Optimization Videos
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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 === | ||
+ | ([http://www.real.com requires RealPlayer to watch]) | ||
+ | |||
+ | [http://www.ima.umn.edu/recordings/New_Directions_Short_Course/ND6.4-15.07/candes6-4-07.ram June 4 2007] '''Sparsity and the l1 norm''' | ||
+ | : Example of sparse signals in genomics (<math>\approx</math> 8 minutes into film). | ||
+ | : Example of sparse signals in genetics (<math>\approx</math> 11 min in). | ||
+ | : Example of sparse signals in audio/image processing (<math>\approx</math> 18 min in). | ||
+ | : Transform-domain image coding (<math>\approx</math> 27 min in). | ||
+ | : Primary visual cortex (<math>\approx</math> 53 min in). | ||
+ | : Efficient estimation (<math>\approx</math> 57 min in). | ||
+ | : Computational harmonic analysis (<math>\approx</math> 1:22 in). | ||
+ | |||
+ | [http://www.ima.umn.edu/recordings/New_Directions_Short_Course/ND6.4-15.07/candes6-5-07.ram June 5 2007] '''Underdetermined Systems of Linear Equations''' (Audio begins 4 minutes into film.) | ||
+ | : Norms. | ||
+ | : Early work by pioneers (<math>\approx</math> 16 minutes into film). | ||
+ | : Deconvolution (<math>\approx</math> 30 minutes into film). | ||
+ | : Lasso, Basis Pursuit (<math>\approx</math> 38 minutes in). | ||
+ | : Wavelets, Curvelets, Ridgelets, sinusoids (<math>\approx</math> 55 minutes in). | ||
+ | : Overcomplete Dictionary (<math>\approx</math> 57 minutes in). | ||
+ | : Basis Pursuit (<math>\approx</math> 1:03 hours in). | ||
+ | : Feature separation (<math>\approx</math> 1:12 hours in). | ||
+ | : ''Barbara'', Jean-Luc Stark (<math>\approx</math> 1:15 hours in). | ||
+ | : Magnetic Resonance Imaging (MRI) (<math>\approx</math> 1:16 hours in). | ||
+ | : Sample rate (<math>\approx</math> 1:36 hours in). | ||
+ | |||
+ | [http://www.ima.umn.edu/recordings/New_Directions_Short_Course/ND6.4-15.07/candes6-6-07.ram 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 (<math>\approx</math> 11 minutes into film). | ||
+ | : 4:1 <i>sample to sparsity</i> rule (<math>\approx</math> 21 minutes into film). | ||
+ | : [[Candes.m|Candes' Matlab code]] (<math>\approx</math> 25 minutes in). | ||
+ | : Fundamental premises of Compressed Sensing: <i>sparsity</i> and <i>incoherence</i> (<math>\approx</math> 29 minutes in). | ||
+ | |||
+ | [http://www.ima.umn.edu/recordings/New_Directions_Short_Course/ND6.4-15.07/candes6-7-07.ram June 7 2007] '''The Uniform Uncertainty Principle''' | ||
+ | |||
+ | [http://www.ima.umn.edu/recordings/New_Directions_Short_Course/ND6.4-15.07/candes6-8-07.ram June 8 2007] '''The Role of Probability in Compressed Sensing''' | ||
+ | |||
+ | [http://www.ima.umn.edu/recordings/New_Directions_Short_Course/ND6.4-15.07/candes6-11-07.ram June 11 2007] '''Part 1 - Robust Compressed Sensing and Connections with Statistics''' (Audio back at 17 minutes into film.) | ||
+ | |||
+ | [http://www.ima.umn.edu/recordings/New_Directions_Short_Course/ND6.4-15.07/candes6-12-07.ram June 12 2007] '''Part 2 - Robust Compressed Sensing and Connections with Statistics''' | ||
+ | : Matlab (<math>\approx</math> 1:15). | ||
+ | : MRI phantom with noise using Dantzig (<math>\approx</math> 1:28). | ||
+ | : Imaging fuel cells (<math>\approx</math> 1:31). | ||
+ | : Subsampling (<math>\approx</math> 1:36). | ||
+ | |||
+ | [http://www.ima.umn.edu/recordings/New_Directions_Short_Course/ND6.4-15.07/candes6-13-07.ram June 13 2007] '''Connections with Information and Coding Theory''' | ||
