Abstract
In this paper, we present a Bayesian image reconstruction approach for positron emission tomography (PET) using the wavelet decomposition. The image is decomposed via the wavelet transform into a selected number of subbands and each subband is modeled as a simultaneous autoregressive (SAR) Gaussian process. This decomposition allows the SAR processes to adjust independently to the distinctive characteristics of the subbands. Desirable features such as smoothness within regions and sharp transitions along the edges can be incorporated into the reconstruction algorithm. An iterative algorithm similar to the EM algorithm is proposed to solve this MAP image reconstruction problem. We seek to maximize the conditional likelihood of the image x, L(x), through the maximization of a sequence of functions {L n (x)} which approximate locally to L(x) near the current estimate x(n). By restricting L n (x) to be a separable function of x, maximizing L n (x) is trivial. We present a method of selecting such a sequence L n (x) based on x(n), and show that the sequence {x(n) converges to the MAP solution of L(x).
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© 1993 Springer-Verlag Berlin Heidelberg
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Wu, Z. (1993). MAP image reconstruction using wavelet decomposition. In: Barrett, H.H., Gmitro, A.F. (eds) Information Processing in Medical Imaging. IPMI 1993. Lecture Notes in Computer Science, vol 687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013799
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DOI: https://doi.org/10.1007/BFb0013799
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