Sparse Representations and Compressive Sensing for Imaging and Vision (SpringerBriefs in Electrical and Computer Enginee
Compressed sensing or compressive sensing is a new concept in signal processing where one measures a small number of non-adaptive linear combinations of the signal. These measurements are usually much smaller than the number of samples that define the signal. From these small numbers of measurements, the signal is then reconstructed by non-linear procedure. Compressed sensing has recently emerged as a powerful tool for efficiently processing data in non-traditional ways. In this book, we highlight some of the key mathematical insights underlying sparse representation and compressed sensing and illustrate the role of these theories in classical vision, imaging and biometrics problems.
Why Read This Book
You should read this brief if you want a compact, application-oriented introduction to how sparse models and compressive sensing principles are applied to imaging and vision problems. It highlights core theory, common reconstruction algorithms, and concrete examples in imaging/biometrics, so you can bridge the gap between mathematical results and practical implementations.
Who Will Benefit
Graduate students, researchers, and practicing engineers in image/signal processing or computer vision who need a focused primer on sparse representations and compressive sensing for imaging applications.
Level: Advanced — Prerequisites: Linear algebra (matrix norms, eigenvalues), basics of convex optimization (L1 minimization), fundamental signal processing concepts, and familiarity with basic image processing operations.
Key Takeaways
- Understand the core compressive sensing principles (sparsity, incoherence, restricted isometry property) and why they enable sub-Nyquist sampling.
- Formulate and analyze common sparse recovery problems (Basis Pursuit, LASSO, greedy methods like OMP, and iterative thresholding).
- Apply sparse representation and compressive sensing techniques to imaging tasks such as compressed imaging, denoising, super-resolution, and biometric recognition.
- Design and evaluate sensing strategies and measurement matrices appropriate for imaging systems.
- Implement practical reconstruction pipelines and assess robustness to noise and model mismatch.
- Gain insight into dictionary learning and how learned sparse models improve performance in vision problems.
Topics Covered
- 1. Introduction and Motivation
- 2. Sparse Representations: Models and Intuition
- 3. Mathematical Foundations of Compressive Sensing
- 4. Measurement Matrices and Incoherence/Random Projections
- 5. Sparse Recovery Algorithms: Convex and Greedy Methods
- 6. Iterative Thresholding and Fast Solvers
- 7. Dictionary Learning and Sparse Coding
- 8. Compressive Imaging: Architectures and Examples
- 9. Applications in Computer Vision and Biometrics
- 10. Noise, Stability, and Performance Guarantees
- 11. Practical Considerations and Experimental Results
- 12. Future Directions and Open Problems
Languages, Platforms & Tools
How It Compares
Shorter and more application-focused than Foucart & Rauhut's rigorous "A Mathematical Introduction to Compressive Sensing" and more imaging/vision–oriented than Eldar & Kutyniok's broader edited volumes on compressed sensing.
