SPARCOM: Sparsity Based Super-Resolution Correlation Microscopy

TL;DR

SPARCOM is a super-resolution microscopy method that leverages sparsity and statistical priors to achieve PALM/STORM-like resolution with significantly faster data acquisition, and it can be extended to various sparsity domains.

Contribution

This paper provides a detailed mathematical formulation and efficient implementation of SPARCOM, extending it to a general sparsity-based super-resolution framework in different domains.

Findings

Achieves sub-diffraction resolution comparable to PALM/STORM

Captures data hundreds of times faster than traditional methods

Extensible to various sparsity domains like wavelet or DCT

Abstract

In traditional optical imaging systems, the spatial resolution is limited by the physics of diffraction, which acts as a low-pass filter. The information on sub-wavelength features is carried by evanescent waves, never reaching the camera, thereby posing a hard limit on resolution: the so-called diffraction limit. Modern microscopic methods enable super-resolution, by employing florescence techniques. State-of-the-art localization based fluorescence subwavelength imaging techniques such as PALM and STORM achieve sub-diffraction spatial resolution of several tens of nano-meters. However, they require tens of thousands of exposures, which limits their temporal resolution. We have recently proposed SPARCOM (sparsity based super-resolution correlation microscopy), which exploits the sparse nature of the fluorophores distribution, alongside a statistical prior of uncorrelated emissions, and showed that SPARCOM achieves spatial resolution comparable to PALM/STORM, while capturing the data hundreds of times faster. Here, we provide a detailed mathematical formulation of SPARCOM, which in turn leads to an efficient numerical implementation, suitable for large-scale problems. We further extend our method to a general framework for sparsity based super-resolution imaging, in which sparsity can be assumed in other domains such as wavelet or discrete-cosine, leading to improved reconstructions in a variety of physical settings.