+ | : error correction (since the beginning). | ||
+ | : Matlab decode (<math>\approx</math> 20 min in). | ||
+ | : second error corruption model: gross error + quantization error (<math>\approx</math> 29 min in). | ||
+ | : Connection with the Sparse Recovery Problem (<math>\approx</math> 57 min in). | ||
+ | : Reed-Solomon code (<math>\approx</math> 1:08 min in). | ||
+ | : Matlab for Reed-Solomon code (<math>\approx</math> 1:26 min in). | ||
+ | |||
+ | [http://www.ima.umn.edu/recordings/New_Directions_Short_Course/ND6.4-15.07/candes6-14-07.ram June 14 2007] '''Modern Convex Optimization''' | ||
+ | : Unconstrained Minimization (<math>\approx</math> 11 min in). | ||
+ | : Matlab example for Gradient Descent with exact Line Search (<math>\approx</math> 19 min in). | ||
+ | : Exact line search ''vs.'' Backtracking line search (<math>\approx</math> 22 min in). | ||
+ | : Newton Step (<math>\approx</math> 26 min in). | ||
+ | : Self Concordance (<math>\approx</math> 35 min in). | ||
+ | : Equality Constrained Minimization (<math>\approx</math> 43 min in). | ||
+ | : Barrier function (<math>\approx</math> 47 min in). | ||
+ | : Central path (<math>\approx</math> 53 min in). | ||
+ | : Complexity analysis (<math>\approx</math> 1:14). | ||
+ | : Matlab for log-barrier (<math>\approx</math> 1:25). | ||
+ | : Primal-dual interior point methods (<math>\approx</math> 1:29). | ||
+ | |||
+ | [http://www.ima.umn.edu/recordings/New_Directions_Short_Course/ND6.4-15.07/candes6-15-07.ram June 15 2007] '''Topics and Applications of Compressive Sampling''' | ||
+ | : Beyond L1 minimization (<math>\approx</math> 3 min in). | ||
+ | : Reweighted TV for MRI phantom: recover using m=1.2S (S is number of non zero gradient terms) (<math>\approx</math> 14 min in). | ||
+ | : Overcomplete representations (<math>\approx</math> 19 min in). | ||
+ | : Geometric separation: Cartoon + Texture (<math>\approx</math> 22 min in). | ||
+ | : L1 synthesis ''vs''. analysis for CS (<math>\approx</math> 28 min in). | ||
+ | : Pulse reconstruction using L1 synthesis, L1 analysis and reweighted L1 analysis(<math>\approx</math> 36 min). | ||
+ | : ADC: nonuniform sampler ''vs''. random pre-integrator (<math>\approx</math> 48 min). | ||
+ | : Universal encoder (<math>\approx</math> 1:16 min). | ||
+ | |||
+ | [http://www.ima.umn.edu/recordings/New_Directions_Short_Course/ND6.4-15.07/discussion6-6-07.ram June 6, 2007] '''Discussion Session''' | ||
+ | |||
== Introduction to Magnetic Resonance Imaging (MRI) == | == Introduction to Magnetic Resonance Imaging (MRI) == |
Revision as of 14:14, 14 October 2008
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
- Example of sparse signals in genomics ( 8 minutes into film).
- Example of sparse signals in genetics ( 11 min in).
- Example of sparse signals in audio/image processing ( 18 min in).
- Transform-domain image coding ( 27 min in).
- Primary visual cortex ( 53 min in).
- Efficient estimation ( 57 min in).
- Computational harmonic analysis ( 1:22 in).
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).
- Universal encoder ( 1:16 min).
June 6, 2007 Discussion Session
Introduction to Magnetic Resonance Imaging (MRI)
Leon Axel (New York University), Steen Moeller (University of Minnesota)
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
Presentations by Participants, University of Minnesota, Summer 2007
June 4, 2007 (Audio begins 31 seconds into film.)
June 14, 2007 MRI
June 14, 2007 Dental Tomography
June 14, 2007 Open Problems in Compressed Sensing
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