Scaled Heavy-Ball Acceleration of the Richardson-Lucy Algorithm for 3D Microscopy Image Restoration

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 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 a proof of the convergence rate of O(K(-2)), 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.