Sparse Representations in Signal and Image Processing: Fundamentals

This program is composed from two separate parts:

1.Part 1: Sparse Representations in Signal and Image Processing: Fundamentals.

2.Part 2: Sparse Representations in Image Processing: From Theory to Practice.

While we recommend taking both courses, each of them can be taken independently of the other. The duration of each course is five weeks, and each part includes: (i) knowledge-check questions and discussions, (ii) series of quizzes, and (iii) Matlab programming projects. Each course will be graded separately, using the average grades of the questions/discussions [K] quizzes [Q], and projects [P], by Final-Grade = 0.1K + 0.5Q + 0.4P.

The following includes more details of the topics we will cover in the first course:

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

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

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

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

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

• Relaxation pursuit algorithms including Basis Pursuit (BP).

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

• 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).

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