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International audience; Multiframe image super-resolution is a technique to obtain a high-resolution image by fusing a sequence of low-resolution ones. This paper deals with a new approach to robust super resolution based on regularization framework. Since registration is an important step that ensures the success of super resolution algorithms, must choose the most suitable method. We suggest a new algorithm specified at low resolution images with small deformations using fourth-order partial differential equations (PDE) regularization in the last step of super resolution. The deformations are not parametric and differs from one image to another. We use a curvature registration specially because image are slightly deformed. Experimental results show the robustness of the proposed method compared to classical super resolution methods.

International audience; The denoising problem is the process of removing the noise from a degraded image. As we know, the Rodin Osher Fatemi (ROF) denoising model based on total variation is a robust approach for solving the ill-posed problem. To avoid the staircasing effects caused by the first order total variation, the second order one is proposed. In this work, we present an orthogonal projection algorithm for solving the ROF model with first and second order total variation. The efficiency and robustness against noise of the proposed model are illustrated and compared with the classical methods through numerical simulations.

International audience; The deconvolution problem in image processing consists of reconstructing an original image from an observed and thus a degraded one. This degradation is often modelized as a linear operator plus an additive noise. The linear operator is called the blurring operator and the goal consists of deblurring the image. Very often, the blurring operator is modelized as a convolution whose kernel (the Point Spread Function) is not directly known in practice. In this paper, we first propose a new model for convolution and we validate it through computer simulations. Basically, we expend the kernel leading to a sequence of real coefficients in link with the moment problem. We particularly emphasize the radial isotropic case.