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Title: A wavelet phase filter for emission tomography

Abstract

The presence of a high level of noise is a characteristic in some tomographic imaging techniques such as positron emission tomography (PET). Wavelet methods can smooth out noise while preserving significant features of images. Mallat et al. proposed a wavelet based denoising scheme exploiting wavelet modulus maxima, but the scheme is sensitive to noise. In this study, the authors explore the properties of wavelet phase, with a focus on reconstruction of emission tomography images. Specifically, they show that the wavelet phase of regular Poisson noise under a Haar-type wavelet transform converges in distribution to a random variable uniformly distributed on [0, 2{pi}). They then propose three wavelet-phase-based denoising schemes which exploit this property: edge tracking, local phase variance thresholding, and scale phase variation thresholding. Some numerical results are also presented. The numerical experiments indicate that wavelet phase techniques show promise for wavelet based denoising methods.

Authors:
;  [1]
  1. Illinois Inst. of Tech., Chicago, IL (United States). Dept. of Mathematics
Publication Date:
Research Org.:
Argonne National Lab., IL (United States)
Sponsoring Org.:
USDOE, Washington, DC (United States)
OSTI Identifier:
95206
Report Number(s):
ANL/MCS/CP-85724; CONF-950472-17
ON: DE95013668; TRN: 95:019206
DOE Contract Number:  
W-31109-ENG-38
Resource Type:
Technical Report
Resource Relation:
Conference: SPIE international symposium on aerospace/defense sensing and dual-use photonics, Orlando, FL (United States), 17-21 Apr 1995; Other Information: PBD: [1995]
Country of Publication:
United States
Language:
English
Subject:
55 BIOLOGY AND MEDICINE, BASIC STUDIES; POSITRON COMPUTED TOMOGRAPHY; DIGITAL FILTERS; NOISE; TECHNOLOGY ASSESSMENT; IMAGE PROCESSING; EXPERIMENTAL DATA

Citation Formats

Olsen, E.T., and Lin, B. A wavelet phase filter for emission tomography. United States: N. p., 1995. Web. doi:10.2172/95206.
Olsen, E.T., & Lin, B. A wavelet phase filter for emission tomography. United States. doi:10.2172/95206.
Olsen, E.T., and Lin, B. Sat . "A wavelet phase filter for emission tomography". United States. doi:10.2172/95206. https://www.osti.gov/servlets/purl/95206.
@article{osti_95206,
title = {A wavelet phase filter for emission tomography},
author = {Olsen, E.T. and Lin, B.},
abstractNote = {The presence of a high level of noise is a characteristic in some tomographic imaging techniques such as positron emission tomography (PET). Wavelet methods can smooth out noise while preserving significant features of images. Mallat et al. proposed a wavelet based denoising scheme exploiting wavelet modulus maxima, but the scheme is sensitive to noise. In this study, the authors explore the properties of wavelet phase, with a focus on reconstruction of emission tomography images. Specifically, they show that the wavelet phase of regular Poisson noise under a Haar-type wavelet transform converges in distribution to a random variable uniformly distributed on [0, 2{pi}). They then propose three wavelet-phase-based denoising schemes which exploit this property: edge tracking, local phase variance thresholding, and scale phase variation thresholding. Some numerical results are also presented. The numerical experiments indicate that wavelet phase techniques show promise for wavelet based denoising methods.},
doi = {10.2172/95206},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sat Jul 01 00:00:00 EDT 1995},
month = {Sat Jul 01 00:00:00 EDT 1995}
}

Technical Report:

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