Compressed Sensing: Theory and Applications
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 recent 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.
Why Read This Book
You should read this book to get a structured, up-to-date tour of compressed sensing: from core theorems (RIP, sparsity guarantees) to practical reconstruction algorithms and real-world applications like MRI, radar, and sub-Nyquist sampling. It collects chapters by leading researchers, so you get both rigorous analysis and algorithmic insights in one place.
Who Will Benefit
Graduate students, researchers, and DSP engineers working on sampling, sparse signal recovery, imaging, radar, and communications who need a rigorous yet application-oriented introduction to compressed sensing.
Level: Advanced — Prerequisites: Solid linear algebra, probability/statistics, basic convex optimization (L1 minimization), and foundational DSP (sampling, Fourier analysis).
Key Takeaways
- Understand the mathematical foundations of compressed sensing, including sparsity models and the Restricted Isometry Property (RIP).
- Implement and compare reconstruction methods such as L1 minimization (basis pursuit), greedy algorithms (OMP), and iterative thresholding.
- Analyze random measurement ensembles and non-asymptotic performance bounds for recovery guarantees.
- Design and evaluate sub-Nyquist/analog compressed sampling schemes for continuous-time signals.
- Apply compressed sensing principles to practical problems (MRI, radar, sensor networks, communications) and assess trade-offs.
- Exploit structured sparsity and model-based approaches to improve recovery in structured signal classes.
Topics Covered
- Introduction and overview of compressed sensing
- Mathematical preliminaries: sparsity, norms, and convexity
- L1 minimization and basis pursuit: theory and algorithms
- Greedy algorithms and iterative thresholding (OMP, CoSaMP, IHT)
- Random matrices and non-asymptotic concentration results
- Structured sparsity and model-based compressed sensing
- Analog compressed sensing and sub-Nyquist sampling (Xampling)
- Adaptive and sequential sensing strategies
- Bayesian and probabilistic approaches to sparse recovery
- Computational methods and software implementations
- Applications: MRI, radar, communications, sensor networks, imaging
- Numerical experiments, practical issues, and open problems
Languages, Platforms & Tools
How It Compares
More application- and survey-oriented than Foucart & Rauhut's 'A Mathematical Introduction to Compressive Sensing' (2013), and broader in theory/algorithms than Elad's 'Sparse and Redundant Representations' which focuses more on dictionaries and practical sparse coding.
