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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 L 1-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)

- M. Monserrat Rincon-Camacho, Jean Baptiste Latre
- 2014

We study the fixed-point equation, given for fixed l > 0 by: where |y| represents the absolute distance of y to 0. Eq. (1.1) induces a duality between 0 and 1, elements of Z 2. We indicate that this duality can be interpreted, in the context of logic, as a paradox. We analyse the theoretical behaviour for l ∈ N * and the experimental results for 0 < l < 1.… (More)

We study the fixed-point equation, given for a fixed l > 0 by: x = h(1 − |2x − 1| l), x, h ∈ R, where |2x − 1| = |x− 1 2 | 1 2 represents the relative distance of x to the mean value of 0 and 1 which are the fixed points of multiplication. The particular cases l = 1 and 2 are classical. This work intends to look at the question: " How much of the specific… (More)

SUMMARY We study the fixed-point equation, given for a fixed ν > 0 by: x = h(1 − |2x − 1| ν), x, h ∈ R, where |2x − 1| = |x− 1 2 | 1 2 represents the relative distance of x to the mean value of 0 and 1. The particular cases ν = 1 and 2 are classical. This work looks at the question: " How much of the specific behaviour for ν = 1 and 2 remains valid when the… (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)

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