236862 – Course Webpage – Winter Semester 2018/2019

Sparse and Redundant Representations

and Their Applications in Signal and Image Processing


Winter Semester, 2018/2019

Note: This course will be given in English if foreign students participate in class


Lecturer: Michael Elad (reception hours: anytime, but please set it up by an email)
Credits: 3 Points !!! (this has changed from last year to reflect the change due to the MOOC)
Time & Place: Thursday, 10:30-12:30, Room: changed to Taub 401 (fourth floor) for all the semester
  1. Elementary image processing course: 234327/236860 or 046200.
  2. Numerical analysis course: 234125

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 Description


A year 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. On October 25th, 2018, we start formally this two-part course, and it will be open in parallel to anyone interested 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 weekly meetings for discussions. This means that most of your work in this part 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 an additional research project assignmentMore explanations (with possible modifications) on this special structure will be given in the beginning of the semester.

Course Content

In the field of signal and image processing there is a fascinating new arena of research that has drawn a lot of interest in the past ~15 years, dealing with sparse and redundant representations. Once can regard this branch of activity 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 developing 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 signal and image 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 years. This course will touch on theory, numerical algorithms, and applications in image processing.

Course Requirements

  • Note that the course has a very unusual format (MOOC + mandatory meetings + a final project).
  • 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.
  • The course requirements include a final project to be performed by pairs (or singles) based on recently published papers. A list of candidate papers to choose from is given here, and instructions on how to proceed are shared with you as well. The project will include
    1. A final report (10-20 pages) summarizing these papers, their contributions, and your own findings (open questions, simulation results, etc.).
    2. A Power-point presentation of the project to present at the end of the semester to the lecturer.
    3. The (hard!!) deadline for the project submission is April 30th 2019. No delays will be allowed.
  • Attendance of the meetings in class is MANDATORY, and will be checked. Each student can skip two meetings without affecting his/her grade. Beyond this, every absence would cost 5% in the final grade.


  • 50% – MOOC grade
  • 50% – Project (content, presentation, & report)
  • Note again: Class attendance is mandatory (up to 2 absences are permitted, each causing a decrease of 5% in the final grade)

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

Course Material

Course 1:

25.10.18: Welcome & Introduction
01.11.18: Section 1
08.11.18: Section 2
15.11.18: Section 3
22.11.18: Section 4
29.11.18: Section 5

Course 2:

20.12.18: Section 1 and Additional slides (Analysis model)
27.12.18: Section 2 and Additional slides (Kernel DL)
03.01.19: Section 3 and additional slides (compression) 
17.01.19: Section 4 and Additional slides (MMSE via Stochastic Resonance) 
24.01.19: Section 5 and Additional slides (The CSC model and relation to Deep-Learning)

Announcements (newest on top)

  • January 1, 2019: Note that next week we will NOT hold our regular meeting. We shall meet again on January 17th to cover Section 4 of Course 2.
  • November 20, 2018: You are required to register to the second course ASAP. EdX is changing its policy soon, and your access might be blocked.
  • October 27, 2018: The list of papers for your projects is given here.