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- | ==Compressive Sampling and Frontiers in Signal Processing==
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- | === Compressive Sampling, Compressed Sensing - Emmanuel Candes (California Institute of Technology) University of Minnesota, Summer 2007 ===
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- | ([http://www.real.com requires RealPlayer to watch])
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- | [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'''
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- | : Example of sparse signals in genomics (<math>\approx</math> 8 minutes into film).
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- | : Example of sparse signals in genetics (<math>\approx</math> 11 min in).
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- | : Example of sparse signals in audio/image processing (<math>\approx</math> 18 min in).
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- | : Transform-domain image coding (<math>\approx</math> 27 min in).
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- | : Primary visual cortex (<math>\approx</math> 53 min in).
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- | : Efficient estimation (<math>\approx</math> 57 min in).
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- | : Computational harmonic analysis (<math>\approx</math> 1:22 in).
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- | [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.)
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- | : Norms.
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- | : Early work by pioneers (<math>\approx</math> 16 minutes into film).
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- | : Deconvolution (<math>\approx</math> 30 minutes into film).
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- | : Lasso, Basis Pursuit (<math>\approx</math> 38 minutes in).
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- | : Wavelets, Curvelets, Ridgelets, sinusoids (<math>\approx</math> 55 minutes in).
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- | : Overcomplete Dictionary (<math>\approx</math> 57 minutes in).
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- | : Basis Pursuit (<math>\approx</math> 1:03 hours in).
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- | : Feature separation (<math>\approx</math> 1:12 hours in).
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- | : ''Barbara'', Jean-Luc Stark (<math>\approx</math> 1:15 hours in).
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- | : Magnetic Resonance Imaging (MRI) (<math>\approx</math> 1:16 hours in).
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- | : Sample rate (<math>\approx</math> 1:36 hours in).
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- | [http://www.ima.umn.edu/recordings/New_Directions_Short_Course/ND6.4-15.07/candes6-6-07.ram June 6 2007]
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- | '''Sparsity and Incoherence''' (If you only watch one Candes video, this is it.)
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- | : Recovery of Dirac comb, derivation of minimum sampling rate (<math>\approx</math> 11 minutes into film).
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- | : 4:1 <i>sample to sparsity</i> rule (<math>\approx</math> 21 minutes into film).
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- | : [[Candes.m|Candes' Matlab code]] (<math>\approx</math> 25 minutes in).
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- | : Fundamental premises of Compressed Sensing: <i>sparsity</i> and <i>incoherence</i> (<math>\approx</math> 29 minutes in).
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- | [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'''
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- | [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'''
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- | [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.)
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- | [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'''
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- | : Matlab (<math>\approx</math> 1:15).
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- | : MRI phantom with noise using Dantzig (<math>\approx</math> 1:28).
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- | : Imaging fuel cells (<math>\approx</math> 1:31).
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- | : Subsampling (<math>\approx</math> 1:36).
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- | [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'''
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- | : error correction (since the beginning).
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- | : Matlab decode (<math>\approx</math> 20 min in).
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- | : second error corruption model: gross error + quantization error (<math>\approx</math> 29 min in).
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- | : Connection with the Sparse Recovery Problem (<math>\approx</math> 57 min in).
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- | : Reed-Solomon code (<math>\approx</math> 1:08 min in).
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- | : Matlab for Reed-Solomon code (<math>\approx</math> 1:26 min in).
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- | [http://www.ima.umn.edu/recordings/New_Directions_Short_Course/ND6.4-15.07/candes6-14-07.ram June 14 2007] '''Modern Convex Optimization'''
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- | : Unconstrained Minimization (<math>\approx</math> 11 min in).
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- | : Matlab example for Gradient Descent with exact Line Search (<math>\approx</math> 19 min in).
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- | : Exact line search ''vs.'' Backtracking line search (<math>\approx</math> 22 min in).
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- | : Newton Step (<math>\approx</math> 26 min in).
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- | : Self Concordance (<math>\approx</math> 35 min in).
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- | : Equality Constrained Minimization (<math>\approx</math> 43 min in).
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- | : Barrier function (<math>\approx</math> 47 min in).
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- | : Central path (<math>\approx</math> 53 min in).
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- | : Complexity analysis (<math>\approx</math> 1:14).
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- | : Matlab for log-barrier (<math>\approx</math> 1:25).
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- | : Primal-dual interior point methods (<math>\approx</math> 1:29).
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- | [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'''
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- | : Beyond L1 minimization (<math>\approx</math> 3 min in).
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- | : Reweighted TV for MRI phantom: recover using m=1.2S (S is number of non zero gradient terms) (<math>\approx</math> 14 min in).
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- | : Overcomplete representations (<math>\approx</math> 19 min in).
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- | : Geometric separation: Cartoon + Texture (<math>\approx</math> 22 min in).
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- | : L1 synthesis ''vs''. analysis for CS (<math>\approx</math> 28 min in).
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- | : Pulse reconstruction using L1 synthesis, L1 analysis and reweighted L1 analysis(<math>\approx</math> 36 min).
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- | : ADC: nonuniform sampler ''vs''. random pre-integrator (<math>\approx</math> 48 min).
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- | : Universal encoder (<math>\approx</math> 1:16 min).
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- | [http://www.ima.umn.edu/recordings/New_Directions_Short_Course/ND6.4-15.07/discussion6-6-07.ram June 6, 2007] '''Discussion Session'''
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| == Introduction to Magnetic Resonance Imaging (MRI) == | | == Introduction to Magnetic Resonance Imaging (MRI) == |