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Generalized approach for accelerated maximum likelihood based image restoration applied to three‐dimensional fluorescence microscopy
Author(s) -
Schaefer L. H.,
Schuster D.,
Herz H.
Publication year - 2001
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1046/j.1365-2818.2001.00949.x
Subject(s) - hessian matrix , tikhonov regularization , image restoration , deconvolution , regularization (linguistics) , algorithm , conjugate gradient method , maximum a posteriori estimation , line search , poisson distribution , mathematics , matrix (chemical analysis) , image processing , mathematical optimization , computer science , inverse problem , image (mathematics) , artificial intelligence , maximum likelihood , materials science , mathematical analysis , statistics , computer security , composite material , radius
For deconvolution applications in three‐dimensional microscopy we derived and implemented a generic, accelerated maximum likelihood image restoration algorithm. A conjugate gradient iteration scheme was used considering either Gaussian or Poisson noise models. Poisson models are better suited to low intensity fluorescent image data; typically, they show smaller restoration errors and smoother results. For the regularization, we modified the standard Tikhonov method. However, the generic design of the algorithm allows for more regularization approaches. The Hessian matrix of the restoration functional was used to determine the step size. We compared restoration error and convergence behaviour between the classical line‐search and the Hessian matrix method. Under typical working conditions, the restoration error did not increase over that of the line‐search and the speed of convergence did not significantly decrease allowing for a twofold increase in processing speed. To determine the regularization parameter, we modified the generalized cross‐validation method. Tests that were done on both simulated and experimental fluorescence wide‐field data show reliable results.