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Blind deconvolution estimation by multi-exponential models and alternated least squares approximations: Free-form and sparse approach

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Listed:
  • Daniel U Campos-Delgado
  • Omar Gutierrez-Navarro
  • Ricardo Salinas-Martinez
  • Elvis Duran
  • Aldo R Mejia-Rodriguez
  • Miguel J Velazquez-Duran
  • Javier A Jo

Abstract

The deconvolution process is a key step for quantitative evaluation of fluorescence lifetime imaging microscopy (FLIM) samples. By this process, the fluorescence impulse responses (FluoIRs) of the sample are decoupled from the instrument response (InstR). In blind deconvolution estimation (BDE), the FluoIRs and InstR are jointly extracted from a dataset with minimal a priori information. In this work, two BDE algorithms are introduced based on linear combinations of multi-exponential functions to model each FluoIR in the sample. For both schemes, the InstR is assumed with a free-form and a sparse structure. The local perspective of the BDE methodology assumes that the characteristic parameters of the exponential functions (time constants and scaling coefficients) are estimated based on a single spatial point of the dataset. On the other hand, the same exponential functions are used in the whole dataset in the global perspective, and just the scaling coefficients are updated for each spatial point. A least squares formulation is considered for both BDE algorithms. To overcome the nonlinear interaction in the decision variables, an alternating least squares (ALS) methodology iteratively solves both estimation problems based on non-negative and constrained optimizations. The validation stage considered first synthetic datasets at different noise types and levels, and a comparison with the standard deconvolution techniques with a multi-exponential model for FLIM measurements, as well as, with two BDE methodologies in the state of the art: Laguerre basis, and exponentials library. For the experimental evaluation, fluorescent dyes and oral tissue samples were considered. Our results show that local and global perspectives are consistent with the standard deconvolution techniques, and they reached the fastest convergence responses among the BDE algorithms with the best compromise in FluoIRs and InstR estimation errors.

Suggested Citation

  • Daniel U Campos-Delgado & Omar Gutierrez-Navarro & Ricardo Salinas-Martinez & Elvis Duran & Aldo R Mejia-Rodriguez & Miguel J Velazquez-Duran & Javier A Jo, 2021. "Blind deconvolution estimation by multi-exponential models and alternated least squares approximations: Free-form and sparse approach," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-29, March.
  • Handle: RePEc:plo:pone00:0248301
    DOI: 10.1371/journal.pone.0248301
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    References listed on IDEAS

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    1. Sean C Warren & Anca Margineanu & Dominic Alibhai & Douglas J Kelly & Clifford Talbot & Yuriy Alexandrov & Ian Munro & Matilda Katan & Chris Dunsby & Paul M W French, 2013. "Rapid Global Fitting of Large Fluorescence Lifetime Imaging Microscopy Datasets," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-17, August.
    2. Bryan Kaye & Peter J Foster & Tae Yeon Yoo & Daniel J Needleman, 2017. "Developing and Testing a Bayesian Analysis of Fluorescence Lifetime Measurements," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-13, January.
    3. Johannes Friedrich & Pengcheng Zhou & Liam Paninski, 2017. "Fast online deconvolution of calcium imaging data," PLOS Computational Biology, Public Library of Science, vol. 13(3), pages 1-26, March.
    4. Forrest Young & Jan Leeuw & Yoshio Takane, 1976. "Regression with qualitative and quantitative variables: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 505-529, December.
    5. Thomas Pengo & Arrate Muñoz-Barrutia & Isabel Zudaire & Carlos Ortiz-de-Solorzano, 2013. "Efficient Blind Spectral Unmixing of Fluorescently Labeled Samples Using Multi-Layer Non-Negative Matrix Factorization," PLOS ONE, Public Library of Science, vol. 8(11), pages 1-11, November.
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