# Fluctuation-based deconvolution in fluorescence microscopy using plug-and-play denoisers

arXiv: https://arxiv.org/abs/2303.11212 · HTML: https://mlsanity.com/paper/2303.11212/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 35 references that are in the map.
- First posted on arXiv 20 Mar 2023.

## Builds on (most cited first, 16 of 16)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie](https://mlsanity.com/paper/2103.04715/) (2021)
- [Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging](https://mlsanity.com/paper/2203.17061/) (2022)
- [Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization](https://mlsanity.com/paper/2201.13256/) (2022)
- [A characterization of proximity operators](https://mlsanity.com/paper/1807.04014/) (2018)
- [Exact Support Recovery for Sparse Spikes Deconvolution](https://mlsanity.com/paper/1306.6909/) (2013)
- [Boosting the Performance of Plug-and-Play Priors via Denoiser Scaling](https://mlsanity.com/paper/2002.11546/) (2020)
- [SPARCOM: Sparsity Based Super-Resolution Correlation Microscopy](https://mlsanity.com/paper/1707.09255/) (2017)
- [COL0RME: COvariance-based ℓ0 super-Resolution Microscopy with intensity Estimation](https://mlsanity.com/paper/2010.13477/) (2020)
- [COL0RME: Super-resolution microscopy based on sparse blinking/fluctuating fluorophore localization and intensity estimation](https://mlsanity.com/paper/2108.07095/) (2021)
- [3D Image Super-Resolution by fluorophore fluctuations and MA-TIRF Microscopy reconstruction (3D-COL0RME)](https://mlsanity.com/paper/2111.03170/) (2021)

## Built on by (most cited first, 1 of 1)

- [Equivariant plug-and-play image reconstruction](https://mlsanity.com/paper/2312.01831/) (2023)

## Abstract (arXiv)

The spatial resolution of images of living samples obtained by fluorescence microscopes is physically limited due to the diffraction of visible light, which makes the study of entities of size less than the diffraction barrier (around 200 nm in the x-y plane) very challenging. To overcome this limitation, several deconvolution and super-resolution techniques have been proposed. Within the framework of inverse problems, modern approaches in fluorescence microscopy reconstruct a super-resolved image from a temporal stack of frames by carefully designing suitable hand-crafted sparsity-promoting regularisers. Numerically, such approaches are solved by proximal gradient-based iterative schemes. Aiming at obtaining a reconstruction more adapted to sample geometries (e.g. thin filaments), we adopt a plug-and-play denoising approach with convergence guarantees and replace the proximity operator associated with the explicit image regulariser with an image denoiser (i.e. a pre-trained network) which, upon appropriate training, mimics the action of an implicit prior. To account for the independence of the fluctuations between molecules, the model relies on second-order statistics. The denoiser is then trained on covariance images coming from data representing sequences of fluctuating fluorescent molecules with filament structure. The method is evaluated on both simulated and real fluorescence microscopy images, showing its ability to correctly reconstruct filament structures with high values of peak signal-to-noise ratio (PSNR).