Sparse Representations in Signal and Image Processing: Fundamentals

Description

In this course, you will learn:

• Exploring features such as uniqueness, equivalence, and stability, as well as the core notions of sparse representation theory.
• About sparse coding algorithms and their track record of success.

Syllabus:

1. Overview of Sparseland, including mathematical warm-up and intro to L1-minimization.

2. Seeking sparse solutions: the L0 norm and P0 problem.

3. Theoretical analysis of the Two-Ortho case of P0, including definitions of Spark and Mutual-Coherence.

4. Theoretical analysis of the general case of the P0 problem.

5. Greedy pursuit algorithms including: Thresholding (THR), Orthogonal Matching Pursuit (OMP) and its variants.

6. Relaxation pursuit algorithms including Basis Pursuit (BP).

7. Theoretical guarantees of pursuit algorithms: THR, OMP and BP.

8. Practical tools to solve approximate problems, including exact solution of unitary case, Iterative Re-weighted Least Squares algorithm (IRLS) and Alternating Direction Method of Multipliers (ADMM).

9. Theoretical guarantees to approximate solutions including definition of Restricted Isometry Property (RIP) and pursuit algorithms' stability.