Scaled Heavy-Ball acceleration of the Richardson-Lucy algorithm

The Richardson-Lucy algorithm is one of the most important algorithms in the image deconvolution area. However, one of its drawbacks is slow convergence. A very significant acceleration is obtained by 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 paper, 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 proof of the convergence rate of O(k^-2), where k is the number of iterations. We demonstrate the superior convergence performance of the scaled H-B method on both synthetic and real 3D images.