Filter banks and the EM algorithm
Abstract
In this paper, we present a wavelet based modification of the MLEM 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 MLEM algorithm. Thus, it has a significant computational advantage over usual Bayesian methods. It differs from recent waveletbased Bayesian methods as it achieves {open_quotes}regularization{close_quotes} by an adaptive, waveletbased 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 MLEM 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 MLEM algorithm since it is able to recover edges in discontinuous images.
 Authors:
 Univ. of Florida, Gainesville, FL (United States)
 Publication Date:
 OSTI Identifier:
 513288
 Report Number(s):
 CONF961123
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), 29 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; MAXIMUMLIKELIHOOD 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 MLEM 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 MLEM algorithm. Thus, it has a significant computational advantage over usual Bayesian methods. It differs from recent waveletbased Bayesian methods as it achieves {open_quotes}regularization{close_quotes} by an adaptive, waveletbased 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 MLEM 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 MLEM algorithm since it is able to recover edges in discontinuous images.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 1996,
month =
}

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