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Total variation image deblurring with space-varying kernel

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Abstract

Image deblurring techniques based on convex optimization formulations, such as total-variation deblurring, often use specialized first-order methods for large-scale nondifferentiable optimization. A key property exploited in these methods is spatial invariance of the blurring operator, which makes it possible to use the fast Fourier transform (FFT) when solving linear equations involving the operator. In this paper we extend this approach to two popular models for space-varying blurring operators, the Nagy–O’Leary model and the efficient filter flow model. We show how splitting methods derived from the Douglas–Rachford algorithm can be implemented with a low complexity per iteration, dominated by a small number of FFTs.

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Acknowledgements

Research supported in part by National Science Foundation Grants DMS-1115963 and ECCS 1509789.

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Authors and Affiliations

  1. Department of Mathematics, University of California Los Angeles, Los Angeles, CA, USA

    Daniel O’Connor

  2. Electrical Engineering Department, University of California Los Angeles, Los Angeles, CA, USA

    Lieven Vandenberghe

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  1. Daniel O’Connor
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  2. Lieven Vandenberghe
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Correspondence to Daniel O’Connor.

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O’Connor, D., Vandenberghe, L. Total variation image deblurring with space-varying kernel. Comput Optim Appl 67, 521–541 (2017). https://doi.org/10.1007/s10589-017-9901-1

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