We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulationâ€¦ (More)

The proximity operator of a convex function is a natural exte nsion of the notion of a projection operator onto a convex set. This tool, which plays a central role in the analysis and the numericalâ€¦ (More)

Several methods for solving systems of equilibrium problems in Hilbert spaces â€“ and for finding best approximations thereof â€“ are presented and their convergence properties are established. Theâ€¦ (More)

We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An importantâ€¦ (More)

A block-iterative parallel decomposition method is proposed to solve general quadratic signal recovery problems under convex constraints. The proposed method proceeds by local linearizations ofâ€¦ (More)

A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solvingâ€¦ (More)

Total variation has proven to be a valuable concept in connection with the recovery of images featuring piecewise smooth components. So far, however, it has been used exclusively as an objective toâ€¦ (More)

The classical problem of finding a point in the intersection of countably many closed and convex sets in a Hilbert space is considered. Extrapolated iterations of convex combinations of approximateâ€¦ (More)

The classical notions of essential smoothness, essential strict convexity, and Legendreness for convex functions are extended from Euclidean to Banach spaces. A pertinent duality theory is developedâ€¦ (More)