Caroline Chaux

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We propose a two-dimensional generalization to the M-band case of the dual-tree decomposition structure (initially proposed by Kingsbury and further investigated by Selesnick) based on a Hilbert pair of wavelets. We particularly address: 1) the construction of the dual basis and 2) the resulting directional analysis. We also revisit the necessary(More)
The use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions. However, the observed images are often corrupted by an additive Gaussian noise. In this paper, we are interested in multichannel image denoising based on a multiscale representation of the images. A(More)
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, namely how to find a good regularizer. While total variation introduces staircase effects, wavelet-domain regularization brings other artefacts, e.g., ringing. However, a(More)
Recently, there has been a growing interest for wavelet frames corresponding to the union of an orthonormal wavelet basis and its dual Hilbert transformed wavelet basis. However, most of the existing works specifically address the dyadic case. In this paper, we consider orthonormal M-band wavelet decompositions, since we are motivated by their adavantages(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)
In this paper, we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white Gaussian noise. The originality of the proposed approach is twofold. First, we formulate the restoration problem as a nonlinear estimation problem leading to the minimization of a criterion derived from Stein's unbiased quadratic(More)
The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex constraint set of the sum of two convex functions f and g, where f may be non-smooth and g is differentiable with a(More)
This paper deals with noise parameter estimation. We assume observations corrupted by noise modelled as a sum of two random processes: one Poisson and the other a (nonzero mean) Gaussian. Such problems arise in various applications, e.g. in astronomy and confocal microscopy imaging. To estimate noise parameters, we propose an iterative algorithm based on an(More)
In this paper, we present a new fully automatic approach for noise parameter estimation in the context of fluorescence imaging systems. In particular, we address the problem of Poisson-Gaussian noise modeling in the nonstationary case. In microscopy practice, the nonstationarity is due to the photobleaching effect. The proposed method consists of an(More)
We propose a 2D generalization to the M -band case of the dualtree structure (initially proposed by N. Kingsbury and further investigated by I. Selesnick) based on a Hilbert pair of wavelets. We particularly address the construction of the dual basis and the resulting directional analysis. We revisit the necessary pre-processing stage in the M -band case.(More)