FORWARD BACKWARD SPLITTING UNROLLING STRATEGIES FOR INVERSE PROBLEMS RESOLUTION

Abstract

An inverse problem is the process of computing a causal object that induced some measured observations. It can be solved by formulating it as an optimization problem, the solution of which is an estimation of the object of interest. Optimization algorithm performance depends largely on hyper-parameters (e.g. regularization parameters, gradient descent step...) thus hyper-parameter tuning for inverse problem resolution is an essential task allowing to compute high quality solution with reasonable computing time. A way to handle this task consists in manually perform a grid-search which is time consuming. A recent approach, named algorithm unrolling, considers each iteration of an iterative algorithm as a layer of a deep neural network. By training the network, we can learn optimal hyper-parameters for the iterative algorithm with supervised learning. Different learning strategies (decomposing the regularization parameter, learning the gradient descent step) can be implemented to improve robustness, generalization and performance of proximal optimization algorithms.