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3D Deconvolution in Optical Microscopy
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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

Description

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.

Free software for 3D Deconvolution and PSF Generation

The software is based on a plugin for ImageJ, a general purpose free image-processing package. ImageJ has a public domain licence; it runs on several plateforms: Unix, Linux, Windows, Mac OS 9 and Mac OS X.
1. Download the plugin
bullet 3D_Deconvolution.zip version march 2005
2. Installation
bulletGet a copy of ImageJ. The plugin requires ImageJ 1.31p or later.
bulletExtract 3D_Deconvolution.zip in the "plugins" folder of ImageJ. All the files should extract in a new folder "3D_Deconvolution".
bulletThe whole process should not take more than a couple of minutes.
3. How of use
bulletIn the "plugin" menu, go under "3D_Deconvolution" and choose the method: "PSF". Create a PSF with your parameters.
bulletOpen a stack of images. Ensure that the stack is 32-bit and that the dimensions are good.
bulletRead the manual 3D_Deconvolution.pdf
4. Conditions of use
bulletYou are free to use this software for research purposes, but you should not redistribute it without our consent.
bulletIn addition, we expect you to include adequate citations and acknowledgments whenever you present or publish results that are based on it.
5. Contact
bulletPierre Besson
6. Examples
Observed image
screenshot
Regularized Deconvolution - Van Cittert's algorithm (40 iterations) - ForWaRD
screenshot screenshot screenshot
Color Observation - Color Van Cittert Deconvolution (40 iterations)
screenshot screenshot
Image of a pancreas - Deconvolution (Van Cittert, 40 iterations)
screenshot screenshot
References
[1] S. F. Gibson, F. Lanni, "Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy", J. Opt. Soc. Am. A, vol. 8, no. 10, pp. 1601-1613, October 1991.
[2] D. A. Agard, "Optical sectioning microscopy: Cellular architecture in three dimensions", Ann. Rev. Biophys. Bioeng., vol. 13, pp. 191-219, 1984.
[3] R. Neelamani, H. Choi and R. Baraniuk, "ForWaRD: Fourier-Wavelet Regularized Deconvolution for Ill-Conditioned Systems", IEEE Transactions on Signal Processing, vol. 52, no. 2, pp. 418-433, February 2004.