Instructor: Chandra R. Murthy (cmurthy at iisc dot ac dot in)
Class hours: MWF 8-9am, MP30. Make-up classes: S 1.30-2.30pm, also at MP30
TA: Chandrasekhar S. (chandrasekhars at iisc)
TA Hours: Tue 5:30-6:30pm, Wed 11am-12pm and Fri 12-1pm. Venue: SPW204.
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.
| S. No. | Topic | Num. Lectures |
|---|---|---|
| 1 | Introduction and math review | 2 |
| 2 | Uniqueness and uncertainty principles | 4 |
| 3 | Recovery algorithms - greedy and convex | 6 |
| 4 | The theory of compressed sensing | 6 |
| 5 | Stable recovery | 4 |
| 6 | Approximate recovery algorithms | 4 |
| 7 | Bayesian recovery algorithms | 4 |
| 8 | Extensions and applications | 2 |
| Total | 32 |
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 are posted here.
This year, we will explore deep learning based sparse signal recovery: theory and algorithms. Details will be discussed in class.