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.

Fast Moving Window Algorithm for QR and Cholesky Decompositions

This paper proposes a fast moving window algorithm for QR and Cholesky decompositions by simultaneously applying data updating and downdating. The developed procedure is based on inner products and entails a similar downdating to that of the Chambers’ approach. For adding and deleting one row of data from the original matrix, a detailed analysis shows that the proposed algorithm outperforms existing ones in terms or computational efficiency, if the number of columns exceeds 7. For a large number of columns, the proposed algorithm is numerically superior compared to the traditional sequential technique.

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 rateof O(K^2), where k is the number of iterations. We demonstrate the superior convergence performance, by a speedup factor off ive, of the scaled H-B method on both synthetic and real 3D images.