SCALED HEAVY-BALL ACCELERATION OF THE RICHARDSON-LUCY ALGORITHM FOR 3D MICROSCOPY IMAGE RESTORATION

Abstract

 

The Richardson-Lucy algorithm is one of the most important in image deconvolution. However, a drawback is its slow convergence. A significant acceleration was obtained using the technique proposed by Biggs and Andrews (BA), which is implemented in the deconvlucy function of the Image Processing MATLAB toolbox. The BA method was developed heuristically with no proof of convergence. In this work, we introduce the Heavy-Ball (H-B) method for Poisson data optimization and extend it to a scaled H-B method, which includes the BA method as a special case. The method has a proof of the convergence rate of , where k is the number of iterations. We demonstrate the superior convergence performance, by a speedup factor of five, of the scaled H-B method on both synthetic and real 3D images.

 One of the main contributions of the paper is the a proof of the following lemma:

 

 

Results

Fig. 1: Graph of C(x) versus iteration number for both the RL algorithm (dotted line) and the scaled H-B (solid line) for the C. Elegans embryo CY3, DAPI and FITC image channels.
Fig. 2: One z-stack view of the CY3 (top), DAPI (middle) and FITC (bottom) channels of a C. Elegans embryo. (Left) Blurred noisy image; (Middle) Restoration by RL; (Right) Restoration by scaled H-B.
Table 1: Speed-up of scaled H-B on the C. Elegans image.

 

Citation

Scaled Heavy-Ball acceleration of the Richardson-Lucy algorithm for 3D microscopy image restoration

H. Wang  and P. Miller

IEEE Transactions on Image Processing, Vol. 23, no. 2 (2014): 848-854.

bibtex
@ARTICLE{Wang2014,
author={Wang, H. and Miller, P. C.},
journal={Image Processing, IEEE Transactions on},
title={Scaled Heavy-Ball acceleration of the Richardson-Lucy algorithm for 3D microscopy image restoration},
year={2014},
volume={23},
number={2},
pages={848-854},
doi={10.1109/TIP.2013.2291324},}