Block Delayed Majorize-Minimize Subspace Algorithm for Large Scale Image Restoration

Modern image acquisition devices, from microscopes to medical imaging machines, require to deal with increasingly large amount of data. To limit the dependence of an optimization algorithm on the dimension of the problem, distributed algorithms have been developed. In these schemes, at each iteration only a subset of the variables are updated simultaneously allowing to distribute computations on different nodes (or machines). The implementation of distributed algorithms requires to pay careful attention to the cost of communication, which can be reduced and controlled by resorting to an asynchronous implementation. However, asynchronous implementation raises challenging questions, in terms of convergence analysis, as the communication delays may introduce instabilities in the algorithm behavior. In this work, we propose an asynchronous majoration-minimization (MM) algorithm for solving large scale differentiable non-convex optimization problems. The proposed algorithm runs efficient MM memory gradient updates on block of coordinates, in a parallel and possibly asynchronous manner. We establish the convergence of the resulting sequence of iterates under mild assumptions. The performance of the algorithm is illustrated on the restoration of 3D images degraded by depth-variant 3D blur, arising in multiphoton microscopy. Significant computational time reduction, scalability and robustness are observed on synthetic data, when compared to state-of-the-art methods. Experiments on the restoration of real acquisitions of a muscle structure illustrate the qualitative performance of our approach and its practical applicability.