Michael Elad
Abstract: In these lectures we will focus on the use of sparse and redundant representations and learned dictionaries for image processing tasks. The topics to be covered will be taken from the following list, based on what time will allow:
Lecture 1 - Introduction to Sparse Approximation - Algorithms
- Sparse (approximate) solutions to underdetermined linear systems of equations
- Approximated pursuit by greedy methods (MP, OMP, Thresholding, Subspace Pursuit, CoSaMP, Iterative Hard-Thresholding)
- Approximation by relaxation methods (FOCUSS, Basis Pursuit, Dantzig Selector)
Lecture 2 - Introduction to Sparse Approximation - Theoretical Foundations
- Spark, RIP, and mutual coherence
- Uniqueness of sparse representations
- Theoretical guarantees - near-oracle performance
Lecture 3 - Sparse and Redundant Representation Signal Modeling
- Modeling data (images) with sparse and redundant representations
- Relation to existing models and the Bayesian point of view
- Signal and image processing with this model - main concepts
- Estimation point of view - MAP and MMSE
- Dictionary learning - the MOD and K-SVD algorithms
Lecture 4 - Sparse Representations in Image Processing
- Image deblurring via iterative-shrinkage algorithms
- Image denoising with a learnt dictionary
- Image separation to cartoon and texture
- Image inpainting
- Image Scale-Up
- Image compression
Tutorial: Greedy algorithms and dictionary leaning for denoising