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Sparse Representations in Image Processing: From Theory to Practice

Technion - Israel Institute of Technology via edX

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Overview

This course is a follow-up to the first introductory course of sparse representations. Whereas the first course puts emphasis on the theory and algorithms in this field, this course shows how these apply to actual signal and image processing needs.

Models play a central role in practically every task in signal and image processing. Sparse representation theory puts forward an emerging, highly effective, and universal such model. Its core idea is the description of the data as a linear combination of few building blocks – atoms – taken from a pre-defined dictionary of such fundamental elements.

In this course, you will learn how to use sparse representations in series of image processing tasks. We will cover applications such as denoising, deblurring, inpainting, image separation, compression, super-resolution, and more. A key feature in migrating from the theoretical model to its practical deployment is the adaptation of the dictionary to the signal. This topic, known as "dictionary learning" will be presented, along with ways to use the trained dictionaries in the above mentioned applications.

Syllabus

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 table includes more details of the topics we will cover in the second course:

Overview of this Field and this Course

What This Field is All About: Modeling Data

Sparseland: Theoretical & Algorithmic Background

This Course: Scope and Style

Image Priors and the Sparseland Model

A Word About Notations

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

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

Sparseland: An Estimation Point of View

A Strange Experiment

A Crash-Course on Estimation Theory

Sparseland : An Estimation Point of View

Sparseland: Approximate Estimation

The Quest for a Dictionary

Background: Choosing vs. Learning the Dictionary

Dictionary Learning (DL): Problem Formulation

The MOD Algorithm

The K-SVD Algorithm

Matlab Demo

Dictionary Learning: Difficulties

The Double-Sparsity Algorithm

Learning Unitary Dictionaries

The Signature Dictionary

Dictionary Learning: Summary

Image Denoising – The Sparseland Way

The Denoising Problem and Its Importance

First Steps in Image Denoising

Variations on the
Global Thresholding Algorithm

SURE for Parameter Tuning:
The Theory

SURE for Parameter Tuning:
The Practice

Patch-Based Denoising – Basics

Patch-Based Denoising: Theoretical Foundations

The K-SVD Image Denoising Algorithm

Patch-Based Denoising – Other Methods

Image Denoising – Summary

Image Separation and Inpainting 

Morphological Component Analysis: The Core Idea

Cartoon-Texture Image Separation via a Global Treatment

From Separation to Inpainting: A Global Approach

Patch-based Image Separation

Patch-Based Image Inpainting

Patch-Based Impulse Noise Removal

Single Image Super-Resolution

Single-Image Super-Resolution: Problem Definition

Single-Image Super-Resolution: Proposed Solution

Single-Image Super-Resolution: Training the Coupled-Dictionaries

Single-Image Super-Resolution: The Overall Algorithm

Single-Image Super-Resolution: Results

Course Summary

Sparseland: What is It All About?

Sparseland: What is Still Missing?

Taught by

Michael Elad and Yaniv Romano

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Reviews for edX's Sparse Representations in Image Processing: From Theory to Practice
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Anonymous
5.0 5 months ago
Anonymous completed this course.
An excellent course for those with knowledge of: Linear Algebra, DSP, and Probability.

The instructor teaches the course material from his own book, which I always think is a good sign as I assume they must know the subject pretty well. After following the course this assumption holds true in this case.

The material can get pretty difficult but if you put in the effort you'll be rewarded.
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Anonymous
5.0 5 months ago
Anonymous completed this course.
I've learnt a lot in this course. It follows Prof. Elads book closely. I really enjoyed the practical projects as well. If you want to no more about this topic you should definitely take this course. I want to thank Prof. Elad for sharing all his knowledge with students and researchers world wide. Have a look at his website if you want to find interesting papers on this topic.
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Anonymous
5.0 5 months ago
Anonymous completed this course.
Excellent but advanced course. It follows Michael Elad's textbook "Sparse and Redundant Representations" closely. You need a good working knowledge of linear algebra to succeed. I recommend Guillermo Shapiro's MOOC "Image and Video Processing: From Mars to Hollywood with a Stop at the Hospital" on Coursera before taking this one.
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Anonymous
5.0 5 months ago
Anonymous completed this course.
An excellent and very interesting course at an advanced level. Familiarity with linear algebra is essential and general familiarity with image and signal processing is also assumed. The accompanying theoretical course is also very well presented and very interesting.
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Anonymous
5.0 5 months ago
Anonymous completed this course.
It was a very challenging course but it completely pays off. All pieces are given and fall right into place fro theory to practice. I recommend to take the two courses!
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