Blind source separation for imaging

TL;DR

This paper advances blind source separation techniques for imaging, establishing new theoretical criteria for correlated sources, verifying them in key regimes, and proposing an improved imaging method over classical approaches.

Contribution

It generalizes separability criteria to correlated complex sources with noise and introduces a novel imaging method based on blind source separation.

Findings

Theoretical separability criteria are validated in speckle and geometrical optics regimes.

The new method improves image quality over classical time reversal operator decomposition.

The approach extends blind source separation applications to complex-valued sources in imaging.

Abstract

This work is concerned with the problem of blind source separation and its applications to imaging. We first establish a theoretical result that we stated in our previous article on imaging in diffusive environments. This result is a generalization of separability criteria found in the literature to arbitrary correlated complex-valued sources with additive noise. In a second step, we verify these separability conditions in two propagation regimes frequently encountered in imaging: the speckle regime and the random geometrical optics regime. Finally, we propose a new imaging method based on the blind source separation problem that improves on images obtained with the classical decomposition of the time reversal operator method.