Block Distributed Majorize-Minimize Memory Gradient Algorithm and its application to 3D image restoration

TL;DR

This paper introduces a novel block distributed optimization algorithm for large-scale 3D image restoration, demonstrating significant computational efficiency and scalability in handling high-dimensional, non-convex problems.

Contribution

The paper proposes the BD3MG algorithm, a new asynchronous parallel optimization method tailored for large-scale 3D image restoration in distributed memory environments.

Findings

Significant reduction in computational time compared to existing methods

Proven convergence under mild assumptions

High scalability potential demonstrated in experiments

Abstract

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.