Sparse and Redundant Representations and Their Applications in

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Sparse and Redundant Representations and Their Applications in Signal and Image Processing (236862) Section 0-1: First Steps in Signal and Image Processing via Sparseland Winter Semester, 2018/2019 Michael (Miki) Elad

Meeting Plan Quick review of the material covered Answering questions from the students and getting their feedback Discussing a new material – The Co-Sparse Analysis Model Administrative issues

Overview of the Material Overview of this Field Image Priors and the Sparseland Model Iterative Shrinkage and Image Deblurring

Overview of the Material Overview of this Field What This Field is All About: Modeling Data Sparseland: Theoretical & Algorithmic Background This Course: Scope and Style A Word About Notations

Overview of the Material Overview of this Field Image Priors and the Sparseland Model A Prior for Images: How and Why? The Evolution of Priors in Image Processing Linear vs. Non-Linear Approximation The Sparseland Model The Geometry behind Sparseland Processing Sparseland’s Signals

Overview of the Material Overview of this Field Image Priors and the Sparseland Model Iterative Shrinkage and Image Deblurring Image-Deblurring via Sparseland: Problem Formulation Starting with Classical Optimization Iterative Shrinkage Thresholding Algorithm (ISTA) Shrinkage: A Matlab Demo Image Deblurring: Results & Discussion Image Deblurring: A Closer Look at the Results

Your Questions and Feedback You have shown 3 algorithms to solve Q1, which is related to P1. These are: IRLS, ADMM (and now ISTA is added) and LARS. Can you perhaps provide more insight on the subject of differences between them? In terms of run-time complexity and objective empirical success ? Tough question ! Generally, these methods are hard to compare (who is better? OMP or BP?) If the picture is not complicated enough, there is a way to design an “ISTA- like” algorithm based on IRLS. However, if you insist on an answer, I would say this: Use LARS for low-dimensions (up to m=500) Use ISTA for higher dimensions.

Your Questions and Feedback

New Material? Analysis vs. Synthesis The Sparseland Story is posed in terms of a Synthesis model, but there is an analysis counterpart In 2007 we exposed this confusion for the first time

New Material? The Co-Sparse Analysis Model In 2013 we made a substantial progress in understanding the analysis alternative This led to a flood of papers on this alternative (see this) Bottom line: till today, we are unclear which of the two to use, etc. BTW: there is a connection between this debate and deep-learning architectures

So, What is The Analysis Model?

Administrative Issues No weekly emails ? What about your projects?