A semi-local paradigm for wavelet denoising

Richard Charnigo, Jiayang Sun, Raymond Muzic

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

Wavelet denoising methods have been proven useful for many one- and two-dimensional problems. Most existing methods can in principle be carried over to three-dimensional problems, such as the denoising of volumetric positron emission tomography (PET) images, but they may not be sufficiently flexible in allowing some regions of an image to be denoised more aggressively than others. In this paper, we propose a semi-local paradigm for wavelet denoising. The semi-local paradigm involves the division of an image into suitable blocks, which are then individually denoised. To denoise the blocks, we use our modification of the generalized cross validation (GCV) technique of Jansen and Bultheel [1] to choose thresholding parameters; we also present risk estimators to guide some of the other choices involved in the implementation. Experiments with phantom PET images show that the semi-local paradigm provides superior denoising compared to standard application of the GCV technique. An asymptotic analysis demonstrates that, under some regularity conditions, semi-local denoising is asymptotically consistent on the logarithmic scale. The paper concludes with a discussion on the nature of semi-local denoising and some topics for future research.

Original languageEnglish
Pages (from-to)666-677
Number of pages12
JournalIEEE Transactions on Image Processing
Volume15
Issue number3
DOIs
StatePublished - Mar 2006

Bibliographical note

Funding Information:
Manuscript received April 24, 2004; revised March 10, 2005. The work of R. Charnigo and J. Sun was supported in part by a grant from the National Science Foundation. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Truong Q. Nguyen. R. Charnigo is with the Department of Statistics, University of Kentucky, Lexington, KY 40506-0027 USA (e-mail: [email protected]). J. Sun is with the Department of Statistics, Case Western Reserve University, Cleveland, OH 44106-7054 USA (e-mail: [email protected]). R. Muzic, Jr., is with Nuclear Medicine, University Hospitals of Cleveland, Cleveland, OH 44106 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TIP.2005.863037

Keywords

  • Imaging
  • Logarithmic consistency
  • Positron emission tomography
  • Thresholding

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design

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