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  Fast algorithms for total-variation based optimization

Barbero Jimenez, A., & Sra, S.(2010). Fast algorithms for total-variation based optimization (194).

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 Creators:
Barbero Jimenez, A1, Author           
Sra, S1, Author           
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              

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 Abstract: We derive a number of methods to solve efficiently simple optimization problems subject to a totalvariation (TV) regularization, under different norms of the TV operator and both for the case of 1-dimensional and 2-dimensional data. In spite of the non-smooth, non-separable nature of the TV terms considered, we show that a dual formulation with strong structure can be derived. Taking advantage of this structure we develop adaptions of existing algorithms from the optimization literature, resulting in efficient methods for the problem at hand. Experimental results show that for 1-dimensional data the proposed methods achieve convergence within good accuracy levels in practically linear time, both for L1 and L2 norms. For the more challenging 2-dimensional case a performance of order O(N2 log2 N) for N x N inputs is achieved when using the L2 norm. A final section suggests possible extensions and lines of further work.

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 Dates: 2010-08
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: -
 Identifiers: Report Nr.: 194
BibTex Citekey: 6763
 Degree: -

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