Image Reconstruction in Light-Sheet Microscopy: Spatially Varying Deconvolution and Mixed Noise

Bogdan Toader, Jérôme Boulanger, Yury Korolev, Martin O. Lenz, James Manton, Carola Bibiane Schönlieb, Leila Mureşan

Research output: Contribution to journalArticlepeer-review


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(3):1196–1233, 2017). 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.

Original languageEnglish
Pages (from-to)968-992
Number of pages25
JournalJournal of Mathematical Imaging and Vision
Early online date14 Jun 2022
Publication statusPublished - 30 Nov 2022


  • Deconvolution
  • Light-sheet microscopy
  • Numerical methods
  • Poisson and Gaussian noise
  • Primal–dual hybrid gradient

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Condensed Matter Physics
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Applied Mathematics


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