Share Email Print

Proceedings Paper

Preconditioned conjugate gradient without linesearch: a comparison with the half-quadratic approach for edge-preserving image restoration
Author(s): Christian Labat; Jérôme Idier
Format Member Price Non-Member Price
PDF $14.40 $18.00
cover GOOD NEWS! Your organization subscribes to the SPIE Digital Library. You may be able to download this paper for free. Check Access

Paper Abstract

Our contribution deals with image restoration. The adopted approach consists in minimizing a penalized least squares (PLS) criterion. Here, we are interested in the search of efficient algorithms to carry out such a task. The minimization of PLS criteria can be addressed using a half-quadratic approach (HQ). However, the nontrivial inversion of a linear system is needed at each iteration. In practice, it is often proposed to approximate this inversion using a truncated preconditioned conjugate gradient (PCG) method. However, we point out that theoretical convergence is not proved for such approximate HQ algorithms, referred here as HQ+PCG. In the proposed contribution, we rely on a different scheme, also based on PCG and HQ ingredients and referred as PCG+HQ1D. General linesearch methods ensuring convergence of PCG type algorithms are difficult to code and to tune. Therefore, we propose to replace the linesearch step by a truncated scalar HQ algorithm. Convergence is established for any finite number of HQ1D sub-iterations. Compared to the HQ+PCG approach, we show that our scheme is preferable on both the theoretical and practical grounds.

Paper Details

Date Published: 2 February 2006
PDF: 10 pages
Proc. SPIE 6065, Computational Imaging IV, 60650I (2 February 2006); doi: 10.1117/12.641663
Show Author Affiliations
Christian Labat, IRCCyN-CNRS, UMR 6597, ECN (France)
Jérôme Idier, IRCCyN-CNRS, UMR 6597, ECN (France)

Published in SPIE Proceedings Vol. 6065:
Computational Imaging IV
Charles A. Bouman; Eric L. Miller; Ilya Pollak, Editor(s)

© SPIE. Terms of Use
Back to Top