4 December 2000 Reconstruction in emission tomography via a Bayesian multiscale statistical framework
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Recently the authors introduced a general Bayesian statistical method for modeling and analysis in linear inverse problems involving certain types of count data. Emission-based tomography is medical imaging is a particularly important and common examples of this type of proem. In this paper we provide an overview of the methodology and illustrate its application to problems in emission tomography through a series of simulated and real- data examples. The framework rests on the special manner in which a multiscale representation of recursive dyadic partitions interacts with the statistical likelihood of data with Poisson noise characteristics. In particular, the likelihood function permits a factorization, with respect to location-scale indexing, analogous to the manner in which, say, an arbitrary signal allows a wavelet transform. Recovery of an object from tomographic data is the posed as a problem involving the statistical estimation of a multiscale parameter vector. A type of statistical shrinkage estimation is used, induced by careful choice of a Bayesian prior probability structure for the parameters. Finally, the ill-posedness of the tomographic imaging problem is accounted for by embedding the above-described framework within a larger, but simpler statistical algorithm problem, via the so-called Expectation-Maximization approach. The resulting image reconstruction algorithm is iterative in nature, entailing the calculation of two closed-form algebraic expression at each iteration. Convergence of the algorithm to a unique solution, under appropriate choice of Bayesian prior, can be assured.
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Eric D. Kolaczyk, Eric D. Kolaczyk, Robert D. Nowak, Robert D. Nowak, } "Reconstruction in emission tomography via a Bayesian multiscale statistical framework", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); doi: 10.1117/12.408647; https://doi.org/10.1117/12.408647

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