Optimization Videos

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

Contents 1 Emmanuel Candes 2 Chromosome structure, University of California, San Diego 2.1 Ronan Fleming 3 International Society for Magnetic Resonance in Medicine (ISMRM Toronto 2008) 3.1 Randy Duensing & Feng Huang 4 Convex Optimization, Stanford University 4.1 Stephen Boyd

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.)

Norms.

Early work by pioneers ( 16 minutes into film).

Deconvolution ( 30 minutes into film).

Lasso, Basis Pursuit ( 38 minutes in).

Wavelets, Curvelets, Ridgelets, sinusoids ( 55 minutes in).

Overcomplete Dictionary ( 57 minutes in).

Basis Pursuit ( 1:03 hours in).

Feature separation ( 1:12 hours in).

Barbara, Jean-Luc Stark ( 1:15 hours in).

Magnetic Resonance Imaging (MRI) ( 1:16 hours in).

Sample rate ( 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 ( 11 minutes into film).

4:1 sample to sparsity rule ( 21 minutes into film).

Candes' Matlab code ( 25 minutes in).

Fundamental premises of Compressed Sensing:  sparsity  and  incoherence  ( 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 ( 1:15).

MRI phantom with noise using Dantzig ( 1:28).

Imaging fuel cells ( 1:31).

Subsampling ( 1:36).

June 13 2007   Connections with Information and Coding Theory

error correction (since the beginning).

Matlab decode ( 20 min in).

second error corruption model: gross error + quantization error ( 29 min in).

Connection with the Sparse Recovery Problem ( 57 min in).

Reed-Solomon code ( 1:08 min in).

Matlab for Reed-Solomon code ( 1:26 min in).

June 14 2007   Modern Convex Optimization

Unconstrained Minimization ( 11 min in).

Matlab example for Gradient Descent with exact Line Search ( 19 min in).

Exact line search vs. Backtracking line search ( 22 min in).

Newton Step ( 26 min in).

Self Concordance ( 35 min in).

Equality Constrained Minimization ( 43 min in).

Barrier function ( 47 min in).

Central path ( 53 min in).

Complexity analysis ( 1:14).

Matlab for log-barrier ( 1:25).

Primal-dual interior point methods ( 1:29).

June 15 2007   Topics and Applications of Compressive Sampling

Beyond L1 minimization ( 3 min in).

Reweighted TV for MRI phantom: recover using m=1.2S (S is number of non zero gradient terms) ( 14 min in).

Overcomplete representations ( 19 min in).

Geometric separation: Cartoon + Texture ( 22 min in).

L1 synthesis vs. analysis for CS ( 28 min in).

Pulse reconstruction using L1 synthesis, L1 analysis and reweighted L1 analysis( 36 min).

ADC: nonuniform sampler vs. random pre-integrator ( 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