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Title: Filter banks and the EM algorithm

Abstract

In this paper, we present a wavelet based modification of the ML-EM algorithm for reconstructing positron emission tomography images. By using the filter bank implementation of the wavelet transform, this algorithm has the flexibility to incorporate a priori information, while maintaining the same computational complexity as the standard ML-EM algorithm. Thus, it has a significant computational advantage over usual Bayesian methods. It differs from recent wavelet-based Bayesian methods as it achieves {open_quotes}regularization{close_quotes} by an adaptive, wavelet-based method of thresholding which minimizes Stein`s Unbiased Estimate of Risk. The basic method consists of applying Donoho and Johnstone`s SureShrink wavelet denoising of the Poisson data, and then applying the standard ML-EM algorithm to the denoised data. A more elaborate method is discussed in which a wavelet denoising step is inserted after each EM iteration. This technique differs from previous smoothing techniques applied to the ML-EM algorithm since it is able to recover edges in discontinuous images.

Authors:
; ;  [1]
  1. Univ. of Florida, Gainesville, FL (United States)
Publication Date:
OSTI Identifier:
513288
Report Number(s):
CONF-961123-
CNN: Grant DMS 9623077; TRN: 97:014340
Resource Type:
Conference
Resource Relation:
Conference: Institute of Electrical and Electronic Engineers (IEEE) nuclear science symposium and medical imaging conference, Anaheim, CA (United States), 2-9 Nov 1996; Other Information: PBD: 1996; Related Information: Is Part Of 1996 IEEE nuclear science symposium - conference record. Volumes 1, 2 and 3; Del Guerra, A. [ed.]; PB: 2138 p.
Country of Publication:
United States
Language:
English
Subject:
44 INSTRUMENTATION, INCLUDING NUCLEAR AND PARTICLE DETECTORS; 55 BIOLOGY AND MEDICINE, BASIC STUDIES; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; POSITRON COMPUTED TOMOGRAPHY; IMAGE PROCESSING; ALGORITHMS; ITERATIVE METHODS; MAXIMUM-LIKELIHOOD FIT; FILTERS

Citation Formats

Mair, B.A., Carroll, R.B., and Anderson, J.M.M.. Filter banks and the EM algorithm. United States: N. p., 1996. Web.
Mair, B.A., Carroll, R.B., & Anderson, J.M.M.. Filter banks and the EM algorithm. United States.
Mair, B.A., Carroll, R.B., and Anderson, J.M.M.. 1996. "Filter banks and the EM algorithm". United States. doi:.
@article{osti_513288,
title = {Filter banks and the EM algorithm},
author = {Mair, B.A. and Carroll, R.B. and Anderson, J.M.M.},
abstractNote = {In this paper, we present a wavelet based modification of the ML-EM algorithm for reconstructing positron emission tomography images. By using the filter bank implementation of the wavelet transform, this algorithm has the flexibility to incorporate a priori information, while maintaining the same computational complexity as the standard ML-EM algorithm. Thus, it has a significant computational advantage over usual Bayesian methods. It differs from recent wavelet-based Bayesian methods as it achieves {open_quotes}regularization{close_quotes} by an adaptive, wavelet-based method of thresholding which minimizes Stein`s Unbiased Estimate of Risk. The basic method consists of applying Donoho and Johnstone`s SureShrink wavelet denoising of the Poisson data, and then applying the standard ML-EM algorithm to the denoised data. A more elaborate method is discussed in which a wavelet denoising step is inserted after each EM iteration. This technique differs from previous smoothing techniques applied to the ML-EM algorithm since it is able to recover edges in discontinuous images.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 1996,
month =
}

Conference:
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  • Abstract not provided.