Valérie R. Wajs

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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 formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently(More)
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 of a smooth term modeling the data formation model as well as other(More)
We consider the problem of deconvolving an image with a priori information on its representation in a frame. Our variational approach consists of minimizing the sum of a residual energy and a separable term penalizing each frame coefficient individually. This penalization term may model various properties, in particular sparsity. A general iterative method(More)
Regularization techniques have been in use in signal recovery for over four decades. In this paper, we propose a new synthetic approach to the study of regularization methods in image denoising problems based on Moreau's proximity operators. We exploit the remarkable properties enjoyed by these operators to establish in a systematic fashion a variety of(More)
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