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A Logarithmic Image Prior for Blind Deconvolution

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Abstract

Blind Deconvolution consists in the estimation of a sharp image and a blur kernel from an observed blurry image. Because the blur model admits several solutions it is necessary to devise an image prior that favors the true blur kernel and sharp image. Many successful image priors enforce the sparsity of the sharp image gradients. Ideally the \(L_0\) “norm” is the best choice for promoting sparsity, but because it is computationally intractable, some methods have used a logarithmic approximation. In this work we also study a logarithmic image prior. We show empirically how well the prior suits the blind deconvolution problem. Our analysis confirms experimentally the hypothesis that a prior should not necessarily model natural image statistics to correctly estimate the blur kernel. Furthermore, we show that a simple Maximum a Posteriori formulation is enough to achieve state of the art results. To minimize such formulation we devise two iterative minimization algorithms that cope with the non-convexity of the logarithmic prior: one obtained via the primal-dual approach and one via majorization-minimization.

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Notes

  1. Although we choose an \(L_2\) norm, any \(L_q\) norm could be used. However, we have found experimentally that for a wide set of values in q this makes little difference in the final performance.

  2. Notice that the 1D problem leads to a third order polynomial equation for which closed-form solutions are known.

  3. A list of all the experiments is available at www.cvg.unibe.ch/dperrone/logtv/.

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Authors and Affiliations

  1. Department of Computer Science and Applied Mathematics, University of Bern, Neubrückstrasse 10, 3012, Bern, Switzerland

    Daniele Perrone & Paolo Favaro

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  1. Daniele Perrone
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  2. Paolo Favaro
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Correspondence to Daniele Perrone.

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Communicated by Thomas Brox.

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Perrone, D., Favaro, P. A Logarithmic Image Prior for Blind Deconvolution. Int J Comput Vis 117, 159–172 (2016). https://doi.org/10.1007/s11263-015-0857-2

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