Abstract / truncated to 115 words (read the full abstract)

This work is concerned with two image-processing problems, image deconvolution with incomplete observations and data fusion of spectral images, and with some of the algorithms that are used to solve these and related problems. In image-deconvolution problems, the diagonalization of the blurring operator by means of the discrete Fourier transform usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard deconvolution techniques normally involve non-diagonalizable operators, resulting in rather slow methods, or, otherwise, use inexact convolution models, resulting in the occurrence of artifacts in the enhanced images. We propose a new deconvolution framework for images with incomplete observations that allows one to work with diagonalizable convolution operators, ... toggle 14 keywords

deconvolution – incomplete observations – hyperspectral imaging – superresolution – data fusion – pansharpening – convex nonsmooth optimization – primal-dual optimization – alternating-direction method of multipliers (admm) – semismooth newton method – forward-backward method – monotone inclusion – averaged operator – variable metric.

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