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Titolo:
Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction
Autore:
Fessler, JA; Booth, SD;
Indirizzi:
Univ Michigan, Dept Elect Engn & Comp Sci, Ann Arbor, MI 48109 USA Univ Michigan Ann Arbor MI USA 48109 & Comp Sci, Ann Arbor, MI 48109 USA Univ Michigan, Dept Biomed Engn, Ann Arbor, MI 48109 USA Univ Michigan Ann Arbor MI USA 48109 Biomed Engn, Ann Arbor, MI 48109 USA Univ Virginia, Med Ctr, Charlottesville, VA 22906 USA Univ Virginia Charlottesville VA USA 22906 Charlottesville, VA 22906 USA
Titolo Testata:
IEEE TRANSACTIONS ON IMAGE PROCESSING
fascicolo: 5, volume: 8, anno: 1999,
pagine: 688 - 699
SICI:
1057-7149(199905)8:5<688:CPMFSP>2.0.ZU;2-A
Fonte:
ISI
Lingua:
ENG
Soggetto:
LEAST-SQUARES PROBLEMS; POSITRON EMISSION TOMOGRAPHY; MAXIMUM-LIKELIHOOD; TOEPLITZ-SYSTEMS; ITERATIVE RECONSTRUCTION; BAYESIAN RECONSTRUCTION; ALGORITHMS; TRANSMISSION; CONVERGENCE; RECOVERY;
Keywords:
circulant matrix; edge-preserving; image restoration; PET; tomography;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Engineering, Computing & Technology
Citazioni:
56
Recensione:
Indirizzi per estratti:
Indirizzo: Fessler, JA Univ Michigan, Dept Elect Engn & Comp Sci, Ann Arbor, MI 48109USA Univ Michigan Ann Arbor MI USA 48109 Ann Arbor, MI 48109 USA
Citazione:
J.A. Fessler e S.D. Booth, "Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction", IEEE IM PR, 8(5), 1999, pp. 688-699

Abstract

Gradient-based iterative methods often converge slowly for tomographic image reconstruction and image restoration problems, but can be accelerated bysuitable preconditioners, Diagonal preconditioners offer some improvement in convergence rate, but do not incorporate the structure of the Hessian matrices in imaging problems. Circulant preconditioners can provide remarkable acceleration for inverse problems that are approximately shift-invariant,i.e., for those with approximately block-Toeplitz or block-circulant Hessians, However, in applications with nonuniform noise variance, such as arises from Poisson statistics in emission tomography and in quantum-limited optical imaging, the Hessian of the weighted least-squares objective function is quite shift-variant, and circulant preconditioners perform poorly, Additional shift-variance is caused by edge-preserving regularization methods based on nonquadratic penalty functions. This paper describes new preconditioners that approximate more accurately the Hessian matrices of shift-variantimaging problems. Compared to diagonal or circulant preconditioning, the new preconditioners lead to significantly faster convergence rates for the unconstrained conjugate-gradient (CG) iteration. We also propose a new efficient method for the line-search step required by CG methods. Applications to positron emission tomography (PET) illustrate the method.

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Documento generato il 04/04/20 alle ore 02:48:49