Image recovery using partitioned-separable paraboloidal surrogate coordinate ascent algorithms

Iterative coordinate ascent algorithms have been shown to be useful for image recovery, but are poorly suited to parallel computing due to their sequential nature. This paper presents a new fast converging parallelizable algorithm for image recovery that can be applied to a very broad class of objective functions. This method is based on paraboloidal surrogate functions and a concavity technique. The paraboloidal surrogates simplify the optimization problem. The idea of the concavity technique is to partition pixels into subsets that can be updated in parallel to reduce the computation time. For fast convergence, pixels within each subset are updated sequentially using a coordinate ascent algorithm. The proposed algorithm is guaranteed to monotonically increase the objective function and intrinsically accommodates nonnegativity constraints. A global convergence proof is summarized. Simulation results show that the proposed algorithm requires less elapsed time for convergence than iterative coordinate ascent algorithms. With four parallel processors, the proposed algorithm yields a speedup factor of 3.77 relative to single processor coordinate ascent algorithms for a three-dimensional (3-D) confocal image restoration problem.

[1]  G. Amdhal,et al.  Validity of the single processor approach to achieving large scale computing capabilities , 1967, AFIPS '67 (Spring).

[2]  Yoram Bresler,et al.  Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography , 1998, IEEE Trans. Image Process..

[3]  Ken D. Sauer,et al.  A unified approach to statistical tomography using coordinate descent optimization , 1996, IEEE Trans. Image Process..

[4]  Donald Geman,et al.  Constrained Restoration and the Recovery of Discontinuities , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  R. White,et al.  Image recovery from data acquired with a charge-coupled-device camera. , 1993, Journal of the Optical Society of America. A, Optics and image science.

[6]  Jose-Angel Conchello,et al.  Fast regularization technique for expectation maximization algorithm for optical sectioning microscopy , 1996, Electronic Imaging.

[7]  Ken D. Sauer,et al.  Parallel computation of sequential pixel updates in statistical tomographic reconstruction , 1995, Proceedings., International Conference on Image Processing.

[8]  Alvaro R. De Pierro,et al.  A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography , 1995, IEEE Trans. Medical Imaging.

[9]  Alfred O. Hero,et al.  Space-alternating generalized expectation-maximization algorithm , 1994, IEEE Trans. Signal Process..

[10]  Jeffrey A. Fessler,et al.  Fast Monotonic Algorithms for Transmission Tomography , 1999, IEEE Trans. Medical Imaging.

[11]  J. Conchello,et al.  Parametric blind deconvolution: a robust method for the simultaneous estimation of image and blur. , 1999, Journal of the Optical Society of America. A, Optics, image science, and vision.

[12]  Jeffrey A. Fessler,et al.  Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction , 1997, IEEE Transactions on Medical Imaging.

[13]  Michel Barlaud,et al.  Deterministic edge-preserving regularization in computed imaging , 1997, IEEE Trans. Image Process..

[14]  Jeffrey A. Fessler,et al.  A paraboloidal surrogates algorithm for convergent penalized-likelihood emission image reconstruction , 1998, 1998 IEEE Nuclear Science Symposium Conference Record. 1998 IEEE Nuclear Science Symposium and Medical Imaging Conference (Cat. No.98CH36255).

[15]  Donald Geman,et al.  Nonlinear image recovery with half-quadratic regularization , 1995, IEEE Trans. Image Process..

[16]  K. Lange.  Convergence of EM image reconstruction algorithms with Gibbs smoothing. , 1990, IEEE transactions on medical imaging.

[17]  Alfred O. Hero,et al.  Ieee Transactions on Image Processing: to Appear Penalized Maximum-likelihood Image Reconstruction Using Space-alternating Generalized Em Algorithms , 2022 .

[18]  Hakan Erdogan,et al.  Monotonic algorithms for transmission tomography , 2002, 5th IEEE EMBS International Summer School on Biomedical Imaging, 2002..

[19]  Hakan Erdogan,et al.  Monotonic algorithms for transmission tomography , 1999, IEEE Transactions on Medical Imaging.

[20]  Jeffrey A. Fessler,et al.  Grouped coordinate descent algorithms for robust edge-preserving image restoration , 1997, Optics & Photonics.

[21]  Loyce Adams,et al.  New Parallel SOR Method by Domain Partitioning , 1999, SIAM J. Sci. Comput..

[22]  Jeffrey A. Fessler,et al.  Partitioned separable paraboloidal surrogate coordinate ascent algorithm for image restoration , 2000, Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101).

[23]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[24]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .