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Image reconstruction in light-sheet microscopy: spatially varying deconvolution and mixed noise. (English) Zbl 07632074

Summary: 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 of a light-sheet microscope is determined by the interaction between the excitation sheet and the detection objective PSF. We introduce a model of the image formation process that incorporates this interaction and 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. [SIAM J. Imaging Sci. 10, No. 3, 1196–1233 (2017; Zbl 1412.94005)]. We establish convergence rates and a discrepancy principle for the infimal convolution fidelity and the inverse problem is solved by applying the primal-dual hybrid gradient (PDHG) algorithm in a novel way. Numerical experiments performed on simulated and real data show superior reconstruction results in comparison with other methods.

MSC:

68-XX Computer science
94-XX Information and communication theory, circuits

Citations:

Zbl 1412.94005
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Full Text: DOI arXiv

References:

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