Image reconstruction in light-sheet microscopy: spatially varying deconvolution and mixed noise
This solves a specific inverse problem for microscopy imaging, representing an incremental improvement through a novel application of existing techniques.
The paper tackles image reconstruction in light-sheet microscopy by addressing spatially varying blur and mixed Poisson-Gaussian noise, achieving superior reconstruction results compared to other methods in numerical experiments on simulated and real data.
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.