Publications about Dual smoothing

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• 2 Conference articles

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2 Conference articles

1 - Complex wavelet regularization for solving inverse problems in remote sensing. M. Carlavan and P. Weiss and L. Blanc-Féraud and J. Zerubia. In Proc. IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Cape Town, South Africa, July 2009. Keywords : Deconvolution, Dual smoothing, nesterov scheme, remote sensing, wavelet. @INPROCEEDINGS{IGARSSCarlavan09, author = {Carlavan, M. and Weiss, P. and Blanc-Féraud, L. and Zerubia, J.}, title = {Complex wavelet regularization for solving inverse problems in remote sensing}, year = {2009}, month = {July}, booktitle = {Proc. IEEE International Geoscience and Remote Sensing Symposium (IGARSS)}, address = {Cape Town, South Africa}, url = {http://www.math.univ-toulouse.fr/~weiss/Publis/Conferences/IGARSS09.pdf}, pdf = {http://www.math.univ-toulouse.fr/~weiss/Publis/Conferences/IGARSS09.pdf}, keyword = {Deconvolution, Dual smoothing, nesterov scheme, remote sensing, wavelet} } Abstract : Many problems in remote sensing can be modeled as the minimization of the sum of a data term and a prior term. We propose to use a new complex wavelet based prior and an efficient scheme to solve these problems. We show some results on a problem of image reconstruction with noise, irregular sampling and blur. We also show a comparison between two widely used priors in image processing: sparsity and regularity priors.

2 - Smoothing techniques for convex problems. Applications in image processing. P. Weiss and M. Carlavan and L. Blanc-Féraud and J. Zerubia. In Proc. SAMPTA (international conference on Sampling Theory and Applications), Marseille, France, May 2009. Keywords : nesterov scheme, convergence rate, Dual smoothing. @INPROCEEDINGS{PWEISS_SAMPTA09, author = {Weiss, P. and Carlavan, M. and Blanc-Féraud, L. and Zerubia, J.}, title = {Smoothing techniques for convex problems. Applications in image processing}, year = {2009}, month = {May}, booktitle = {Proc. SAMPTA (international conference on Sampling Theory and Applications)}, address = {Marseille, France}, url = {http://www.math.univ-toulouse.fr/~weiss/Publis/Conferences/Eusipco09.pdf}, pdf = {http://www.math.univ-toulouse.fr/~weiss/Publis/Conferences/Sampta09.pdf}, keyword = {nesterov scheme, convergence rate, Dual smoothing} } Abstract : In this paper, we present two algorithms to solve some inverse problems coming from the field of image processing. The problems we study are convex and can be expressed simply as sums of lp-norms of affine transforms of the image. We propose 2 different techniques. They are - to the best of our knowledge - new in the domain of image processing and one of them is new in the domain of mathematical programming. Both methods converge to the set of minimizers. Additionally, we show that they converge at least as O(1/N) (where N is the iteration counter) which is in some sense an ``optimal'' rate of convergence. Finally, we compare these approaches to some others on a toy problem of image super-resolution with impulse noise.

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