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

TL;DR

This paper presents a novel variational deconvolution model for light-sheet microscopy that accounts for spatially varying PSF and mixed Poisson-Gaussian noise, demonstrating improved reconstruction on simulated and real data.

Contribution

It introduces a new model incorporating spatially varying PSF and mixed noise, with a convergence analysis and a novel application of the PDHG algorithm for image reconstruction.

Findings

Superior reconstruction results compared to existing methods

Effective handling of spatially varying blur and mixed noise

Convergence guarantees under certain conditions

Abstract

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.