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Reconstruction d’image : régularisation avec prise en compte des discontinuités. : Thèse de doctorat

Abstract : This thesis deals with regularized image reconstruction. We seek images consisting of smooth regions separated by sharp edges, or discontinuities. This is called edge-preserving regularization. The reconstructed image is found by minimizing an objective function, which we call the criterion. Firstly, we propose sufficient conditions for the design of an edge-preserving objective function. Then, we show that, under these conditions, it is possible to transform the criterion by introducing an auxiliary variable, which interacts with the main variable either in an additive or in a multiplicative way. The role of the auxiliary variable is twofold: it marks discontinuities and facilitates the optimization of the criterion. The augmented objective function is quadratic with respect to the main variable when the auxiliary variable is fixed, and convex with respect to the auxiliary variable when the main variable is fixed. Moreover, in the last case, we give the expression of the optimal value of the auxiliary variable. Secondly, we exploit the properties of such a half-quadratic regularization to design new reconstruction algorithms. Our optimization strategy is based on alternated minimizations with respect to the auxiliary and the main variable. This leads to two progressive discontinuity introduction algorithms: ARTUR and LEGEND. We propose a theoretical and practical study of these algorithms. We apply them to tomographic reconstruction. ARTUR and LEGEND offer a good trade-off between computation time and image quality. However, huge linear systems have to be solved. We propose, as a perspective, a means of reducing the volume of information involved for reconstruction. Thereby, greater image dimensions can be envisionned.
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Contributor : Pierre Charbonnier Connect in order to contact the contributor
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  • HAL Id : tel-01183977, version 1



Pierre Charbonnier. Reconstruction d’image : régularisation avec prise en compte des discontinuités. : Thèse de doctorat. Traitement du signal et de l'image [eess.SP]. Université de Nice - Sophia Antipolis, 1994. Français. ⟨NNT : 1994NICE4763⟩. ⟨tel-01183977⟩



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