Fast image deconvolution using hyper-laplacian priors

Dilip Krishnan, Rob Fergus

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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. These distributions are well modeled by a hyper-Laplacian (p(x) ∞ e -k|x|α), typically with 0.5 ≤ α ≤ 0.8. 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.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference
Pages1033-1041
Number of pages9
StatePublished - 2009
Event23rd Annual Conference on Neural Information Processing Systems, NIPS 2009 - Vancouver, BC, Canada
Duration: Dec 7 2009Dec 10 2009

Other

Other23rd Annual Conference on Neural Information Processing Systems, NIPS 2009
CountryCanada
CityVancouver, BC
Period12/7/0912/10/09

Fingerprint

Deconvolution
Pixels
Table lookup
Image processing
Polynomials

ASJC Scopus subject areas

  • Information Systems

Cite this

Krishnan, D., & Fergus, R. (2009). Fast image deconvolution using hyper-laplacian priors. In Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference (pp. 1033-1041)

Fast image deconvolution using hyper-laplacian priors. / Krishnan, Dilip; Fergus, Rob.

Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference. 2009. p. 1033-1041.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Krishnan, D & Fergus, R 2009, Fast image deconvolution using hyper-laplacian priors. in Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference. pp. 1033-1041, 23rd Annual Conference on Neural Information Processing Systems, NIPS 2009, Vancouver, BC, Canada, 12/7/09.
Krishnan D, Fergus R. Fast image deconvolution using hyper-laplacian priors. In Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference. 2009. p. 1033-1041
Krishnan, Dilip ; Fergus, Rob. / Fast image deconvolution using hyper-laplacian priors. Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference. 2009. pp. 1033-1041
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