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.
This program is composed from two separate parts:
Part 1: Sparse Representations in Signal and Image Processing: Fundamentals.
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:
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
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:
SURE for Parameter Tuning:
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
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