Modern 3D image recovery problems require powerful optimization frameworks to handle high dimensionality while providing reliable numerical solutions in a reasonable time. In this perspective, asynchronous parallel optimization algorithms have received an increasing attention by overcoming memory limitation issues and communication bottlenecks. In this work, we propose a block distributed Majorize-Minorize Memory Gradient (BD3MG) optimization algorithm for solving large scale non-convex differentiable optimization problems. Assuming a distributed memory environment, the algorithm casts the efficient 3MG scheme into smaller dimension subproblems where blocks of variables are addressed in an asynchronous manner. Convergence of the sequence built by the proposed BD3MG method is established under mild assumptions. Application to the restoration of 3D images degraded by a depth-variant blur shows that our method yields significant computational time reduction compared to several synchronous and asynchronous competitors, while exhibiting great scalability potential.
Variable Metric Forward-Backward Algorithm for Composite Minimization Problems
We present a forward-backward-based algorithm to minimize a sum of a differentiable function and a nonsmooth function, both being possibly nonconvex. The main contribution of this work is to consider the challenging case where the nonsmooth function corresponds to a sum of non- convex functions , resulting from composition between a strictly increasing, concave, differentiable function and a convex nonsmooth function. The proposed variable metric Composite Function Forward-Backward algorithm (C2FB) circumvents the explicit, and often challenging, computation of the proximity operator of the co…
Variable Bregman Majorization-Minimization algorithms for nonconvex nonsmooth optimization, with application to Poisson imaging
Université Paris-Saclay, CentraleSupélec, Inria, Centre pour la Vision Numérique（巴黎萨克雷大学、中央苏佩莱克学院、法国国家信息与自动化研究所、数字视觉中心）；Université Paris-Saclay, Laboratoire BioMaps, CEA（巴黎萨克雷大学、BioMaps实验室、法国原子能和替代能源委员会）
An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems
Instituto de Telecomunicações（电信研究所）；Department of Electrical and Computer Engineering, Instituto Superior Técnico（技术高等学院电气与计算机工程系）；Instituto Superior Técnico（技术高等学院）
