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

• URL: http://arxiv.org/abs/2108.03642v1
• Date: Sun, 8 Aug 2021 14:14:35 GMT
• Title: Image reconstruction in light-sheet microscopy: spatially varying deconvolution and mixed noise
• Authors: Bogdan Toader and Jerome Boulanger and Yury Korolev and Martin O. Lenz and James Manton and Carola-Bibiane Schonlieb and Leila Muresan
• Abstract summary: We study the problem of deconvolution for light-sheet microscopy. The data is corrupted by spatially varying blur and a combination of Poisson and Gaussian noise. numerical experiments performed on both simulated and real data show superior reconstruction results in comparison with other methods.
• Score: 1.1545092788508224
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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