A New Approach for Deconvolution and Filtering of 3-D Microscopy Images

Abstract A new approach to the deconvolution and filtering of 3-D microscopy images is introduced in this paper. A state-space representation of the image is derived according to the assumption that the whole image can be modelled by an ensemble of smooth 3-D Gaussian random fields. Blurring and noise are then easily included in the representation. Making use of this model the image restoration is carried out by means of a Kalman-based minimum variance estimation algorithm. The reported simulation results show high performances of the proposed approach.

[1]  M. Unser,et al.  The colored revolution of bioimaging , 2006, IEEE Signal Processing Magazine.

[2]  A. V. Balakrishnan,et al.  Kalman Filtering Theory , 1984 .

[3]  Alfredo Germani,et al.  Space-variant recursive restoration of noisy images , 1994 .

[4]  A. Nehorai,et al.  Deconvolution methods for 3-D fluorescence microscopy images , 2006, IEEE Signal Processing Magazine.

[5]  Jose-Angel Conchello,et al.  Fast regularization technique for expectation maximization algorithm for optical sectioning microscopy , 1996, Electronic Imaging.

[6]  L. Jetto,et al.  Stochastic Modelling and 3D Minimum Variance Recursive Estimation of Image Sequences , 1999, Multidimens. Syst. Signal Process..

[7]  H. M. Voort,et al.  Restoration of confocal images for quantitative image analysis , 1995 .

[8]  Hiroaki Takajo,et al.  Improved Methods of Maximum a Posteriori Restoration , 1980 .

[9]  Peter J. Verveer,et al.  Efficient superresolution restoration algorithms using maximum a posteriori estimations with application to fluorescence microscopy , 1997 .

[10]  F S Fay,et al.  Superresolution three-dimensional images of fluorescence in cells with minimal light exposure. , 1995, Science.

[11]  Timothy J. Holmes.  Maximum-likelihood image restoration adapted for noncoherent optical imaging , 1988 .

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

[13]  L. J. Thomas,et al.  Regularized linear method for reconstruction of three-dimensional microscopic objects from optical sections. , 1992, Journal of the Optical Society of America. A, Optics and image science.

[14]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[15]  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 .