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A Framework for Fast Image Deconvolution With Incomplete Observations

By Miguel Simoes, Luis B. Almeida, José M. Bioucas-Dias and Jocelyn Chanussot


This work was supported by the Fundação para a Ciência e a Tecnologi a within the Portuguese Ministry of Science and Higher Education under Project UID/EEA/5008/2013 and Project SFRH/BD/87693/2012.International audienceIn image deconvolution problems, the diagonalization of the underlying operators by means of the fast Fourier transform (FFT) 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. In this paper, we propose a new deconvolution framework for images with incomplete observations that allows us to work with diagonalized convolution operators, and therefore is very fast. We iteratively alternate the estimation of the unknown pixels and of the deconvolved image, using, e.g., an FFT-based deconvolution method. This framework is an efficient, high-quality alternative to existing methods of dealing with the image boundaries, such as edge tapering. It can be used with any fast deconvolution method. We give an example in which a state-of-the-art method that assumes periodic boundary conditions is extended, using this framework, to unknown boundary conditions. Furthermore, we propose a specific implementation of this framework, based on the alternating direction method of multipliers (ADMM). We provide a proof of convergence for the resulting algorithm, which can be seen as a “partial” ADMM, in which not all variables are dualized. We report experimental comparisons with other primal-dual methods, where the proposed one performed at the level of the state of the art. Four different kinds of applications were tested in the experiments: deconvolution, deconvolution with inpainting, superresolution, and demosaicing, all with unknown boundaries

Topics: Deconvolution, Convolution, Computational modeling, Boundary conditions, Estimation, Image resolution, Optimization, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Publisher: 'Institute of Electrical and Electronics Engineers (IEEE)'
Year: 2016
DOI identifier: 10.1109/TIP.2016.2603920
OAI identifier: oai:HAL:hal-01442601v1
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