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Sparsity: algorithms, approximations, and analysis
Published on Jan 25, 20129221 Views
The last 15 years we have seen an explosion in the role of sparsity in mathematical signal and image processing, signal and image acquisition and reconstruction algorithms, and myriad applications.
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Chapter list
Sparsity: algorithms, approximations, and analysis00:00
Basic image/signal/data compression: transform coding00:03
Approximate signals sparsely02:06
Redundancy - 102:44
Redundancy - 203:55
Mathematics awareness week03:58
Dictionary06:12
Matrix representation07:13
Examples: Fourier - Dirac08:37
Sparse Problems09:13
NP-hardness12:21
Exact Cover by 3-sets: X3C13:17
Bad news, Good news - 116:46
Bad news, Good news - 218:02
Hardness depends on instance19:27
Sparse algorithms: exploit geometry - 121:16
Sparse algorithms: exploit geometry - 223:07
Coherence24:36
Large, incoherent dictionaries25:48
Greedy algorithms28:23
Orthogonal Matching Pursuit OMP29:33
Many greedy algorithms with similar outline31:06
Convergence of OMP - 132:00
Convergence of OMP - 233:06
Exact Recovery Condition and coherence33:12
Sparse representation with OMP35:07
SPARSE35:56
Alternative algorithmic approach - 138:07
Alternative algorithmic approach - 238:28
Alternative algorithmic approach - 338:49
Convex relaxation: algorithmic formulation39:09
Exact Recovery Condition - 140:20
Exact Recovery Condition - 240:21
Alternate optimization formulations40:38
Sparse approximation: Optimization vs. Greedy40:54
Connection between ...41:33
Sparsity in statistical learning41:33
Algorithms in statistical learning41:34
Connection between ...42:10
Interchange roles42:24
Problem statement42:43
Comparison with Sparse Approximation42:43
Analogy: root - fi nding43:04
Parameters43:29
Applications43:34
Two approaches43:40
Summary43:42