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.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.