(i) {α - Convex Optimization
(i) {α - Convex Optimization (i) {α - Convex Optimization
Take-away messages A general framework of optimization problems in CS: maximal monotone operator splitting. Good and fast solvers for large-scale problems: Iterative-thresholding. Grounded theoretical results. A wide variety of applications beyond CS. Stanford seminar 08- 30
Ongoing and future work Beyond the linear case with AWGN [FXD-F.-JLS 07-08]. More comparison to other algorithms. Work harder for algorithms faster than linear. Other problems, e.g. Dantzig selector. Other applications. Stanford seminar 08-31
- 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 and 44: Inpainting and CS H = Dirac, Φ = C
- Page 45: Computation time CS H = Fourier, Φ
Ongoing and future work<br />
Beyond the linear case with AWGN [FXD-F.-JLS 07-08].<br />
More comparison to other algorithms.<br />
Work harder for algorithms faster than linear.<br />
Other problems, e.g. Dantzig selector.<br />
Other applications.<br />
Stanford seminar 08-31
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