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We study the problem of deconvolution for light-sheet microscopy, where thedata is corrupted by spatially varying blur and a combination of Poisson andGaussian noise. The spatial variation of the point spread function (PSF) of alight-sheet microscope is determined by the interaction between the excitationsheet and the detection objective PSF. First, we introduce a model of the imageformation process that incorporates this interaction, therefore capturing themain characteristics of this imaging modality. Then, we formulate a variationalmodel that accounts for the combination of Poisson and Gaussian noise through adata fidelity term consisting of the infimal convolution of the single noisefidelities, first introduced in L. Calatroni et al. "Infimal convolution ofdata discrepancies for mixed noise removal", SIAM Journal on Imaging Sciences10.3 (2017), 1196-1233. We establish convergence rates in a Bregman distanceunder a source condition for the infimal convolution fidelity and a discrepancyprinciple for choosing the value of the regularisation parameter. The inverseproblem is solved by applying the primal-dual hybrid gradient (PDHG) algorithmin a novel way. Finally, numerical experiments performed on both simulated andreal data show superior reconstruction results in comparison with othermethods.

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