Monotonic algorithms for transmission tomography

Presents a framework for designing fast and monotonic algorithms for transmission tomography penalized-likelihood image reconstruction. The new algorithms are based on paraboloidal surrogate functions for the log likelihood, Due to the form of the log-likelihood function it is possible to find low curvature surrogate functions that guarantee monotonicity. Unlike previous methods, the proposed surrogate functions lead to monotonic algorithms even for the nonconvex log likelihood that arises due to background events, such as scatter and random coincidences. The gradient and the curvature of the likelihood terms are evaluated only once per iteration. Since the problem is simplified at each iteration, the CPU time is less than that of current algorithms which directly minimize the objective, yet the convergence rate is comparable. The simplicity, monotonicity, and speed of the new algorithms are quite attractive. The convergence rates of the algorithms are demonstrated using real and simulated PET transmission scans.

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

[2]  E. Hoffman,et al.  Quantitation in positron emission computed tomography: 2. Effects of inaccurate attenuation correction. , 1979, Journal of computer assisted tomography.

[3]  K. Lange,et al.  EM reconstruction algorithms for emission and transmission tomography. , 1984, Journal of computer assisted tomography.

[4]  P. G. Ciarlet,et al.  Introduction to Numerical Linear Algebra and Optimisation , 1989 .

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

[6]  Jolyon A. Browne,et al.  Developments with maximum likelihood X-ray computed tomography , 1992, IEEE Trans. Medical Imaging.

[7]  John T. Kent,et al.  Some Suggestions for Transmission Tomography Based on the EM Algorithm , 1992 .

[8]  S Grootoonk,et al.  Performance Evaluation of the Positron Scanner ECAT EXACT , 1992, Journal of computer assisted tomography.

[9]  A. R. De Pierro,et al.  On the relation between the ISRA and the EM algorithm for positron emission tomography , 1993, IEEE Trans. Medical Imaging.

[10]  Jeffrey A. Fessler,et al.  On complete-data spaces for PET reconstruction algorithms , 1993 .

[11]  Ken D. Sauer,et al.  A local update strategy for iterative reconstruction from projections , 1993, IEEE Trans. Signal Process..

[12]  Simon R. Cherry,et al.  Fast gradient-based methods for Bayesian reconstruction of transmission and emission PET images , 1994, IEEE Trans. Medical Imaging.

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

[14]  Jeffrey A. Fessler.  Penalized weighted least-squares image reconstruction for positron emission tomography , 1994, IEEE Trans. Medical Imaging.

[15]  John M. Ollinger,et al.  Maximum-likelihood reconstruction of transmission images in emission computed tomography via the EM algorithm , 1994, IEEE Trans. Medical Imaging.

[16]  Jeffrey A. Fessler,et al.  Ieee Transactions on Image Processing: to Appear Globally Convergent Algorithms for Maximum a Posteriori Transmission Tomography , 2022 .

[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]  B F Hutton,et al.  Simultaneous emission and transmission measurements for attenuation correction in whole-body PET. , 1995, Journal of nuclear medicine : official publication, Society of Nuclear Medicine.

[19]  Jeffrey A. Fessler,et al.  Ieee Transactions on Image Processing: to Appear Hybrid Poisson/polynomial Objective Functions for Tomographic Image Reconstruction from Transmission Scans , 2022 .

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

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

[22]  Ken D. Sauer,et al.  Provably convergent coordinate descent in statistical tomographic reconstruction , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[23]  Jeffrey A. Fessler,et al.  Spatial resolution properties of penalized-likelihood image reconstruction: space-invariant tomographs , 1996, IEEE Trans. Image Process..

[24]  Jeffrey A. Fessler,et al.  Statistical image reconstruction methods for simultaneous emission/transmission PET scans , 1996, 1996 IEEE Nuclear Science Symposium. Conference Record.

[25]  E U Mumcuoğlu,et al.  Bayesian reconstruction of PET images: methodology and performance analysis. , 1996, Physics in medicine and biology.

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

[27]  Jorge Nocedal,et al.  Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization , 1997, TOMS.

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

[29]  Jeffrey A. Fessler,et al.  New Statistical Models for Randoms-Precorrected PET Scans , 1997, IPMI.

[30]  Ken D. Sauer,et al.  Functional Substitution Methods in Optimization for Bayesian Tomography , 1997 .

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

[32]  Hakan Erdogan,et al.  An Ordered Subsets Algorithm for Transmission Tomography , 1998 .

[33]  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).