1,721,039 research outputs found
Introduction to Inverse Problems in Imaging
No full textThe book provides an introduction to the theory of inverse problems and their application to imagin
A simple method for the reduction of boundary effects in the Richardson-Lucy approach to image deconvolution
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Wide-field imaging at mid-infrared wavelengths: reconstruction of chopped and nodded data
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Analysis of an approximate model for Poisson data reconstruction and a related discrepancy principle
No full textIn this paper, we investigate an approximate model for Poisson data reconstruction inspired by a discrepancy principle for the selection of the regularization parameter, recently proposed by Bardsley and Goldes. The model can be obtained by approximating the generalized Kullback-Leibler (KL) divergence in terms of a weighted least-squares function, with weights depending on the object to be reconstructed. We show that it is possible to develop a complete theory, based on this approximation, including results of existence and uniqueness of regularized solutions and simple gradient-based reconstruction algorithms for their computation. Moreover, in this context, the criterion of Bardsley and Goldes is a natural one and it is possible to prove that, in several important cases, it provides a unique value of the regularization parameter. We describe a few numerical tests for comparing the approximate approach with the exact one based on the generalized KL divergence. In the case of a moderate or large number of photons, they provide essentially the same results and therefore the approximate model can be considered as a possible alternative to the exact one
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