Deconvolution of confocal microscopy images using proximal iteration and sparse representations

TL;DR

This paper introduces a novel deconvolution algorithm for confocal microscopy images degraded by Poisson noise, utilizing proximal iteration and sparse representations to improve image clarity.

Contribution

It presents a fast proximal backward-forward splitting method that effectively incorporates non-linear Poisson noise modeling and sparsity regularization for image deconvolution.

Findings

Competitive performance on simulated microscopy images.

Non-linearity due to Poisson noise is crucial at low and medium intensities.

Successful application on real confocal microscopy data.

Abstract

We propose a deconvolution algorithm for images blurred and degraded by a Poisson noise. The algorithm uses a fast proximal backward-forward splitting iteration. This iteration minimizes an energy which combines a \textit{non-linear} data fidelity term, adapted to Poisson noise, and a non-smooth sparsity-promoting regularization (e.g $\ell_1$-norm) over the image representation coefficients in some dictionary of transforms (e.g. wavelets, curvelets). Our results on simulated microscopy images of neurons and cells are confronted to some state-of-the-art algorithms. They show that our approach is very competitive, and as expected, the importance of the non-linearity due to Poisson noise is more salient at low and medium intensities. Finally an experiment on real fluorescent confocal microscopy data is reported.