The Analysis of Richardson-Lucy Deconvolution Algorithm with Application to Microscope Images

A thesis accepted by Tallinn University of Technology for the Degree of Master of Science

Martin Laasmaa

Tallinn University of Technology, Estonia

Marko Vendelin, PhD

Institute of Cybernetics at Tallinn Technical University, Estonia

Pearu Peterson, PhD

Institute of Cybernetics at Tallinn Technical University, Estonia

Jaan Kalda, PhD.

Institute of Cybernetics at Tallinn Technical University, Estonia


Deconvolution is an efficient tool for enhancing both fluorescence and confocal microscopy images. Although in confocal microscopy the point spread function (PSF) is rather small and images are much sharper compared to fluorescence microscopy, deconvolution can improve image contrast and reduce noise considerably in confocal microscopy.

Several deconvolution methods have been proposed for 3D microscopy. In this work, we used Richardson-Lucy (RL) iterative algorithm assuming Poisson noise (because the noise on confocal microscope images corresponds to Poisson noise). However, RL does not always converge to a suitable solution. Convergence is improved, when combining RL with total variation regularization, using optimal regularization parameter.

The aim of this work was to find the range of optimal values of the regularization parameter. For that, a synthetic image representing different shapes and intensities were generated, convolved and added Poisson noise. We deconvolved degraded images with different λ values. As result, from iteration history, we found that the range of TV regularization parameter λ = 0.008 to 0.03 gives satisfying results with respect to sharpness and the homogeneity of details. At smaller values of λ, all objects are smoothed out, but the oscillations near the sharp transitions of intensity are relatively small. In contrast, larger values of λ lead to a better edge detection but with the larger oscillations in the homogeneous regions.

After the test on synthetic images, we applied the deconvolution algorithm to experimental data. Rat and trout cardiomyocytes were labeled with different fluorescence dyes, recorded with a confocal microscope and deconvolved. The deconvolution algorithm with the regularization parameter of λ = 0.01 led to significant improvement in image quality. We showed that the deconvolution process should be stopped after a certain number of iterations. Prolonged iterations can lead to misleading results, start amplifying noise or producing artifacts.


The presentation of the thesis took place on June, 2009, at Tallinn University of Technology, Tallinn, Estonia.

Softcopy: (6.1MB).

Related papers:

M. Laasmaa, M. Vendelin, P. Peterson. Application of regularized Richardson-Lucy algorithm for deconvolution of confocal microscopy images. J. Microscopy. Volume 243, Issue 2, pages 124–140, August 2011.