Sparse Modeling: Theory, Algorithms, and Applications (Chapman & Hall/CRC Machine Learning & Pattern Recognition)
Sparse models are particularly useful in scientific applications, such as biomarker discovery in genetic or neuroimaging data, where the interpretability of a predictive model is essential. Sparsity can also dramatically improve the cost efficiency of signal processing.
Sparse Modeling: Theory, Algorithms, and Applications provides an introduction to the growing field of sparse modeling, including application examples, problem formulations that yield sparse solutions, algorithms for finding such solutions, and recent theoretical results on sparse recovery. The book gets you up to speed on the latest sparsity-related developments and will motivate you to continue learning about the field.
The authors first present motivating examples and a high-level survey of key recent developments in sparse modeling. The book then describes optimization problems involving commonly used sparsity-enforcing tools, presents essential theoretical results, and discusses several state-of-the-art algorithms for finding sparse solutions.
The authors go on to address a variety of sparse recovery problems that extend the basic formulation to more sophisticated forms of structured sparsity and to different loss functions. They also examine a particular class of sparse graphical models and cover dictionary learning and sparse matrix factorizations.
Why Read This Book
You will learn how sparse models turn high-dimensional signal problems into interpretable, computationally efficient solutions — ideal for lowering costs and improving performance in audio, radar, and communications systems. The book balances algorithmic recipes (greedy methods, convex relaxations, dictionary learning) with theory (recovery guarantees) and application examples so you can both implement and justify sparse solutions in real DSP pipelines.
Who Will Benefit
DSP engineers, signal-processing researchers, and graduate students with a solid mathematical background who want to apply sparsity to audio/speech, radar, spectral analysis, and communications problems.
Level: Advanced — Prerequisites: Linear algebra (matrix factorizations, eigenanalysis), probability and statistics, basic convex optimization, and familiarity with digital signal processing concepts (Fourier/wavelet transforms and filtering).
Key Takeaways
- Understand the conceptual foundations of sparse representations and why sparsity helps in audio, radar, and communications tasks
- Apply L0/L1 formulations and convex relaxations (Lasso, basis pursuit) to derive sparse estimators for signals
- Implement common algorithms (OMP, BP, ISTA/FISTA, coordinate descent) and use them effectively on DSP problems
- Design and train overcomplete dictionaries and sparse coding models for feature extraction in audio and imaging
- Analyze recovery guarantees (RIP, coherence) and trade-offs between sample complexity, noise, and sparsity
- Integrate sparse modeling with FFT, wavelet transforms, and spectral-analysis tools to build end-to-end DSP solutions
Topics Covered
- 1. Introduction and Motivating Applications (audio, neuroimaging, radar, communications)
- 2. Sparse Representation Models and Problem Formulations
- 3. Convex Relaxation: L1 Minimization, Lasso, and Basis Pursuit
- 4. Greedy and Matching-Pursuit Algorithms (OMP, MP variants)
- 5. Iterative Shrinkage and Thresholding Methods (ISTA, FISTA, ADMM)
- 6. Dictionary Learning and Sparse Coding
- 7. Compressive Sensing and Sampling with Fewer Measurements
- 8. Wavelets, Multiresolution Bases, and Sparsifying Transforms
- 9. Adaptive and Online Sparse Filtering
- 10. Statistical Recovery Guarantees: RIP, Coherence, and Oracle Inequalities
- 11. Practical Implementation Issues and Numerical Considerations
- 12. Applications: Audio/speech, Radar, Communications, and Biomedical Signals
- 13. Case Studies and Future Directions
Languages, Platforms & Tools
How It Compares
Covers similar practical breadth to Michael Elad's 'Sparse and Redundant Representations' but with broader application examples and stronger emphasis on statistical recovery results; Foucart & Rauhut's 'A Mathematical Introduction to Compressive Sensing' offers deeper mathematical proofs if you want a more theory-centric complement.
