# Coherence retrieval using trace regularization

## TL;DR

This paper introduces a trace-regularized optimization approach and an accelerated algorithm for coherence retrieval, improving reconstruction quality and convergence speed in phase-space tomography of optical fields.

## Contribution

The paper presents a novel trace-regularized model and a provably-convergent adaptive accelerated proximal gradient algorithm for coherence retrieval.

## Key findings

- Improved reconstruction quality over previous models.
- Faster convergence compared to existing methods.
- Effective on both simulated and experimental data.

## Abstract

The mutual intensity and its equivalent phase-space representations quantify an optical field's state of coherence and are important tools in the study of light propagation and dynamics, but they can only be estimated indirectly from measurements through a process called coherence retrieval, otherwise known as phase-space tomography. As practical considerations often rule out the availability of a complete set of measurements, coherence retrieval is usually a challenging high-dimensional ill-posed inverse problem. In this paper, we propose a trace-regularized optimization model for coherence retrieval and a provably-convergent adaptive accelerated proximal gradient algorithm for solving the resulting problem. Applying our model and algorithm to both simulated and experimental data, we demonstrate an improvement in reconstruction quality over previous models as well as an increase in convergence speed compared to existing first-order methods.