Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution

Confocal laser scanning microscopy is a powerful and popular technique for 3D imaging of biological specimens. Although confocal microscopy images are much sharper than standard epifluorescence ones, they are still degraded by residual out‐of‐focus light and by Poisson noise due to photon‐limited detection. Several deconvolution methods have been proposed to reduce these degradations, including the Richardson–Lucy iterative algorithm, which computes maximum likelihood estimation adapted to Poisson statistics. As this algorithm tends to amplify noise, regularization constraints based on some prior knowledge on the data have to be applied to stabilize the solution. Here, we propose to combine the Richardson–Lucy algorithm with a regularization constraint based on Total Variation, which suppresses unstable oscillations while preserving object edges. We show on simulated and real images that this constraint improves the deconvolution results as compared with the unregularized Richardson–Lucy algorithm, both visually and quantitatively. Microsc. Res. Tech. 69:260–266, 2006. © 2006 Wiley‐Liss, Inc.

[1]  E. Wolf,et al.  Principles of Optics (7th Ed) , 1999 .

[2]  J. Goodman.  Introduction to Fourier optics , 1969 .

[3]  Carol J. Cogswell,et al.  Three‐dimensional image formation in confocal microscopy , 1990 .

[4]  L. Lucy.  An iterative technique for the rectification of observed distributions , 1974 .

[5]  P. Stokseth.  Properties of a Defocused Optical System , 1969 .

[6]  P. Green.  On Use of the EM Algorithm for Penalized Likelihood Estimation , 1990 .

[7]  G. M. P. VAN KEMPEN,et al.  A quantitative comparison of image restoration methods for confocal microscopy , 1997 .

[8]  Geert M. P. van Kempen,et al.  Image Restoration in Fluorescence Microscopy , 1999 .

[9]  Geert M. P. van Kempen,et al.  Background estimation in nonlinear image restoration , 2000 .

[10]  Van Kempen,et al.  The influence of the regularization parameter and the first estimate on the performance of tikhonov regularized non-linear image restoration algorithms , 2000 .

[11]  William H. Richardson,et al.  Bayesian-Based Iterative Method of Image Restoration , 1972 .

[12]  Josiane Zerubia,et al.  A deconvolution method for confocal microscopy with total variation regularization , 2004, 2004 2nd IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE Cat No. 04EX821).

[13]  Mats Ulfendahl,et al.  Image-adaptive deconvolution for three-dimensional deep biological imaging. , 2003, Biophysical journal.

[14]  I. Csiszár.  Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems , 1991 .

[15]  J. Zerubia,et al.  3D Microscopy Deconvolution using Richardson-Lucy Algorithm with Total Variation Regularization , 2004 .

[16]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[17]  David A. Agard,et al.  Three-dimensional architecture of a polytene nucleus , 1983, Nature.

[18]  L. Ambrosio,et al.  Functions of Bounded Variation and Free Discontinuity Problems , 2000 .

[19]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[20]  E. H. Linfoot.  Principles of Optics , 1961 .