We consider the problem of image denoising in the presence of noise whose statistical properties are a combination of two different distributions. We focus on noise distributions that are frequently considered in applications, in particular mixtures of salt & pepper and Gaussian noise, and Gaussian and Poisson noise. We derive a variational image denoising model that features a total variation ...

PURPOSE To accelerate dynamic MR applications using infimal convolution of total generalized variation functionals (ICTGV) as spatio-temporal regularization for image reconstruction. THEORY AND METHODS ICTGV comprises a new image prior tailored to dynamic data that achieves regularization via optimal local balancing between spatial and temporal regularity. Here it is applied for the first tim...

In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal convolution in Monotone Operator Theory. Among other things, we recapture the Minty surjectivity theorem in Hilbert space, and present a new proof of the sum t...

As well known, the Moreau-Rockafellar-Robinson internal point qualification condition is sufficient to ensure that the infimal convolution of the conjugates of two extended-real-valued convex lower semi-continuous functions defined on a locally convex space is exact, and that the sub-differential of the sum of these functions is the sum of their sub-differentials. This note is devoted to provin...

We propose a variational method for artifact-free video decompression that is capable of processing any MPEG-2 encoded movie. The method extracts, from a given MPEG-2 file, a set of admissible image sequences and minimizes an artifact-penalizing spatio-temporal regularization functional over this set, giving an optimal decompressed image sequence. For regularization, we use the infimal convolut...

As well known, the Moreau-Rockafellar-Robinson internal point qualification condition is sufficient to ensure that the infimal convolution of the conjugates of two extended-real-valued convex lower semi-continuous functions defined on a locally convex space is exact, and that the subdifferential of the sum of these functions is the sum of their subdifferentials. This note is devoted to proving ...

A standard finite dimensional nonlinear control system is considered, along with a state constraint set S and a target set Σ. It is proven that open loop S-constrained controllability to Σ implies closed loop Sconstrained controllability to the closed δ-neighborhood of Σ, for any specified δ > 0. When the target set Σ satisfies a small time S-constrained controllability condition, conclusions o...

In this paper, we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution cone convexity, is straightforward. The results are established under verifiable Slater-type condition, with relaxed monotonicity without lower semicontinuity assumptions the play. versatility of our findings illust...

When computing the infimal convolution of a convex function f with the squared norm, the so-called Moreau–Yosida regularization of f is obtained. Among other things, this function has a Lipschitzian gradient. We investigate some more of its properties, relevant for optimization. The most important part of our study concerns second-order differentiability: existence of a secondorder development ...