E9 203: Compressed Sensing and Sparse Signal Processing: Video Lectures and Notes

Lecture 1: Introduction to underdetermined linear systems, penalty functions, l1 minimization, and linear programming. Video, Notes-SVG, Notes-PDF.

Lecture 2: Best s-term approximation, and why lp-ball with p < 1 promotes sparsity. Video1, Video2,Notes-SVG, Notes-PDF.

Lecture 3: Tighter bounds on compressible signals, minimal number of measurements for unique sparse vector recovery. Video, Notes-SVG, Notes-PDF.

Lecture 4: Minimal number of measurements for the recovery of all s-sparse vectors. Video, Notes-SVG, Notes-PDF.

Lecture 5: Recovery of individual sparse vectors. NP-hardness of l0 minimization. Video, Notes-SVG, Notes-PDF.

Lecture 6: L1 minimization leads to sparse solutions. Video, Notes-SVG, Notes-PDF.

Lecture 7: The orthogonal matching pursuit algorithm. Video, Notes-SVG, Notes-PDF.

Lecture 8: Thresholding based algorithms. Video, Notes-SVG, Notes-PDF.

Lecture 9: Regularization based methods. Extreme points, basic feasible solutions, and concave optimization. Video, Notes-SVG, Notes-PDF.

Lecture 10: Majorization-minimization based methods. Video, Notes-SVG, Notes-PDF.

Lecture 11: Reweighting based methods. Analysis of local minima. Video, Notes-SVG, Notes-PDF.

Lecture 12: Convergence of reweighting based methods. Video, Notes-SVG, Notes-PDF.

Lecture 13: Sparse Bayesian learning. Video, Notes-SVG, Notes-PDF.

Lecture 14: Sparse Bayesian learning – continued. Video, Notes-SVG, Notes-PDF.

Lecture 15: Discussion on the SBL prior, reweighted algorithms for SBL. Video, Notes-SVG, Notes-PDF.

Lecture 16: Reweighted l2 algorithms for SBL (continued), non-negative sparse recovery. Video, Notes-SVG, Notes-PDF.

Lecture 17: Basis pursuit (BP). Video, Notes-SVG, Notes-PDF.

Lecture 18: Stable null space property, robust null space property. Video, Notes-SVG, Notes-PDF.

Lecture 19: Recovery of sparse vectors via robust null space property. Video, Notes-SVG, Notes-PDF.

Lecture 20: Recovery of individual sparse vectors. Video, Notes-SVG, Notes-PDF.

Lecture 21: A stable and robust recovery result. Recovery via tangent cones. Video, Notes-SVG, Notes-PDF.

Lecture 22: Low rank matrix recovery. Video, Notes-SVG, Notes-PDF.

Lecture 23: Coherence. Video, Notes-SVG, Notes-PDF.

Lecture 24: Properties of spark. Guarantees based on coherence. Video, Notes-SVG, Notes-PDF.

Lecture 25: Analysis of BP and thresholding-based algorithms via coherence. Video, Notes-SVG, Notes-PDF.

Lecture 26: The restricted isometry property. Video, Notes-SVG, Notes-PDF.

Lecture 27: Properties of and bounds on the restricted isometry constant (RIC). Video, Notes-SVG, Notes-PDF.

Lecture 28: Analysis of BP via RIC. Video, Notes-SVG, Notes-PDF.

Lecture 29: Analysis of thresholding algorithms via RIC. Video, Notes-SVG, Notes-PDF.

Lecture 30: Proof of the result on the analysis of thresholding algorithms via RIC. Video, Notes-SVG, Notes-PDF.

Lecture 31: Analysis of greedy algorithms (OMP) via RIC. Video, Notes-SVG, Notes-PDF.

Lecture 32: Gaussian matrices satisfy RIP. Video, Notes-SVG, Notes-PDF.

Lecture 33: Gaussian matrices satisfy RIP (continued). Video, Notes-SVG, Notes-PDF.

Lecture 34: RIP results for subgaussian matrices, Johnson Lindenstrauss lemma. Video, Notes-SVG, Notes-PDF.

Lecture 35: Algorithms for l1 regularization. Video, Notes-SVG, Notes-PDF.

Lecture 36: Proximal and gradient projection methods. Gelfand m-widths defined. Video, Notes-SVG, Notes-PDF.

Lecture 37: Bounds on Gelfand m-widths. Video, Notes-SVG, Notes-PDF.

Lecture 38: Proof of the result on the bounds on Gelfand m-widths. Video, Notes-SVG, Notes-PDF.

Lecture 39: Further results and explanation of bounds on Gelfand m-widths. Video, Notes-SVG, Notes-PDF.