M. Monserrat Rincon-Camacho

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Multi-scale total variation models for image restoration are introduced. The models utilize a spatially dependent regularization parameter in order to enhance image regions containing details while still sufficiently smoothing homogeneous features. The fully automated adjustment strategy of the regularization parameter is based on local variance estimators.(More)
A total variation (TV) model with an L1-fidelity term and a spatially adapted regularization parameter is presented in order to reconstruct images contaminated by impulse noise. This model intends to preserve small details while homogeneous features still remain smooth. The regularization parameter is locally adapted according to a local expected absolute(More)
We propose to use an observation-thinning method for the efficient numerical solution of large-scale incremental fourdimensional (4D-Var) data assimilation problems. This decomposition is based on exploiting an adaptive hierarchy of the observations. Starting with a low-cardinality set and the solution of its corresponding optimization problem, observations(More)
A general multi-scale vectorial total variation model with spatially adapted regularization parameter for color image restoration is introduced in this paper. This total variation model contains an L τ -data fidelity for any τ∈[1,2]. The use of a spatial dependent regularization parameter improves the reconstruction of features in the image as well as an(More)
The paper presents the information processing that can be performed by a general hermitian matrix when two of its distinct eigenvalues are coupled, such as λ < λ′. Setting a = λ+λ ′ 2 and e = λ′−λ 2 > 0, the new spectral information that is provided by coupling is expressed in terms of the ratios e |a| (if λλ ′ > 0) or |a| e (if λλ ′ < 0) and of the product(More)
We propose to use a decomposition of large-scale incremental four dimensional (4D-Var) data assimilation problems in order to make their numerical solution more efficient. This decomposition is based on exploiting an adaptive hierarchy of the observations. Starting with a low-cardinality set and the solution of its corresponding optimization problem,(More)
Over the last century, linear algebra theory and matrix computations became irreplaceable, not only for high-tech industries, but also in every corner of our computerised society. Most of the time, any given problem (linear or not) is reduced to finding the solution of a linear system. Thus, the possibility of solving large linear systems in a reasonable(More)
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