(i) {α - Convex Optimization
(i) {α - Convex Optimization (i) {α - Convex Optimization
Stylized applications Stanford seminar 08-24
CS reconstruction (1) H = Fourier, Φ = DWT, Ψ(α) = ‖α‖ l1 , m/n = 17% Projections RealFourier m/n=0.17 SNR=30 dB Original image (P τ ) (Peq)-DR (P )-DR LASSO−Prox Iter=1000 PSNR=22.0734 dB BP−DR (noiseless) Iter=1000 PSNR=23.0226 dB BPDN−DR Iter=1000 PSNR=22.1286 dB Stanford seminar 08-25
- 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: Pros and cons (P σ ) and (P eq ) h
- Page 41 and 42: Inpainting and CS H = Dirac, Φ = C
- Page 43 and 44: Inpainting and CS H = Dirac, Φ = C
- Page 45 and 46: Computation time CS H = Fourier, Φ
- Page 47 and 48: Ongoing and future work Beyond the
CS reconstruction (1)<br />
H = Fourier, Φ = DWT, Ψ(α) = ‖α‖ l1<br />
, m/n = 17%<br />
Projections RealFourier m/n=0.17 SNR=30 dB<br />
Original image<br />
(P τ ) (Peq)-DR (P )-DR<br />
LASSO−Prox Iter=1000 PSNR=22.0734 dB BP−DR (noiseless) Iter=1000 PSNR=23.0226 dB BPDN−DR Iter=1000 PSNR=22.1286 dB<br />
Stanford seminar 08-25
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