Optimization methods are at the core of many problems in signal/image processing, computer
vision, and machine learning. For a long time, it has been recognized that looking at the …

… In the unrelaxed case defined by λj ≡ 1, we then retrieve a particular case of the decaying
condition γj ∝ j−1/2−δ with δ ∈]0, 1/2] usually imposed on the stepsize in the convergence …

The proximity operator of a convex function is a natural extension of the notion of a projection
operator onto a convex set. This tool, which plays a central role in the analysis and the …

… frequency tree whose nodes are indexed by (j, m) and whose leaves correspond to the
indices (j, m) such that … = ZICg,o(x)], k E Z, and 7 E Z,6 we then have, for all j E IN and m E (0, …

… approximation pairs relative to two closed convex sets in Hilbert spaces,” J. Approx. Theory,
vol. … Chaux, PL Combettes, J.-C. Pesquet, and VR Wajs, “A variational formulation for frame-…

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…

… To cite this article: Patrick L Combettes and Jean-Christophe Pesquet 2008 Inverse … 23)
that (xn)n∈N converges weakly to a point j(x) for some x ∈ G. Thus, (xn)n∈N = (j −1 (xn))n∈N …

A convex variational framework is proposed for solving inverse problems in Hilbert spaces
with a priori information on the representation of the target solution in a frame. The objective …

We consider the minimization of a function G defined on ${ \mathbb{R} } ^{N}$ , which is the
sum of a (not necessarily convex) differentiable function and a (not necessarily differentiable…

… Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imag. …
Noll, “Adaptive image reconstruction using information measures,” SIAM J. Control Optim., vol. …