# SPARCOM: Sparsity Based Super-Resolution Correlation Microscopy

arXiv: https://arxiv.org/abs/1707.09255 · HTML: https://mlsanity.com/paper/1707.09255/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2017.

## Built on by (most cited first, 6 of 6)

- [Deep Unrolled Recovery in Sparse Biological Imaging](https://mlsanity.com/paper/2109.14025/) (2021)
- [Deep Algorithm Unrolling for Biomedical Imaging](https://mlsanity.com/paper/2108.06637/) (2021)
- [Fluctuation-based deconvolution in fluorescence microscopy using plug-and-play denoisers](https://mlsanity.com/paper/2303.11212/) (2023)
- [Self-STORM: Deep Unrolled Self-Supervised Learning for Super-Resolution Microscopy](https://mlsanity.com/paper/2403.16974/) (2024)
- [Deep Learning Empowered Super-Resolution: A Comprehensive Survey and Future Prospects](https://mlsanity.com/paper/2509.22692/) (2025)
- [DeepCEL0 for 2D Single Molecule Localization in Fluorescence Microscopy](https://mlsanity.com/paper/2107.02281/) (2021)

## Abstract (arXiv)

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.