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Fast Image Deconvolution using Hyper-Laplacian Priors
Dilip Krishnan · Rob Fergus

Wed Dec 09 03:24 PM -- 03:25 PM (PST) @ None

The heavy-tailed distribution of gradients in natural scenes have proven effective priors for a range of problems such as denoising, deblurring and super-resolution. However, the use of sparse distributions makes the problem non-convex and impractically slow to solve for multi-megapixel images. In this paper we describe a deconvolution approach that is several orders of magnitude faster than existing techniques that use hyper-Laplacian priors. We adopt an alternating minimization scheme where one of the two phases is a non-convex problem that is separable over pixels. This per-pixel sub-problem may be solved with a lookup table (LUT). Alternatively, for two specific values of α, 1/2 and 2/3 an analytic solution can be found, by finding the roots of a cubic and quartic polynomial, respectively. Our approach (using either LUTs or analytic formulae) is able to deconvolve a 1 megapixel image in less than ∼3 seconds, achieving comparable quality to existing methods such as iteratively reweighted least squares (IRLS) that take ∼20 minutes. Furthermore, our method is quite general and can easily be extended to related image processing problems, beyond the deconvolution application demonstrated.

Author Information

Dilip Krishnan (NYU)
Rob Fergus (DeepMind / NYU)

Rob Fergus is an Associate Professor of Computer Science at the Courant Institute of Mathematical Sciences, New York University. He received a Masters in Electrical Engineering with Prof. Pietro Perona at Caltech, before completing a PhD with Prof. Andrew Zisserman at the University of Oxford in 2005. Before coming to NYU, he spent two years as a post-doc in the Computer Science and Artificial Intelligence Lab (CSAIL) at MIT, working with Prof. William Freeman. He has received several awards including a CVPR best paper prize, a Sloan Fellowship & NSF Career award and the IEEE Longuet-Higgins prize.

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