Efficient Constrained Signal Reconstruction by Randomized Epigraphical Projection

TL;DR

This paper introduces a randomized optimization method using epigraphical projections for constrained signal reconstruction, improving efficiency especially with large matrices, demonstrated on CT image reconstruction.

Contribution

It presents a novel randomized solver based on stochastic proximal algorithms and epigraphical projections for constrained signal reconstruction problems.

Findings

Enhanced efficiency over deterministic methods in large-scale problems

Effective application to CT image reconstruction

Flexible handling of data-fidelity constraints

Abstract

This paper proposes a randomized optimization framework for constrained signal reconstruction, where the word "constrained" implies that data-fidelity is imposed as a hard constraint instead of adding a data-fidelity term to an objective function to be minimized. Such formulation facilitates the selection of regularization terms and hyperparameters, but due to the non-separability of the data-fidelity constraint, it does not suit block-coordinate-wise randomization as is. To resolve this, we give another expression of the data-fidelity constraint via epigraphs, which enables to design a randomized solver based on a stochastic proximal algorithm with randomized epigraphical projection. Our method is very efficient especially when the problem involves non-structured large matrices. We apply our method to CT image reconstruction, where the advantage of our method over the deterministic counterpart is demonstrated.