A variational formulation for frame-based inverse problems
Inverse ProblemsPublished 14 June 2007
Caroline Chaux, Patrick L. Combettes, Jean‐Christophe Pesquet, Valérie R. Wajs
Citations235
SJR quartileQ1
SJR score0.90
SNIP1.22
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TL;DR
A splitting algorithm is presented to solve this problem and its convergence is established in infinite-dimensional spaces under mild conditions on the penalization functions, which need not be differentiable.
Abstract
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 function to be minimized consists of a separable term penalizing each frame coefficient individually, and a smooth term modelling the data formation model as well as other constraints. Sparsity-constrained and Bayesian formulations are examined as special cases. A splitting algorithm is presented to solve this problem and its convergence is established in infinite-dimensional spaces under mild conditions on the penalization functions, which need not be differentiable. Numerical simulations demonstrate applications to frame-based image restoration.
Keywords
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