\nMoncef Hidane completed a post-doctoral 2013-2014 under the Labex CPU. He previously completed a doctoral thesis at the laboratory GREYC in Caen, the decomposition problem of graphs of signals. He is currently research professor at INSA Loire Valley.<\/p>\n
The topic of the post-doc concerns the 3D image reconstruction from a low-resolution full acquisition and partial acquisition in very high resolution. So this is a super-resolution inverse problem.<\/p>\n
The model adopted for the low resolution acquisition is that of a convolution operator followed by a spatial or spectral sub-sampling. Initially, the impulse response of the sensor is assumed to be known. An additive white noise is integrated into the model.<\/p>\n
The model adopted for the high resolution acquisition is one of an occlusion in which the support is known. An additive white noise is also integrated into the model.<\/p>\n
The first track is followed by that of a regularization using an a priori isotropically total variation. Two versions are contemplated: one with inequality constraints, on the other hand with equality constraints. In this context, an important part of the work concerns minimization criteria in each case. Due to the non-differentiability of the measure total variance algorithms from the non-smooth convex optimization are considered. The goal is to have fast and robust algorithms for computing solutions.<\/p>\n
The second track is followed by an adjustment using a non-local operator. The idea is to take advantage of both the volume low resolution and high resolution images to construct a priori regularization type nonlocal total variation.<\/p>\n
The following figure illustrates the problem and the results obtained with the two previous approaches.
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![\"(a)](\"http:\/\/www.math.u-bordeaux1.fr\/~cdeledal\/image\/wp-content\/uploads\/2014\/03\/moncef_hidane_illustration.png\")
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