On the super-resolution capacity of imagers using unknown speckle illuminations

TL;DR

This paper investigates the super-resolution capabilities of speckle-based imaging systems with unknown illuminations, demonstrating that their covariance can recover spatial frequencies beyond the data's native support, with implications for various imaging modalities.

Contribution

It provides a theoretical analysis showing that speckle-based imagers can achieve super-resolution through covariance analysis, even with unknown illuminations, under realistic conditions.

Findings

Covariance of data has super-resolution power matching the squared point spread function.

Theoretical results apply to acoustic, electromagnetic, and optical imaging systems.

Numerical validation in fluorescence microscopy confirms the theory.

Abstract

Speckle based imaging consists of forming a super-resolved reconstruction of an unknown sample from low-resolution images obtained under random inhomogeneous illuminations (speckles). In a blind context where the illuminations are unknown, we study the intrinsic capacity of speckle-based imagers to recover spatial frequencies outside the frequency support of the data, with minimal assumptions about the sample. We demonstrate that, under physically realistic conditions, the covariance of the data has a super-resolution power corresponding to the squared magnitude of the imager point spread function. This theoretical result is important for many practical imaging systems such as acoustic and electromagnetic tomographs, fluorescence and photoacoustic microscopes, or synthetic aperture radar imaging. A numerical validation is presented in the case of fluorescence microscopy.