Journal of Mathematical Imaging and Vision

, Volume 61, Issue 7, pp 1037–1050 | Cite as

Optimal Multivariate Gaussian Fitting with Applications to PSF Modeling in Two-Photon Microscopy Imaging

  • Emilie ChouzenouxEmail author
  • Tim Tsz-Kit Lau
  • Claire Lefort
  • Jean-Christophe Pesquet


Fitting Gaussian functions to empirical data is a crucial task in a variety of scientific applications, especially in image processing. However, most of the existing approaches for performing such fitting are restricted to two dimensions and they cannot be easily extended to higher dimensions. Moreover, they are usually based on alternating minimization schemes which benefit from few theoretical guarantees in the underlying nonconvex setting. In this paper, we provide a novel variational formulation of the multivariate Gaussian fitting problem, which is applicable to any dimension and accounts for possible nonzero background and noise in the input data. The block multiconvexity of our objective function leads us to propose a proximal alternating method to minimize it in order to estimate the Gaussian shape parameters. The resulting FIGARO algorithm is shown to converge to a critical point under mild assumptions. The algorithm shows a good robustness when tested on synthetic datasets. To demonstrate the versatility of FIGARO, we also illustrate its excellent performance in the fitting of the point spread functions of experimental raw data from a two-photon fluorescence microscope.


Gaussian fitting Kullback–Leibler divergence Alternating minimization Proximal methods PSF identification Two-photon fluorescence microscopy 



This work was supported by the CNRS under grant MI-AAP Interne2018-SupRéMA.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Center for Visual Computing, CentraleSupélec, INRIA SaclayUniversité Paris-SaclayGif-sur-YvetteFrance
  2. 2.Laboratoire d’Informatique Gaspard Monge, UMR CNRS 8049Université Paris-Est Marne-la-ValléeChamps-sur-MarneFrance
  3. 3.Department of StatisticsNorthwestern UniversityEvanstonUSA
  4. 4.XLIM Research Institute, UMR CNRS 7252Université de LimogesLimogesFrance

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