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I am studying some deconvolution techniques, In order to remove motion blur, like:

Are there any pros / cons of using one versus another?
For example which are the pros / cons of Richardson-Lucy technique?

Royi
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dynamic
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  • Chapter 3 of "Image Restoration in Fluorescence Microscopy" (1999) by Geert M. P. Van Kempen gives a comparison between the two techniques – Gelliant Aug 02 '22 at 10:49

2 Answers2

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Both are the MMSE estimators.

The main difference is Wiener is the optimal for Gaussian Noise while Richardson Lucy assumes Poisson Noise.

Poisson Noise is a better model for noise in photos captured by a Photo Diode.

Computationally, in the case of Gaussian Noise and Linear Convolution the solution has a closed form solution in the Maximum Likelihood / LS sense.

The Lucy Richardson method, which is a Maximum Likelihood in the Poisson case, has no closed form solution and requires iterative approach.

See Noise, Image Reconstruction with Noise (EE367/CS448I: Computational Imaging and Display, Class 10, Gordon Wetzstein, Stanford University).

Royi
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  • A derivation of the Wiener filter is on Wikipedia. The Lucy-Richardson filter is derived (to some degree) here: http://bigwww.epfl.ch/deconvolution/challenge2013/index.html?p=doc_math_rl – Christian Chapman Apr 15 '14 at 16:30
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The efficiency of these approaches depends on your image, and Rechardson-Lucy has two forms both for Gaussian and Poisson noise. Rechardson-Lucy is an iterative method which can also correct spherical aberration.

Samaneh Pahlevani
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  • The paper you linked to is taking the hard path to do what I did here: https://dsp.stackexchange.com/questions/11208. For Gaussian Noise there is no need for iterative solution. There is a closed form solution. Fro large problems we solve the linear problem using iterative methods. But not Gradient Descent as the paper derives. Welcome to our community, – Royi Aug 15 '21 at 14:38