# Optimization Videos

## Compressive Sampling and Frontiers in Signal Processing

### Compressive Sampling, Compressed Sensing - Emmanuel Candes (California Institute of Technology) University of Minnesota, Summer 2007

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 ( $LaTeX: \approx$ 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).
Universal encoder ( $LaTeX: \approx$ 1:16 min).

June 6, 2007  Discussion Session

## Compressive Sampling, Compressed Sensing

### Richard Baraniuk (Rice University) Summer 2007

June 11, 2007  Compressive sensing for time signals: Analog to information conversion

June 12, 2007  Compressive sensing for detection and classification problems

June 12, 2007  Multi-signal, distributed compressive sensing

June 13, 2007  Compressive imaging with a single pixel camera

## Compressive Sampling, Compressed Sensing

### Ronald DeVore (University of South Carolina) Summer 2007

June 4, 2007  Signal encoding

June 5, 2007  Compression

June 6, 2007  Discrete compressed sensing

June 7, 2007  The Restricted Isometry Property

June 8, 2007  Construction of CS matrices with best Restricted Isometry Property

June 11, 2007  Performance of CS matrices revisited

June 12, 2007  Performance in probability

June 13, 2007  Decoders

June 14, 2007  Performance of iterated least squares

June 15, 2007  Open Problems

## Compressive Sampling, Compressed Sensing

### Anna Gilbert (University of Michigan) Summer 2007

June 7, 2007  Algorithms for Compressed Sensing, I

June 8, 2007  Algorithms for Compressed Sensing, II

## Compressive Sampling, Compressed Sensing

### Presentations by Participants, University of Minnesota, Summer 2007

June 4, 2007 (Audio begins 31 seconds into film.)