# Image reconstruction in light-sheet microscopy: spatially varying deconvolution and mixed noise

arXiv: https://arxiv.org/abs/2108.03642 · HTML: https://mlsanity.com/paper/2108.03642/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 53 references that are in the map.
- First posted on arXiv 8 Aug 2021.

## Builds on (most cited first, 5 of 5)

- [Entropic regularization of continuous optimal transport problems](https://mlsanity.com/paper/1906.01333/) (2019)
- [Variational regularisation for inverse problems with imperfect forward operators and general noise models](https://mlsanity.com/paper/2005.14131/) (2020)
- [Bilinear Constraint based ADMM for Mixed Poisson-Gaussian Noise Removal](https://mlsanity.com/paper/1910.08206/) (2019)
- [Infimal convolution of data discrepancies for mixed noise removal](https://mlsanity.com/paper/1611.00690/) (2016)
- [A scalable estimator of sets of integral operators](https://mlsanity.com/paper/1811.12192/) (2018)

## Built on by (most cited first, 2 of 2)

- [CoordGate: Efficiently Computing Spatially-Varying Convolutions in Convolutional Neural Networks](https://mlsanity.com/paper/2401.04680/) (2024)
- [3-D Image-to-Image Fusion in Lightsheet Microscopy by Two-Step Adversarial Network: Contribution to the FuseMyCells Challenge](https://mlsanity.com/paper/2503.16075/) (2025)

## Abstract (arXiv)

We study the problem of deconvolution for light-sheet microscopy, where the data is corrupted by spatially varying blur and a combination of Poisson and Gaussian noise. The spatial variation of the point spread function (PSF) of a light-sheet microscope is determined by the interaction between the excitation sheet and the detection objective PSF. First, we introduce a model of the image formation process that incorporates this interaction, therefore capturing the main characteristics of this imaging modality. Then, we formulate a variational model that accounts for the combination of Poisson and Gaussian noise through a data fidelity term consisting of the infimal convolution of the single noise fidelities, first introduced in L. Calatroni et al. "Infimal convolution of data discrepancies for mixed noise removal", SIAM Journal on Imaging Sciences 10.3 (2017), 1196-1233. We establish convergence rates in a Bregman distance under a source condition for the infimal convolution fidelity and a discrepancy principle for choosing the value of the regularisation parameter. The inverse problem is solved by applying the primal-dual hybrid gradient (PDHG) algorithm in a novel way. Finally, numerical experiments performed on both simulated and real data show superior reconstruction results in comparison with other methods.