A splitting algorithm for directional regularization and sparsification

Lars Lau Rakêt; Mads Nielsen

A splitting algorithm for directional regularization and sparsification

Department of Computer Science

Abstract

We present a new split-type algorithm for the minimization of a p-harmonic energy with added data fidelity term. The half-quadratic splitting reduces the original problem to two straightforward problems, that can be minimized efficiently. The minimizers to the two sub-problems can typically be computed pointwise and are easily implemented on massively parallel processors. Furthermore the splitting method allows for the computation of solutions to a large number of more advanced directional regularization problems. In particular we are able to handle robust, non-convex data terms, and to define a 0-harmonic regularization energy where we sparsify directions by means of an L⁰ norm.

Original language	English
Title of host publication	Proceedings of the 21st International Conference on Pattern Recognition (ICPR)
Number of pages	5
Publisher	IEEE
Publication date	2012
Pages	3094-3098
ISBN (Print)	978-4-9906441-0-9
Publication status	Published - 2012
Event	International Conference on Pattern Recognition - Tsukuba International Congress Center, Tsukuba, Japan Duration: 11 Nov 2012 → 15 Nov 2012 Conference number: 21

Conference

Conference	International Conference on Pattern Recognition
Number	21
Location	Tsukuba International Congress Center
Country/Territory	Japan
City	Tsukuba
Period	11/11/2012 → 15/11/2012

Access to Document

http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=6460819&abstractAccess=no&userType=inst

Cite this

Rakêt, LL & Nielsen, M 2012, A splitting algorithm for directional regularization and sparsification. in Proceedings of the 21st International Conference on Pattern Recognition (ICPR). IEEE, pp. 3094-3098, International Conference on Pattern Recognition, Tsukuba, Japan, 11/11/2012. <http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=6460819&abstractAccess=no&userType=inst>

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AB - We present a new split-type algorithm for the minimization of a p-harmonic energy with added data fidelity term. The half-quadratic splitting reduces the original problem to two straightforward problems, that can be minimized efficiently. The minimizers to the two sub-problems can typically be computed pointwise and are easily implemented on massively parallel processors. Furthermore the splitting method allows for the computation of solutions to a large number of more advanced directional regularization problems. In particular we are able to handle robust, non-convex data terms, and to define a 0-harmonic regularization energy where we sparsify directions by means of an L0 norm.

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