Sparse and Redundant Representations
and Their Applications in Signal and Image Processing

Winter Semester, 2017/2018


Note: This course will be given in English


             Date of last update: November 23rd, 2017



Michael Elad

Reception hours: anytime, but please set it up by an email.

I am in office 712 in Taub Bldg. phone # 4169


2 points

Time and Place

Thursday, 10:30-12:30, Room: Taub 3


Elementary image processing course: 234327/236860 or 046200. Graduate students are not obliged to these requirements


Recently published paper and the book "Sparse and Redundant Representations- From Theory to Applications in Signal and Image Processing" that can be found in the library



Course Description



In the past year we have been working 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 now be taught through short videos, interactive work, and more, all through the Internet. On October 25th, 2017, we start formally this two-part course, and it will be open 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 ~75% of your activity in our course. As for the rest 25%, it includes weekly meetings and an additional research project assignment.


More explanations (with possible modifications) on this special structure will be given towards the beginning of the semester. Note that we have not uploaded the complete course yet to the EdX system, as we are still building it (half has been uploaded so far).


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


o   Note that the course has a very unusual format (MOOC + meetings + a final project), and this coming semester is the first time it is ran this way.

o   There will be 4 wet HW assignments within the EdX course and various quizzes. The wet HW will concentrate on Matlab implementation of algorithms that will be discussed in class.  

o   The course requirements include a final project to be performed by pairs based on recently published papers [list of papers and the papers themselves (this is a big ZIP file. In it, file names starting with "ALREADY-CHOSEN" mean exactly that)]. Instructions are given here. The project will include

§  A final report (10-20 pages) summarizing these papers, their contributions, and your own findings (open questions, simulation results, etc.).

§  A Power-point presentation of the project in a mini-workshop that we will organize at the end of the semester.




o   50% - MOOC grade

o   50% - Project (content, presentation, & report)


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


o   Free listeners are welcome.

o   Please send (to both & an email so that I add you to the course mailing list.


Announcements / Material Distribution (newest on top):


·       November 23rd, 2017: Here are the slides presented in our meeting today, covering Section 4 of Course 1. Here is the Matlab Demo shown in class on the LARS algorithm.


·       November 16th, 2017: Here are the slides presented in our November 16th meeting, covering Section 3 of Course 1.


·       November 10th, 2017: We now provide you with the list of papers for the final project in the course. Here is the list of papers and the papers themselves (beware: this is a big file).


·       November 10th, 2017: Here are the slides presented in our November 9th meeting, covering Section 2 of Course 1.


·       November 4th, 2017: Here are the slides presented in our November 2nd meeting, covering Section 1 of Course 1.


·       October 26th, 2017: Instructions on the project are now available here


·       October 24th, 2017: The following slides will be presented in our meeting on the 26th, and they are shared with you for your convenience.


·       October 22nd, 2017: Our first meeting will be held on October 26th at 10:30, and it is expected to be relatively short (~40 minutes). We plan to (i) introduce the course format, style, team, assignments, and grading policy; and (ii) show you the edX site and how to use it. Since the MOOC starts formally on the 25th (one day before), we'll discuss the covered material a week later.