Course Structure

Lecture

Topics covered

1

General Introduction of the course. Slides
Chapter 1: Proving the tendency of L1 to sparsify.

2

Chapter 1: Lp and L0, definition of P_0 as our ideal goal.
Chapter 2: Uniqueness of sparse solutions: definition of mutual coherence

3

Chapter 2: Mutual coherence and spark and their relation, uniqueness of the sparsest solution of a linear system.
Chapter 3: The Thresholding Algorithm

4

Chapter 2: Constructing Grassmanian frames [code]
Chapter 3: Introducing pursuit algorithms – Greedy and relaxation methods. Exponential convergence of the residual for MP.

5

Chapter 4: Pursuit Performance – Equivalence theorems for OMP and THR
Proving the success of the BP in the noiseless case, the role of the sign pattern.
[HW1: Inpainting by Greedy Algorithms]

6

Chapter 5: Introducing P_0^eps that adds noise – introduction to uniqueness versus equivalence, the RIP, relation to spark and the mutual coherence, stability of P_0^eps, pursuit algorithms for the noisy case – Greedy, IRLS, LARS, stability of BP.

7

Chapter 6: LARS, Pursuit in the unitary case, iterative shrinkage algorithms.

8

Chapter 9: Priors and their role in signal and image processing, The Sparse-Land model and its use, The role of P_0^eps for various signal processing tasks
Slides by Michael Elad
[HW2: Iterative-Shrinkage]

9 The low-rank model [1]
Chapter 9: The co-sparse analysis model Slides

10

Chapter 12: Dictionary learning – using existing transforms, learning a dictionary, the MOD and the K-SVD algorithms, and their modifications. Double-sparsity, learning unitary transforms. Slides by Michael Elad

11

Task Driven Dictionary learning [2]

12

Chapter 14: Image denoising – global thresholding, Guleryuz patch-based processing, Shaked-Hel-Or scheme, K-SVD denoising

13 Poisson denoising Slides
Recent advances in sparse representation