Algorithmes d'optimisation de critères pénalisés pour la restauration d'images. Application à la déconvolution de trains d'impulsions en imagerie ultrasonore.

摘要

The solution to many image restoration and reconstruction problems is often defined as the minimizer of a penalized criterion that accounts simultaneously for the data and the prior. This thesis deals more specifically with the minimization of edge-preserving penalized criteria. We focus on algorithms for large-scale problems. The minimization of penalized criteria can be addressed using a half-quadratic approach (HQ). Converging HQ algorithms have been proposed. However, their numerical cost is generally too high for large-scale problems. An alternative is to implement inexact HQ algorithms. Nonlinear conjugate gradient algorithms can also be considered using scalar HQ algorithms for the line search (NLCG+HQ1D). Some issues on the convergence of the aforementioned algorithms remained open until now. In this thesis we :- Prove the convergence of inexact HQ algorithms and NLCG+HQ1D.- Point out strong links between HQ algorithms and NLCG+HQ1D.- Experimentally show that inexact HQ algorithms and NLCG+HQ1D perform better than exact HQ algorithms, for an image deconvolution test problem.- Apply the penalized approach to a deconvolution problem in the field of ultrasonic imaging for nondestructive testing.