Edge-preserving tomographic reconstruction with nonlocal regularizarion

F Yu, JA Fessler

Research output: Contribution to journalArticle (Academic Journal)peer-review

114 Citations (Scopus)

Abstract

Tomographic image reconstruction using statistical methods can provide more accurate system modeling, statistical models, and physical constraints than the conventional filtered backprojection (FBP) method. Because of the ill posedness of the reconstruction problem, a roughness penalty is often imposed on the solution to control noise. To avoid smoothing of edges, which are important image attributes, various edge-preserving regularization methods have been proposed. Most of these schemes rely on information from local neighborhoods to determine the presence of edges. In this paper, we propose a cost function that incorporates nonlocal boundary information into the regularization method. We use an alternating minimization algorithm with deterministic annealing to minimize the proposed cost function, jointly estimating region boundaries and object pixel values. We apply variational techniques implemented using level-sets methods to update the boundary estimates, then, using the most recent boundary estimate, we minimize a space-variant quadratic cost function to update the image estimate. For the positron emission tomography transmission reconstruction application, we compare the bias-variance tradeoff of this method with that of a "conventional" penalized-likelihood algorithm with local Huber roughness penalty.
Translated title of the contributionEdge-preserving tomographic reconstruction with nonlocal regularizarion
Original languageEnglish
Pages (from-to)159 - 173
Number of pages15
JournalIEEE Transactions on Medical Imaging
Volume21 (2)
DOIs
Publication statusPublished - Feb 2002

Bibliographical note

Publisher: IEEE - Inst Electrical Electronics Engineers Inc

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