(i) {α - Convex Optimization
(i) {α - Convex Optimization (i) {α - Convex Optimization
Super-resolution Stanford seminar 08-28
Computation time CS H = Fourier, Φ = Dirac m/n !=Dirac, = H=RST, 20%, m/n=25%, sparsity sparsity=5% = 5% CS H = Hadamard, Φ = Dirac m/n = 20%, sparsity = 5% !=Dirac, H=Hadamard, m/n=25%, sparsity=5% 10 4 log 2 (m) 10 3 BP−DR LARS LP−Interior Point StOMP 10 1 10 2 log 2 (m) BP−DR LARS LP−Interior Point StOMP Computation time (s) 10 0 Computation time (s) 10 2 10 1 10 0 10 −1 10 −1 6 7 8 9 10 11 12 6 7 8 9 10 11 12 13 14 Stanford seminar 08-29
- Page 1 and 2: Optimization problems in compressed
- Page 3 and 4: Compressed/ive Sensing Stanford sem
- Page 5 and 6: Compressed/ive Sensing Common wisdo
- Page 7 and 8: Compressed/ive Sensing Common wisdo
- Page 9 and 10: Compressed/ive Sensing (cont’d) C
- Page 11 and 12: Compressed/ive Sensing (cont’d) C
- Page 13 and 14: Convex analysis and operator splitt
- Page 15 and 16: Class of problems in CS (cont’d)
- Page 17 and 18: Class of problems in CS (cont’d)
- Page 19 and 20: Characterization Theorem 1 (i) Exis
- Page 21 and 22: Operator splitting schemes Idea: re
- Page 23 and 24: Proximity operators Some properties
- Page 25 and 26: Example of proximity operator Stanf
- Page 27 and 28: Compressed sensing optimization pro
- Page 29 and 30: Characterizing Problem (P τ ) Stan
- Page 31 and 32: Proximity operators of Ψ Conclusio
- Page 33 and 34: DR to solve Problem (P σ ) Theorem
- Page 35 and 36: DR to solve Problem (Peq) Theorem 1
- Page 37 and 38: Pros and cons (P σ ) and (P eq ) h
- Page 39 and 40: CS reconstruction (1) H = Fourier,
- Page 41 and 42: Inpainting and CS H = Dirac, Φ = C
- Page 43: Inpainting and CS H = Dirac, Φ = C
- Page 47 and 48: Ongoing and future work Beyond the
Computation time<br />
CS H = Fourier, Φ = Dirac<br />
m/n !=Dirac, = H=RST, 20%, m/n=25%, sparsity sparsity=5% = 5%<br />
CS H = Hadamard, Φ = Dirac<br />
m/n = 20%, sparsity = 5%<br />
!=Dirac, H=Hadamard, m/n=25%, sparsity=5%<br />
10<br />
4<br />
log 2 (m)<br />
10 3<br />
BP−DR<br />
LARS<br />
LP−Interior Point<br />
StOMP<br />
10 1<br />
10 2 log 2<br />
(m)<br />
BP−DR<br />
LARS<br />
LP−Interior Point<br />
StOMP<br />
Computation time (s)<br />
10 0<br />
Computation time (s)<br />
10 2<br />
10 1<br />
10 0<br />
10 −1<br />
10 −1<br />
6 7 8 9 10 11 12<br />
6 7 8 9 10 11 12 13 14<br />
Stanford seminar 08-29
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