Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction

Presents a new class of algorithms for penalized-likelihood reconstruction of attenuation maps from low-count transmission scans. We derive the algorithms by applying to the transmission log-likelihood a version of the convexity technique developed by De Pierro for emission tomography. The new class includes the single-coordinate ascent (SCA) algorithm and Lange's convex algorithm for transmission tomography as special cases. The new grouped-coordinate ascent (GCA) algorithms in the class overcome several limitations associated with previous algorithms. (1) Fewer exponentiations are required than in the transmission maximum likelihood-expectation maximization (ML-EM) algorithm or in the SCA algorithm. (2) The algorithms intrinsically accommodate nonnegativity constraints, unlike many gradient-based methods. (3) The algorithms are easily parallelizable, unlike the SCA algorithm and perhaps line-search algorithms. We show that the GCA algorithms converge faster than the SCA algorithm, even on conventional workstations. An example from a low-count positron emission tomography (PET) transmission scan illustrates the method.

[1]  J.M.M. Anderson,et al.  A weighted least-squares method for PET , 1995, 1995 IEEE Nuclear Science Symposium and Medical Imaging Conference Record.

[2]  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 .

[3]  Anthony J. Weiss,et al.  Maximum likelihood array processing for the estimation of superimposed signals , 1988, Proc. IEEE.

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

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

[6]  K. Lange,et al.  A Theoretical Study of Some Maximum Likelihood Algorithms for Emission and Transmission Tomography , 1987, IEEE Transactions on Medical Imaging.

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

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

[9]  Jeffrey A. Fessler,et al.  Uniform quadratic penalties cause nonuniform spatial resolution , 1994, Proceedings of 1994 IEEE Nuclear Science Symposium - NSS'94.

[10]  M R Palmer,et al.  Scatter distribution in transmission measurements with positron emission tomography. , 1986, Journal of computer assisted tomography.

[11]  E. Hoffman,et al.  Quantitation in positron emission computed tomography: 7. A technique to reduce noise in accidental coincidence measurements and coincidence efficiency calibration. , 1986, Journal of computer assisted tomography.

[12]  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.

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

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

[15]  J. Besag.  On the Statistical Analysis of Dirty Pictures , 1986 .

[16]  Simon R. Cherry,et al.  A statistical approach to transmission image reconstruction from ring source calibration measurements in PET , 1992, IEEE Conference on Nuclear Science Symposium and Medical Imaging.

[17]  Joseph A. O'Sullivan,et al.  Roughness penalties on finite domains , 1995, IEEE Trans. Image Process..

[18]  M Schwaiger,et al.  Comparison of americium-241 and technetium-99m as transmission sources for attenuation correction of thallium-201 SPECT imaging of the heart. , 1994, Journal of nuclear medicine : official publication, Society of Nuclear Medicine.

[19]  Ehud Weinstein,et al.  Parameter estimation of superimposed signals using the EM algorithm , 1988, IEEE Trans. Acoust. Speech Signal Process..

[20]  Ilan Ziskind,et al.  Maximum likelihood localization of multiple sources by alternating projection , 1988, IEEE Trans. Acoust. Speech Signal Process..

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

[22]  S. Lauritzen,et al.  Globally convergent algorithms for maximizing a likelihood function , 1991 .

[23]  Kenneth Lange,et al.  Numerical analysis for statisticians , 1999 .

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

[25]  E.U. Mumcuoglu,et al.  A gradient projection conjugate gradient algorithm for Bayesian PET reconstruction , 1994, Proceedings of 1994 IEEE Nuclear Science Symposium - NSS'94.

[26]  Jeffrey A. Fessler.  Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): applications to tomography , 1996, IEEE Trans. Image Process..

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

[28]  Kenneth Lange,et al.  Overview of Bayesian methods in image reconstruction , 1990, Optics & Photonics.

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

[30]  Albert Macovski,et al.  A Maximum Likelihood Approach to Transmission Image Reconstruction from Projections , 1977, IEEE Transactions on Nuclear Science.

[31]  Jean-Jacques Fuchs,et al.  Detection and estimation of superimposed signals , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

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

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

[34]  E.J. Hoffman,et al.  High sensitivity, total body PET scanning using 3D data acquisition and reconstruction , 1991, Conference Record of the 1991 IEEE Nuclear Science Symposium and Medical Imaging Conference.

[35]  Jeffrey A. Fessler,et al.  Fast parallelizable algorithms for transmission image reconstruction , 1995, 1995 IEEE Nuclear Science Symposium and Medical Imaging Conference Record.

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

[37]  S R Cherry,et al.  Attenuation correction using count-limited transmission data in positron emission tomography. , 1993, Journal of nuclear medicine : official publication, Society of Nuclear Medicine.

[38]  Gabor T. Herman,et al.  Image reconstruction from projections : the fundamentals of computerized tomography , 1980 .

[39]  Linda Kaufman,et al.  Maximum likelihood, least squares, and penalized least squares for PET , 1993, IEEE Trans. Medical Imaging.

[40]  J. Cadzow,et al.  Signal processing via least squares error modeling , 1990, IEEE ASSP Magazine.

[41]  David S. Lalush,et al.  MAP-EM And WLS-MAP-CG Reconstruction Methods For Transmission Imaging In Cardiac SPECT , 1993, 1993 IEEE Conference Record Nuclear Science Symposium and Medical Imaging Conference.

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

[43]  Benjamin M. W. Tsui,et al.  Maximum Entropy Reconstruction with Constraints: Iterative Algorithms for Solving the Primal and Dual Programs , 1988 .

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