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E9 203: Compressive Sensing and Sparse Signal Processing

Logistics

Instructor: Chandra R. Murthy (cmurthy at iisc dot ac dot in)
Class hours: TuTh 11am-12.30pm, MP30.
TA: Chandrasekhar S. (chandrasekhars at iisc)
TA Hours: TBD

Textbooks:
1. M. Elad, “Sparse and Redundant Representations”, Springer, 2010.

2. H. Rauhut, “Compressive Sensing and Structured Random Matrices,” Radon Series Comp. Appl. Math., 2011.

3. M. A. Davenport, M. F. Duarte, Y. C. Eldar, G. Kutyniok, “Introduction to Compressed Sensing,” available here.

4. http://dsp.rice.edu/cs
5. S. Foucart and H. Rauhut, “A mathematical introduction to compressive sensing,” Birkhauser Press.

Prerequisites: Random processes (E2-202 or equivalent), Matrix theory (E2-212 or equivalent).

Overview:
The goal of this course is to provide an overview of the recent advances in compressed sensing and sparse signal processing. We start with a discussion of classical techniques to solve undetermined linear systems, and then introduce the l0 norm minimization problem as the central problem of compressed sensing. We then discuss the theoretical underpinnings of sparse signal representations and uniqueness of recovery in detail. We study the popular sparse signal recovery algorithms and their performances guarantees. We will also cover signal processing interpretations of sparse signal recovery in terms of MAP and NMSE estimation.

Syllabus:

S. No. Topic Num. Lectures
1Introduction and math review 2
2Uniqueness and uncertainty principles 4
3Recovery algorithms - greedy and convex 6
4The theory of compressed sensing 6
5Stable recovery 4
6Approximate recovery algorithms 4
7Bayesian recovery algorithms 4
8Extensions and applications 2
Total 32

Grading

Homeworks: due 2 weeks after the date the homework is announced: 15%
Exam 1: Date TBD, in class: 25%.
Exam 2: Date TBD, in class: 25%.
Initial project presentations: date TBD: 10%
Final project presentations and report: date TBD: 25%
Note: there will be no makeup exams.

Homeworks

Homeworks are posted here.

Project

This year, we will explore deep learning based sparse signal recovery: theory and algorithms. Details will be discussed in class.

Announcements

  • The first class will be held on Jan. 02, 2020 at MP30.

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