Bound alternative direction optimization for image deblurring
Summary: This paper proposes a new method, \textit{bound alternative direction method} (BADM), to address the \(\ell_p (p \in \left(0,1\right))\) minimization problems in image deblurring. The approach is to first obtain a bound unconstrained problem through bounding the \(\ell_p\) regularizer by a novel majorizer and then, based on a variable splitting, to reformulate the bound unconstrained problem into a constrained one, which is then addressed via an augmented Lagrangian method. The proposed algorithm actually combines the reweighted \(\ell_1\) minimization method and the \textit{alternating direction method of multiples} (ADMM) such that it succeeds in extending the application of ADMM to \(\ell_p\) minimization problems. The conducted experimental studies demonstrate the superiority of the proposed algorithm for the synthesis \(\ell_p\) minimization over the state-of-the-art algorithms for the synthesis \(\ell_1\) minimization on image deblurring.
scientific article; zbMATH DE number 7015911
scientific article