A Bayesian Joint Mixture Framework for the Integration of Anatomical Information in Functional Image Reconstruction

We present a Bayesian joint mixture framework for integrating anatomical image intensity and region segmentation information into emission tomographic reconstruction in medical imaging. The joint mixture framework is particularly well suited for this problem and allows us to integrate additional available information such as anatomical region segmentation information into the Bayesian model. Since this information is independently available as opposed to being estimated, it acts as a good constraint on the joint mixture model. After specifying the joint mixture model, we combine it with the standard emission tomographic likelihood. The Bayesian posterior is a combination of this likelihood and the joint mixture prior. Since well known EM algorithms separately exist for both the emission tomography (ET) likelihood and the joint mixture prior, we have designed a novel EM2 algorithm that comprises two EM algorithms—one for the likelihood and one for the prior. Despite being dove-tailed in this manner, the resulting EM2 algorithm is an alternating descent algorithm that is guaranteed to converge to a local minimum of the negative log Bayesian posterior. Results are shown on synthetic images with bias/variance plots used to gauge performance. The EM2 algorithm resulting from the joint mixture framework has the best bias/variance performance when compared with six other closely related algorithms that incorporate anatomical information to varying degrees.

[1]  R. Hathaway.  Another interpretation of the EM algorithm for mixture distributions , 1986 .

[2]  Stephen J. Riederer,et al.  Medical imaging [6] , 1995 .

[3]  Joshua B. Tenenbaum,et al.  Separating Style and Content , 1996, NIPS.

[4]  Paul A. Viola,et al.  Multi-modal volume registration by maximization of mutual information , 1996, Medical Image Anal..

[5]  Richard M. Leahy,et al.  PET image reconstruction incorporating anatomical information using segmented regression , 1997, Medical Imaging.

[6]  M E Raichle,et al.  Regional Correction of Positron Emission Tomography Data for the Effects of Cerebral Atrophy , 1988, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[7]  V. D. de Sa.  Category learning through multimodality sensing. , 1998, Neural computation.

[8]  Alan L. Yuille,et al.  Statistical Physics, Mixtures of Distributions, and the EM Algorithm , 1994, Neural Computation.

[9]  Eric Mjolsness,et al.  Algebraic transformations of objective functions , 1990, Neural Networks.

[10]  Richard E. Carson,et al.  Multimodality Bayesian algorithm for image reconstruction in positron emission tomography: a tissue composition model , 1997, IEEE Transactions on Medical Imaging.

[11]  R. Redner,et al.  Mixture densities, maximum likelihood, and the EM algorithm , 1984 .

[12]  A. Evans,et al.  Correction for partial volume effects in PET: principle and validation. , 1998, Journal of nuclear medicine : official publication, Society of Nuclear Medicine.

[13]  B F Hutton,et al.  Minimum cross-entropy reconstruction of PET images using prior anatomical information. , 1996, Physics in medicine and biology.

[14]  Eric Mjolsness,et al.  Learning with Preknowledge: Clustering with Point and Graph Matching Distance Measures , 1996, Neural Computation.

[15]  Richard M. Leahy,et al.  Incorporation of Anatomical MR Data for Improved Dunctional Imaging with PET , 1991, IPMI.

[16]  H. Mayberg,et al.  Correction of PET Data for Partial Volume Effects in Human Cerebral Cortex by MR Imaging , 1990, Journal of computer assisted tomography.

[17]  Gene Gindi,et al.  The thin plate as a regularizer in Bayesian SPECT reconstruction , 1996, 1996 IEEE Nuclear Science Symposium. Conference Record.

[18]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.

[19]  Chin-Tu Chen,et al.  Incorporation of correlated structural images in PET image reconstruction , 1994, IEEE Trans. Medical Imaging.

[20]  Geoffrey J. McLachlan,et al.  Mixture models : inference and applications to clustering , 1989 .

[21]  Walter Oberschelp,et al.  Expectation maximization reconstruction of positron emission tomography images using anatomical magnetic resonance information , 1997, IEEE Transactions on Medical Imaging.

[22]  Dana H. Ballard,et al.  Category Learning Through Multimodality Sensing , 1998, Neural Computation.

[23]  Jerry L Prince,et al.  Measurement of Radiotracer Concentration in Brain Gray Matter Using Positron Emission Tomography: MRI-Based Correction for Partial Volume Effects , 1992, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

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

[25]  J. Fessler,et al.  Joint estimation for incorporating MRI anatomic images into SPECT reconstruction , 1994, Proceedings of 1994 IEEE Nuclear Science Symposium - NSS'94.

[26]  Anand Rangarajan,et al.  Bayesian reconstruction of functional images using anatomical information as priors , 1993, IEEE Trans. Medical Imaging.

[27]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.

[28]  T. Hebert,et al.  A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors. , 1989, IEEE transactions on medical imaging.

[29]  Ronald J. Jaszczak,et al.  Bayesian reconstruction and use of anatomical a priori information for emission tomography , 1996, IEEE Trans. Medical Imaging.