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Compressive Sampling and Frontiers in Signal Processing

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

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

June 6, 2007  Discussion Session

Introduction to Magnetic Resonance Imaging (MRI)

Leon Axel (New York University), Steen Moeller (University of Minnesota)

June 5, 2007

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.)

June 14, 2007

June 14, 2007

June 14, 2007

June 14, 2007

June 14, 2007

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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