E9 203-O Compressed Sensing and Sparse Signal Processing 3:1 (January 2022)

Course Instructor: K V S Hari, ECE

Syllabus

Introduction to underdetermined linear Systems; Sparse linear systems.Basic theory of l0 and l1 minimization and necessary and sufficient conditions for l0 - l1 equivalence. Uncertainty of Redundant Solutions.

Spark of a matrix, Mutual coherence and the Restricted Isometry property (RIP).

Greedy pursuit algorithms for sparse signal recovery: Orthogonal Matching Pursuit (OMP), Basis Pursuit (BP), basis Pursuit De-Noising (BPDN), Iteratively Reweighted Least Squares (IRLS) method, Stage-wise OMP (StOMP), Dantzig-Selector approach,

Dictionary Learning: Method of Optimal Directions (MOD), K-SVD algorithm

Application areas: Image processing: Image deblurring, Image compression, Image denoising examples, wireless communication: Channel estimation.

Textbooks / References

  1. M. Elad, "Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing", Springer, 2010.
  2. S. Foucart and H Rauhut, "A Mathematical Introduciton to Compressive Sensing", Birkhauser, 2010.

Prerequisites: Matrix Theory

Grading:

  • Assignments 40%
  • Midterm exam 30%
  • Final exam 30%.

Assignments will be given roughly once in two weeks.