Relaxed ordered-subset algorithm for penalized-likelihood image restoration.

The expectation-maximization (EM) algorithm for maximum-likelihood image recovery is guaranteed to converge, but it converges slowly. Its ordered-subset version (OS-EM) is used widely in tomographic image reconstruction because of its order-of-magnitude acceleration compared with the EM algorithm, but it does not guarantee convergence. Recently the ordered-subset, separable-paraboloidal-surrogate (OS-SPS) algorithm with relaxation has been shown to converge to the optimal point while providing fast convergence. We adapt the relaxed OS-SPS algorithm to the problem of image restoration. Because data acquisition in image restoration is different from that in tomography, we employ a different strategy for choosing subsets, using pixel locations rather than projection angles. Simulation results show that the relaxed OS-SPS algorithm can provide an order-of-magnitude acceleration over the EM algorithm for image restoration. This new algorithm now provides the speed and guaranteed convergence necessary for efficient image restoration.

[1]  Charles L. Byrne,et al.  Convergent block-iterative algorithms for image reconstruction from inconsistent data , 1997, IEEE Trans. Image Process..

[2]  T J Holmes,et al.  Blind deconvolution of quantum-limited incoherent imagery: maximum-likelihood approach. , 1992, Journal of the Optical Society of America. A, Optics and image science.

[3]  Alvaro R. De Pierro,et al.  A row-action alternative to the EM algorithm for maximizing likelihood in emission tomography , 1996, IEEE Trans. Medical Imaging.

[4]  Á. R. De Pierro,et al.  Fast EM-like methods for maximum "a posteriori" estimates in emission tomography. , 2001, IEEE transactions on medical imaging.

[5]  Charles L. Byrne,et al.  Accelerating the EMML algorithm and related iterative algorithms by rescaled block-iterative methods , 1998, IEEE Trans. Image Process..

[6]  Timothy J. Holmes.  Maximum-likelihood image restoration adapted for noncoherent optical imaging , 1988 .

[7]  Christopher G. Relf,et al.  Image Acquisition and Processing with LabVIEW , 2003 .

[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]  Jeffrey A. Fessler,et al.  Relaxed ordered subsets algorithm for image restoration of confocal microscopy , 2002, Proceedings IEEE International Symposium on Biomedical Imaging.

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

[11]  M. Bertero,et al.  Application of the OS-EM method to the restoration of LBT images , 2000 .

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

[13]  Jeffrey A. Fessler,et al.  Globally convergent ordered subsets algorithms: application to tomography , 2001, 2001 IEEE Nuclear Science Symposium Conference Record (Cat. No.01CH37310).

[14]  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.

[15]  Hakan Erdogan,et al.  Ordered subsets algorithms for transmission tomography. , 1999, Physics in medicine and biology.

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

[17]  Dimitri P. Bertsekas,et al.  A New Class of Incremental Gradient Methods for Least Squares Problems , 1997, SIAM J. Optim..

[18]  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.

[19]  Sanjit K. Mitra,et al.  Digital Signal Processing: A Computer-Based Approach , 1997 .

[20]  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).

[21]  Jeffrey A. Fessler,et al.  Globally convergent image reconstruction for emission tomography using relaxed ordered subsets algorithms , 2003, IEEE Transactions on Medical Imaging.

[22]  Guillermo A. Jaquenod,et al.  Digital Signal Processing, A Computer Based Approach . 2nd Edition , 2003 .

[23]  H. Malcolm Hudson,et al.  Accelerated image reconstruction using ordered subsets of projection data , 1994, IEEE Trans. Medical Imaging.

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

[25]  É. Thiébaut,et al.  Strict a priori constraints for maximum-likelihood blind deconvolution , 1995 .

[26]  Lam,et al.  Iterative statistical approach to blind image deconvolution , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[27]  William H. Richardson,et al.  Bayesian-Based Iterative Method of Image Restoration , 1972 .

[28]  T. Åstebro,et al.  Maximum Likelihood Approach to Reject Inference , 2005 .

[29]  Richard G. Lane.  Methods for maximum-likelihood deconvolution , 1996 .

[30]  Jeffrey A. Fessler,et al.  Image recovery using partitioned-separable paraboloidal surrogate coordinate ascent algorithms , 2002, IEEE Trans. Image Process..

[31]  S. Joshi,et al.  Maximum a posteriori estimation with Good's roughness for three-dimensional optical-sectioning microscopy. , 1993, Journal of the Optical Society of America. A, Optics and image science.

[32]  C. Helstrom,et al.  Compensation for readout noise in CCD images , 1995 .

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