236862 – Course Webpage – Winter Semester 2021/2022

Sparse and Redundant Representations

and Their Applications in Signal and Image Processing


Winter Semester, 2021/2022


1: This course may be given in English (depending on foreign participants).

2. I may run a followup course (2 credit points) in the spring Semester that will focus on advanced topics in image processing. This will be given in a seminar format and primarily meant for students who took this (236862) course.

Lecturer: Michael Elad (reception hours: anytime, but please set it up by an email)
Credits: 3 Points
Time & Place: Monday 16:30-18:30

Zoom link to our meetings: https://technion.zoom.us/j/96081067862

Grade Policy: 50% – MOOC grade and 50% – Final exam

Exam – MOED A: 08.02.2022

Exam – MOED B: 08.03.2022

  1. Numerical Algorithms (234125) + Elementary Signal/Image Processing (236200) or
  2. Electrical Engineering’s course on Image Processing (046200)

Graduate students are not obliged to these requirements

Literature: Recently published papers and my book “Sparse and Redundant Representations – From Theory to Applications in Signal and Image Processing” that can be found in the library

Course Content

In the fields of signal and image processing and machine learning there is a fascinating arena of research that has drawn a lot of interest in the past ~20 years, dealing with sparse and redundant representations. One way to regard this branch of activity is as a natural continuation to the vast activity on wavelet theory, which thrived in the 90’s. Another perspective – the one we shall adopt in this course – is to consider this field as the emergence of a highly effective model for data that extends and generalizes previous models. As models play a central role in practically every task in data processing, the effect of the new model is far reaching. The core idea in sparse representation theory is a development of a novel redundant transform, where the number of representation coefficients is larger compared to the signal’s original dimension. Alongside this “waste” in the representation comes a fascinating new opportunity – seeking the sparsest possible representation, i.e., the one with the fewest non-zeros. This idea leads to a long series of beautiful (and surprisingly, solvable) theoretical and numerical problems, and many applications that can benefit directly from the new developed theory. In this course we will survey this field, starting with the theoretical foundations, and systematically covering the knowledge that has been gathered in the past 20 years. This course will touch on theory, numerical algorithms, applications in image processing, and connections to machine learning and more specifically to deep learning.

Course Description

­­­­­Few years ago we worked hard to convert this advanced course into a MOOC (Massive Open Online Course) serviced through EdX. This means that all the material we cover can be taught through short videos, interactive work, wet projects, and more, all through the Internet. By the way, you are most welcome looking at the recorded videos on YouTube (Part 1, Part 2) in order to get a feeling for this course’ content.  On October 25th 2021 we start formally this two-part course, and it will be open in parallel to anyone interested, all around the world.

What about you – Technion’s students? A major part of this (236862) course will be taught as the above described MOOC, augmented by mandatory weekly meetings for discussions. This means that a major part of your work will be done independently through the Internet. This will cover 50% of your activity in our course. As for the rest 50%, it includes weekly meetings and a final exam. More explanations on this special structure will be given in the beginning of the semester.

Course Requirements

  • Note that the course has a very unusual format (MOOC + meetings + a final exam).
  • We are yet to decide whether these will be frontal or zoom-based – if it will be frontal, the zoom link given above becomes irrelevant.
  • There will be 5 wet HW assignments within the EdX course and various quizzes. The wet HW will concentrate on Matlab/Python implementation of algorithms that will be discussed in class. More on this is given below.
  • New!! The course requirements include a final exam. This replaces the research projects we used to run.
  • Attendance of the meetings in class is mandatory (2 absences are permitted, and beyond these, each leads to 2% loss in the final grade).

edX Submission Guidelines

  • All wet exercises should be submitted before midnight of the dates written below.
  • If submitted in pairs, both members should submit the assignment to edX.
  • Bonus assignment is Mandatory to Technion students.
  • All other non-wet assignments including quizzes and discussion should be submitted before the end of the semester at: 27.1.22.

Submission dates of wet assignments:

  • Course 1, Wet #1: 29.11.21
  • Course 1, Wet #2: 13.12.21
  • Course 2, Wet #1: 10.1.22
  • Course 2: Wet #2: 27.1.22
  • Course 2 Bonus: 27.1.22


  • 50% – MOOC grade
  • 50% – Final exam

 For those interested (applies to Technion’s students only):

  • Free listeners are welcome.
  • Please send an email to both Alona and me (elad@cs.technion.ac.il and zadneprovski@gmail.com) so that we add you to the course mailing list, and grant you free access to the EdX system.
  • Just show up to the first meeting on October 25th and we’ll take it from there.

Course Material

Course 1:

25.10.21: Welcome & Introduction
01.11.21: Section 1
08.11.21: Section 2
15.11.21: Section 3
22.11.21: Section 4
06.12.21: Section 5

Course 2:

13.12.21: Section 1 and Additional slides (Analysis model)
20.12.21: Section 2 and Additional slides (Kernel Dictionary Learning)
27.12.21:Section 3 and additional slides (compression) 
10.01.22: Section 4 and Additional slides (MMSE via Stochastic Resonance) 
17.01.22: Section 5 and Additional slides (CSC and Deep-Learning)


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