Student Project: 3D Deconvolution in Optical Microscopy
|Author: Pierre Besson
|Notice Of Disclaimers:
The information, opinions, data, and statements contained herein are not necessarily those of the Biomedical Imaging Group at the Swiss Federal Institute of Technology Lausanne (EPFL) and should
not be interpreted, acted on or represented as such.
Please contact the author of this algorithm if you have a specific question.
|| March 2005
When looking at a three-dimensional (3D) specimen through a transmitted brightfield optical microscope, only the part of the specimen contained in the focal plane appears sharp while the remainder looks smooth. The deconvolution task consists in deblurring the observed image in order to recover the original shapes of the object. Although 2D deconvolution softwares are available freely, the 3D consideration gives rise to many problems leading to the impossibility to recover the original images without any assumptions. Moreover some noise is added to the signal, it has been considered as a white Gaussian noise.
Point Spread Function
The first step is the characterization of the Point Spread Function (PSF), which is the impulse response of the microscope. Since this function is the mathematical link between the observation and the actual object, a precise knowledge of the PSF is necessary for optimum results. A simplified model (Agard, 1984) and a more accurate one (Gibson, 1991) have been implemented.
(Left to right) Agard's model, measurement, Gibson's model
Image Restoration Algorithms
The algorithms that have been implemented are : inverse filtering, regularized inverse filtering, iterative Van Cittert's method and a ForWaRD-like algorithm. ForWaRD uses regularization in both Fourier and wavelets domains.