Since publication of the initial papers in 2006, compressed sensing has captured the imagination of the international signal processing community, and the mathematical foundations are nowadays quite well understood. Parallel to the progress in mathematics, the potential applications of compressed sensing have been explored by many international groups of, in particular, engineers and applied mathematicians, achieving very promising advances in various areas such as communication theory, imaging sciences, optics, radar technology, sensor networks, or tomography. Since many applications have reached a mature state, the research center MATHEON in Berlin focusing on "Mathematics for Key Technologies", invited leading researchers on applications of compressed sensing from mathematics, computer science, and engineering to the "MATHEON Workshop 2013: Compressed Sensing and its Applications” in December 2013. It was the first workshop specifically focusing on the applications of compressed sensing. This book features contributions by the plenary and invited speakers of this workshop. To make this book accessible for those unfamiliar with compressed sensing, the book will not only contain chapters on various applications of compressed sensing written by plenary and invited speakers, but will also provide a general introduction into compressed sensing. The book is aimed at both graduate students and researchers in the areas of applied mathematics, computer science, and engineering as well as other applied scientists interested in the potential and applications of the novel methodology of compressed sensing. For those readers who are not already familiar with compressed sensing, an introduction to the basics of this theory will be included.

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.

This contributed volume showcases the most significant results obtained from the DFG Priority Program on Compressed Sensing in Information Processing. Topics considered revolve around timely aspects of compressed sensing with a special focus on applications, including compressed sensing-like approaches to deep learning; bilinear compressed sensing - efficiency, structure, and robustness; structured compressive sensing via neural network learning; compressed sensing for massive MIMO; and security of future communication and compressive sensing.

Compressed Sensing (CS) in theory deals with the problem of recovering a sparse signal from an under-determined system of linear equations. The topic is of immense practical significance since all naturally occurring signals can be sparsely represented in some domain. In recent years, CS has helped reduce scan time in Magnetic Resonance Imaging (making scans more feasible for pediatric and geriatric subjects) and has also helped reduce the health hazard in X-Ray Computed CT. This book is a valuable resource suitable for an engineering student in signal processing and requires a basic understanding of signal processing and linear algebra. Covers fundamental concepts of compressed sensing Makes subject matter accessible for engineers of various levels Focuses on algorithms including group-sparsity and row-sparsity, as well as applications to computational imaging, medical imaging, biomedical signal processing, and machine learning Includes MATLAB examples for further development

Learn about the latest theoretical and practical advances in radar signal processing using tools from compressive sensing.

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.

Compressed Sensing in Li-Fi and Wi-Fi Networks features coverage of the first applications in optical telecommunications and wireless. After extensive development of basic theory, many techniques are presented, such as non-asymptotic analysis of random matrices, adaptive detection, greedy algorithms, and the use of graphical models. The book can be used as a comprehensive manual for teaching and research in courses covering advanced signal processing, efficient data processing algorithms, and telecommunications. After a thorough review of the basic theory of compressed sensing, many mathematical techniques are presented, including advanced signal modeling, Nyquist sub-sampling of analog signals, the non-asymptotic analysis of random matrices, adaptive detection, greedy algorithms, and the use of graphical models. - Offers extensive development of basic theory behind telecommunications and wireless networks - Contains broad coverage of treat compressed sensing, including electromagnetism signals - Provides insights into the two key areas of telecommunications, WIFI and LIFI - Includes information on advanced signal modeling, Nyquist sub-sampling of analog signals, the non-asymptotic analysis of random matrices, adaptive detection, greedy algorithms, and more

This book describes algorithmic methods and hardware implementations that aim to help realize the promise of Compressed Sensing (CS), namely the ability to reconstruct high-dimensional signals from a properly chosen low-dimensional “portrait”. The authors describe a design flow and some low-resource physical realizations of sensing systems based on CS. They highlight the pros and cons of several design choices from a pragmatic point of view, and show how a lightweight and mild but effective form of adaptation to the target signals can be the key to consistent resource saving. The basic principle of the devised design flow can be applied to almost any CS-based sensing system, including analog-to-information converters, and has been proven to fit an extremely diverse set of applications. Many practical aspects required to put a CS-based sensing system to work are also addressed, including saturation, quantization, and leakage phenomena.

The idea of balancing the resources spent in the acquisition and encoding of natural signals strictly to their intrinsic information content has interested nearly a decade of research under the name of compressed sensing. In this doctoral dissertation we develop some extensions and improvements upon this technique's foundations, by modifying the random sensing matrices on which the signals of interest are projected to achieve efficiency and security in its applications.

This book discusses compressive sensing in the presence of side information. Compressive sensing is an emerging technique for efficiently acquiring and reconstructing a signal. Interesting instances of Compressive Sensing (CS) can occur when, apart from sparsity, side information is available about the source signals. The side information can be about the source structure, distribution, etc. Such cases can be viewed as extensions of the classical CS. In these cases we are interested in incorporating the side information to either improve the quality of the source reconstruction or decrease the number of samples required for accurate reconstruction. In this book we assume availability of side information about the feasible region. The main applications investigated are image deblurring for optical imaging, 3D surface reconstruction, and reconstructing spatiotemporally correlated sources. The author shows that the side information can be used to improve the quality of the reconstruction compared to the classic compressive sensing. The book will be of interest to all researchers working on compressive sensing, inverse problems, and image processing.