http://www.ceremade.dauphine.fr/~peyre/cs-tv/OptimReview.pdf

Best,

Laurent

http://www.ceremade.dauphine.fr/~peyre/upload/cs-tv/OptimReview.pdf

more details about iterative thresholding and Chambolle’s algorithm ! ]]>

Laurent

]]>Surely you have noted that there is new version of SPGL1 (v. 1.6). It’ll be featured on Nuit Blanche on Monday.

Cheers,

Igor.

]]>The initial iteration reads

and the modified one

where should be larger than the operator norm of A for the iterations to converge.

]]>Actually yes (if I am not wrong), the algorithm generalizes to the case where A is not an orthogonal projector. You need to replace the orthogonal projection on the constraints Au=b

u <- u + A^+ ( b – A u )

(where A^+=A* is the pseudo inverse, equal to A* because we are dealing with an orthogonal projector), by a gradient descent step

u than the operator norm of A (same as in the paper of Daubechies et al, and Combettes proved that it can be extended to twice the operator norm).

Then you apply Chambolle’s algorithm with a regularization parameter lambda/tau instead of lambda.

This corresponds to proximal iterations, since Chambolle algorithm is actually computing the proximal operator associated to the TV norm.

Intuitively, as emphasized by Laurent, this corresponds to replacing the soft thresholding by the ROF resolution, which are prox operator of respectively the L1 norm in an ortho-basis and the TV norm.

I am not sure wether the update of lambda to match the L2 constraint is still garantied to work in this case.

]]>Laurent

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