(i) {Î± - Convex Optimization

More documents

Recommendations

Info

FB to solve Problem (P τ ) Theorem 1 Let {µ t ,t ∈ N} be a sequence such that 0 < inf t µ t ≤ sup t µ t < 2/ ‖HΦ‖ 2 , let {β t ,t∈ N} be a sequence in (0, 1], and let {a t ,t∈ N} and {b t ,t∈ N} be sequences in H such that ∑ t ‖a t‖ < +∞ and ∑ t ‖b t‖ < +∞. Fix α 0 , and define the sequence of iterates: α t+1 = α t + β t ( proj BΨ,τ ( α t + µ t ( Φ ∗ H ∗ ( y − HΦα t)) − b t ) + at − α (t)) where proj BΨ,τ is the projector onto the Ψ-ball of radius τ. (i) {α (t) ,t≥ 0} converges weakly to a minimizer of (P λ ). (ii) For Ψ(α) =‖α‖ l1 , there exists a subsequence {α (t) ,t ≥ 0} that converges strongly to a minimizer of (P λ ). (iii) The projection operator proj BΨ,τ is ⎧ ⎨α if Ψ (α) ≤ τ, proj BΨ,τ (α) = ⎩prox κΨ α otherwise. , where κ (depending on α and τ) is chosen such that Ψ (prox κΨ (α)) = τ. Stanford seminar 08-16
Proximity operators of Ψ Conclusion Thresholding/shrinkage operator: e.g. soft-thresholding for the Computational cost: O(L) for L coefficients. norm. Stanford seminar 08-17
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: Characterizing Problem (P τ ) Stan
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 and 46: Computation time CS H = Fourier, Φ
Page 47 and 48: Ongoing and future work Beyond the

(i) {Î± - Convex Optimization

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?