An Error Reduction Technique in Richardson-Lucy Deconvolution Method


#1

I wonder if this would be helpful in understanding and perhaps improving RL. Personally, I don’t use RL because it is slow and produces artifacts (with which I am uncomfortable; perhaps, I don’t know how to make it work). The paper is licensed as follows:

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Abstract

An error reduction technique for Richardson-Lucy deconvolution (RL-deconv) is proposed. The deconvolution is indispensable technique for inversely analysing the SRAM fail-bit probability variations caused by the Random Telegraph Noise (RTN). The proposed technique reduces the phase difference between the two distributions of the deconvoluted RTN and the feedback-gain in the maximum likelihood (MLE) gradient iteration cycles. This avoids an unwanted positive feedback, resulting in a significant decrease in probability of undesired ringing occurrence. A quicker convergence benefit of the RL-deconv algorithm while avoiding the ringing is achieved. It has been demonstrated that the proposed technique reduces its relative deconvolution errors by 100 times compared with the conventional RL-deconv. This provides an increase in accuracy of the fail-bit-count prediction by over 2-orders of magnitude while accelerating its convergence speed by 33 times of the conventional one.


G'MIC exercises
#2

It would be really cool to see that implemented.

There are also lots of papers about improving the basic RL algorithm to prevent boundary effects, for instance: https://www.aanda.org/articles/aa/pdf/2005/25/aa2717-05.pdf and http://www2.tku.edu.tw/~tkjse/16-3/06-IE10211.pdf

The number of iterations could be determined automatically:
http://iopscience.iop.org/article/10.1088/1742-6596/630/1/012003

Other point-spread function methods could also be explored. These have already been implemented in GIMP.

One uses a Hopfield neural network:
http://refocus-it.sourceforge.net/

The other uses a Wiener filter:
http://refocus.sourceforge.net/doc.html

The assumptions of the LR and Wiener algorithms are different (Poisson versus Gaussian noise, I believe), so I would be curious to see what performs better in practice. From the examples in this paper it seem to be LR: