A Generalized Forward-Backward Splitting

It solves, over any real Hilbert space ℋ, monotone inclusion problems of the form
find x ∈ zer ( B + i=1n Ai ) := { x ∈ ℋ | 0 ∈ Bx + i=1n Aix } , where:

In particular, it enables minimization over ℋ of convex problems of the form
minx∈ℋ F(x) := f(x) + i=1n gi(x) , where:

Published in SIAM Journal of Imaging Sciences: Permalink - Author's manuscript - BibTeX entry.
Erratum: on top of page 10 (1208 in the volume), in the application of the Sherman–Morrison–Woodbury formula in equation (3.3), a factor γ has been forgotten.
Download MATLAB codes and materials used in this paper.
Some supplementary results: deblurring task - inpainting task - composite task - composite task with TV regularization.

A more complete version of this work can be found in chapters III and IV of my Ph.D. thesis.

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