisLow Complexity Iterative Algorithms in Channel Coding and Compressed Sensing
Author: Ludovic DanjeanPublisher:
ISBN:
Category :
Languages : en
Pages : 153
Book Description
Iterative algorithms are now widely used in all areas of signal processing and digital communications. In modern communication systems, iterative algorithms are notably used for decoding low-density parity-check (LDPC) codes, a popular class of error-correction codes known to have exceptional error-rate performance under iterative decoding. In a more recent field known as compressed sensing, iterative algorithms are used as a method of reconstruction to recover a sparse signal from a linear set of measurements. This work primarily deals with the development of low-complexity iterative algorithms for the two aforementioned fields, namely, the design of low-complexity decoding algorithms for LDPC codes, and the development and analysis of a low complexity reconstruction algorithm for compressed sensing. In the first part of this dissertation, we focus on the decoding algorithms for LDPC codes. It is now well known that LDPC codes suffer from an error floor phenomenon in spite of their exceptional performance. This phenomenon originates from the failures of traditional iterative decoders, like belief propagation (BP), on certain low-noise configurations. Recently, a novel class of decoders, called finite alphabet iterative decoders (FAIDs), were proposed with the capability of surpassing BP in the error floor region at a much lower complexity. We show that numerous FAIDs can be designed, and among them only a few will have the ability of surpassing traditional decoders in the error floor region. In this work, we focus on the problem of the selection of good FAIDs for column-weight-three codes over the binary symmetric channel. Traditional methods for decoder selection use asymptotic techniques such as the density evolution method, but the designed decoders do not guarantee good performance for finite-length codes especially in the error floor region. Instead we propose a methodology to identify FAIDs with good error-rate performance in the error floor. This methodology relies on the knowledge of potentially harmful topologies that could be present in a code. The selection method uses the concept of noisy trapping set. Numerical results are provided to show that FAIDs selected based on our methodology outperform BP in the error floor on a wide range of codes. Moreover first results on column-weight-four codes demonstrate the potential of such decoders on codes which are more used in practice, for example in storage systems. In the second part of this dissertation, we address the area of iterative reconstruction algorithms for compressed sensing. This field has attracted a lot of attention since Donoho's seminal work due to the promise of sampling a sparse signal with less samples than the Nyquist theorem would suggest. Iterative algorithms have been proposed for compressed sensing in order to tackle the complexity of the optimal reconstruction methods which notably use linear programming. In this work, we modify and analyze a low complexity reconstruction algorithm that we refer to as the interval-passing algorithm (IPA) which uses sparse matrices as measurement matrices. Similar to what has been done for decoding algorithms in the area of coding theory, we analyze the failures of the IPA and link them to the stopping sets of the binary representation of the sparse measurement matrices used. The performance of the IPA makes it a good trade-off between the complex l1-minimization reconstruction and the very simple verification decoding. The measurement process has also a lower complexity as we use sparse measurement matrices. Comparison with another type of message-passing algorithm, called approximate message-passing, show the IPA can have superior performance with lower complexity. We also demonstrate that the IPA can have practical applications especially in spectroscopy.
Worst Configurations (instantons) for Compressed Sensing Over Reals
Author: Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
We consider Linear Programming (LP) solution of a Compressed Sensing (CS) problem over reals, also known as the Basis Pursuit (BasP) algorithm. The BasP allows interpretation as a channel-coding problem, and it guarantees the error-free reconstruction over reals for properly chosen measurement matrix and sufficiently sparse error vectors. In this manuscript, we examine how the BasP performs on a given measurement matrix and develop a technique to discover sparse vectors for which the BasP fails. The resulting algorithm is a generalization of our previous results on finding the most probable error-patterns, so called instantons, degrading performance of a finite size Low-Density Parity-Check (LDPC) code in the error-floor regime. The BasP fails when its output is different from the actual error-pattern. We design CS-Instanton Search Algorithm (ISA) generating a sparse vector, called CS-instanton, such that the BasP fails on the instanton, while its action on any modification of the CS-instanton decreasing a properly defined norm is successful. We also prove that, given a sufficiently dense random input for the error-vector, the CS-ISA converges to an instanton in a small finite number of steps. Performance of the CS-ISA is tested on example of a randomly generated 512 * 120 matrix, that outputs the shortest instanton (error vector) pattern of length 11.
Sparse representation of visual data for compression and compressed sensing
Author: Ehsan MiandjiPublisher: Linköping University Electronic Press
ISBN: 9176851869
Category :
Languages : en
Pages : 180
Book Description
The ongoing advances in computational photography have introduced a range of new imaging techniques for capturing multidimensional visual data such as light fields, BRDFs, BTFs, and more. A key challenge inherent to such imaging techniques is the large amount of high dimensional visual data that is produced, often requiring GBs, or even TBs, of storage. Moreover, the utilization of these datasets in real time applications poses many difficulties due to the large memory footprint. Furthermore, the acquisition of large-scale visual data is very challenging and expensive in most cases. This thesis makes several contributions with regards to acquisition, compression, and real time rendering of high dimensional visual data in computer graphics and imaging applications. Contributions of this thesis reside on the strong foundation of sparse representations. Numerous applications are presented that utilize sparse representations for compression and compressed sensing of visual data. Specifically, we present a single sensor light field camera design, a compressive rendering method, a real time precomputed photorealistic rendering technique, light field (video) compression and real time rendering, compressive BRDF capture, and more. Another key contribution of this thesis is a general framework for compression and compressed sensing of visual data, regardless of the dimensionality. As a result, any type of discrete visual data with arbitrary dimensionality can be captured, compressed, and rendered in real time. This thesis makes two theoretical contributions. In particular, uniqueness conditions for recovering a sparse signal under an ensemble of multidimensional dictionaries is presented. The theoretical results discussed here are useful for designing efficient capturing devices for multidimensional visual data. Moreover, we derive the probability of successful recovery of a noisy sparse signal using OMP, one of the most widely used algorithms for solving compressed sensing problems.
A Mathematical Introduction to Compressive Sensing
Author: Simon FoucartPublisher: Springer Science & Business Media
ISBN: 0817649484
Category : Computers
Languages : en
Pages : 634
Book Description
At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. Based on the premise that data acquisition and compression can be performed simultaneously, compressive sensing finds applications in imaging, signal processing, and many other domains. In the areas of applied mathematics, electrical engineering, and theoretical computer science, an explosion of research activity has already followed the theoretical results that highlighted the efficiency of the basic principles. The elegant ideas behind these principles are also of independent interest to pure mathematicians. A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. It also serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing.
Compressed Sensing
Author: Yonina C. EldarPublisher: Cambridge University Press
ISBN: 1107394392
Category : Technology & Engineering
Languages : en
Pages : 557
Book Description
Compressed sensing is an exciting, rapidly growing field, attracting considerable attention in electrical engineering, applied mathematics, statistics and computer science. This book provides the first detailed introduction to the subject, highlighting theoretical advances and a range of applications, as well as outlining numerous remaining research challenges. After a thorough review of the basic theory, many cutting-edge techniques are presented, including advanced signal modeling, sub-Nyquist sampling of analog signals, non-asymptotic analysis of random matrices, adaptive sensing, greedy algorithms and use of graphical models. All chapters are written by leading researchers in the field, and consistent style and notation are utilized throughout. Key background information and clear definitions make this an ideal resource for researchers, graduate students and practitioners wanting to join this exciting research area. It can also serve as a supplementary textbook for courses on computer vision, coding theory, signal processing, image processing and algorithms for efficient data processing.