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Italic text== Compressive Sampling, Compressed Sensing, University Minnesota ==


Emmanuel Candes

(requires RealPlayer to watch)

June 4 2007  Sparsity and the l1 norm.

June 5 2007  Underdetermined Systems of Linear Equations. (Audio begins 4 minutes into film.)

Early work by pioneers (LaTeX: \approx 16 minutes into film).
Deconvolution (LaTeX: \approx 30 minutes into film).
Lasso, Basis Pursuit (LaTeX: \approx 38 minutes in).
Wavelets, Curvelets, Ridgelets, sinusoids (LaTeX: \approx 55 minutes in).
Overcomplete Dictionary (LaTeX: \approx 57 minutes in).
Basis Pursuit (LaTeX: \approx 1:03 hours in).
Feature separation (LaTeX: \approx 1:12 hours in).
Barbara, Jean-Luc Stark (LaTeX: \approx 1:15 hours in).
Magnetic Resonance Imaging (MRI) (LaTeX: \approx 1:16 hours in).
Sample rate (LaTeX: \approx 1:36 hours in).

June 6 2007  Sparsity and Incoherence. (If you only watch one Candes video, this is it.)

Recovery of Dirac comb, derivation of minimum sampling rate (LaTeX: \approx 11 minutes into film).
4:1 sample to sparsity rule (LaTeX: \approx 21 minutes into film).
Candes' Matlab code (LaTeX: \approx 25 minutes in).
Fundamental premises of Compressed Sensing:  sparsity  and  incoherence  (LaTeX: \approx 29 minutes in).

June 7 2007  The Uniform Uncertainty Principle.

June 8 2007  The Role of Probability in Compressed Sensing.

June 11 2007  Part 1 - Robust Compressed Sensing and Connections with Statistics. (Audio back at 17 minutes into film.)

June 12 2007  Part 2 - Robust Compressed Sensing and Connections with Statistics.

Matlab (LaTeX: \approx 1:15).
MRI phantom with noise using Dantzig (LaTeX: \approx 1:28).
Imaging fuel cells (LaTeX: \approx 1:31).
Subsampling (LaTeX: \approx 1:36).

June 13 2007   Connections with Information and Coding Theory

error correction (since the beginning).
Matlab decode (LaTeX: \approx 20 min in).
second error corruption model: gross error + quantization error (LaTeX: \approx 29 min in).
Connection with the Sparse Recovery Problem (LaTeX: \approx 57 min in).
Reed-Solomon code (LaTeX: \approx 1:08 min in).
Matlab for Reed-Solomon code (LaTeX: \approx 1:26 min in).

June 14 2007   Modern Convex Optimization

Unconstrained Minimization (LaTeX: \approx 11 min in).
Matlab example for Gradient Descent with exact Line Search (LaTeX: \approx 19 min in).
Exact line search vs. Backtracking line search (LaTeX: \approx 22 min in).
Newton Step (LaTeX: \approx 26 min in).
Self Concordance (LaTeX: \approx 35 min in).
Equality Constrained Minimization (LaTeX: \approx 43 min in).
Barrier function (LaTeX: \approx 47 min in).
Central path (LaTeX: \approx 53 min in).
Complexity analysis (LaTeX: \approx 1:14).
Matlab for log-barrier (LaTeX: \approx 1:25).
Primal-dual interior point methods (LaTeX: \approx 1:29).

June 15 2007   Topics and Applications of Compressive Sampling

Beyond L1 minimization (LaTeX: \approx 3 min in).
Reweighted TV for MRI phantom: recover using m=1.2S (S is number of non zero gradient terms) (LaTeX: \approx 14 min in).
Overcomplete representations (LaTeX: \approx 19 min in).
Geometric separation: Cartoon + Texture (LaTeX: \approx 22 min in).
L1 synthesis vs. analysis for CS (LaTeX: \approx 28 min in).
Pulse reconstruction using L1 synthesis, L1 analysis and reweighted L1 analysis(LaTeX: \approx 36 min).
ADC: nonuniform sampler vs. random pre-integrator (LaTeX: \approx 48 min).

Chromosome structure, University of California, San Diego

Ronan Fleming

Auto-correlation coefficients (6MB video)  from Chromosome structure via Euclidean Distance Matrices.

International Society for Magnetic Resonance in Medicine (ISMRM Toronto 2008)

Randy Duensing & Feng Huang

(requires Adobe Flash Player)

Objective Comparison of Alternate Reconstruction Strategies: An Unmet Need

  • Username: 44141
  • Password: Law

Convex Optimization, Stanford University

Stephen Boyd

Tutorials for a graduate level course, 2008

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