BICAV: A block-iterative parallel algorithm for sparse systems with pixel-related weighting

Yair Censor; Dan Gordon; Rachel Gordon

doi:10.1109/42.959302

BICAV: A block-iterative parallel algorithm for sparse systems with pixel-related weighting

Research output: Contribution to journal › Article › peer-review

Abstract

Component averaging (CAV) was recently introduced by Censor, Gordon, and Gordon as a new iterative parallel technique suitable for large and sparse unstructured systems of linear equations. Based on earlier work of Byrne and Censor, it uses diagonal weighting matrices, with pixel-related weights determined by the sparsity of the system matrix. CAV is inherently parallel (similar to the very slowly converging Cimmino method) but its practical convergence on problems of image reconstruction from projections is similar to that of the algebraic reconstruction technique (ART). Parallel techniques are becoming more important for practical image reconstruction since they are relevant not only for supercomputers but also for the increasingly prevalent multiprocessor workstations. This paper reports on experimental results with a block-iterative version of component averaging (BICAV). When BICAV is optimized for block size and relaxation parameters, its very first iterates are far superior to those of CAV, and more or less on a par with ART. Similar to CAV, BICAV is also inherently parallel. The fast convergence is demonstrated on problems of image reconstruction from projections, using the SNARK93 image reconstruction software package. Detailed plots of various measures of convergence, and reconstructed images are presented.

Original language	English
Pages (from-to)	1050-1060
Number of pages	11
Journal	IEEE Transactions on Medical Imaging
Volume	20
Issue number	10
DOIs	https://doi.org/10.1109/42.959302
State	Published - Oct 2001

Bibliographical note

Funding Information:
Manuscript received May 24, 2000; revised July 10, 2001. This work was supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities under Grant 293/97 and Grant 592/00. The work of Y. Censor was supported by the National Institutes of Health (NIH) under Grant HL-28438 at the Medical Image Processing Group (MIPG), Department of Radiology, Hospital of the University of Pennsylvania, Philadelphia, PA. The Associate Editor responsible for coordinating the review of this paper and recommending its publication was R. Leahy. Asterisk indicates corresponding author. *Y. Censor is with the Department of Mathematics, University of Haifa, Mt. Carmel, Haifa 31905, Israel (e-mail: [email protected]).

Keywords

Block-iterative
Component averaging
Image reconstruction
Parallel processing
Pixel-related weighting
Sparse systems

ASJC Scopus subject areas

Software
Radiological and Ultrasound Technology
Computer Science Applications
Electrical and Electronic Engineering

Access to Document

10.1109/42.959302

Cite this

@article{f96fc93c56714362a5a74e588c2d0739,

title = "BICAV: A block-iterative parallel algorithm for sparse systems with pixel-related weighting",

abstract = "Component averaging (CAV) was recently introduced by Censor, Gordon, and Gordon as a new iterative parallel technique suitable for large and sparse unstructured systems of linear equations. Based on earlier work of Byrne and Censor, it uses diagonal weighting matrices, with pixel-related weights determined by the sparsity of the system matrix. CAV is inherently parallel (similar to the very slowly converging Cimmino method) but its practical convergence on problems of image reconstruction from projections is similar to that of the algebraic reconstruction technique (ART). Parallel techniques are becoming more important for practical image reconstruction since they are relevant not only for supercomputers but also for the increasingly prevalent multiprocessor workstations. This paper reports on experimental results with a block-iterative version of component averaging (BICAV). When BICAV is optimized for block size and relaxation parameters, its very first iterates are far superior to those of CAV, and more or less on a par with ART. Similar to CAV, BICAV is also inherently parallel. The fast convergence is demonstrated on problems of image reconstruction from projections, using the SNARK93 image reconstruction software package. Detailed plots of various measures of convergence, and reconstructed images are presented.",

keywords = "Block-iterative, Component averaging, Image reconstruction, Parallel processing, Pixel-related weighting, Sparse systems",

author = "Yair Censor and Dan Gordon and Rachel Gordon",

note = "Funding Information: Manuscript received May 24, 2000; revised July 10, 2001. This work was supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities under Grant 293/97 and Grant 592/00. The work of Y. Censor was supported by the National Institutes of Health (NIH) under Grant HL-28438 at the Medical Image Processing Group (MIPG), Department of Radiology, Hospital of the University of Pennsylvania, Philadelphia, PA. The Associate Editor responsible for coordinating the review of this paper and recommending its publication was R. Leahy. Asterisk indicates corresponding author. *Y. Censor is with the Department of Mathematics, University of Haifa, Mt. Carmel, Haifa 31905, Israel (e-mail: [email protected]).",

year = "2001",

month = oct,

doi = "10.1109/42.959302",

language = "English",

volume = "20",

pages = "1050--1060",

journal = "IEEE Transactions on Medical Imaging",

issn = "0278-0062",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "10",

}

TY - JOUR

T1 - BICAV

T2 - A block-iterative parallel algorithm for sparse systems with pixel-related weighting

AU - Censor, Yair

AU - Gordon, Dan

AU - Gordon, Rachel

N1 - Funding Information: Manuscript received May 24, 2000; revised July 10, 2001. This work was supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities under Grant 293/97 and Grant 592/00. The work of Y. Censor was supported by the National Institutes of Health (NIH) under Grant HL-28438 at the Medical Image Processing Group (MIPG), Department of Radiology, Hospital of the University of Pennsylvania, Philadelphia, PA. The Associate Editor responsible for coordinating the review of this paper and recommending its publication was R. Leahy. Asterisk indicates corresponding author. *Y. Censor is with the Department of Mathematics, University of Haifa, Mt. Carmel, Haifa 31905, Israel (e-mail: [email protected]).

PY - 2001/10

Y1 - 2001/10

N2 - Component averaging (CAV) was recently introduced by Censor, Gordon, and Gordon as a new iterative parallel technique suitable for large and sparse unstructured systems of linear equations. Based on earlier work of Byrne and Censor, it uses diagonal weighting matrices, with pixel-related weights determined by the sparsity of the system matrix. CAV is inherently parallel (similar to the very slowly converging Cimmino method) but its practical convergence on problems of image reconstruction from projections is similar to that of the algebraic reconstruction technique (ART). Parallel techniques are becoming more important for practical image reconstruction since they are relevant not only for supercomputers but also for the increasingly prevalent multiprocessor workstations. This paper reports on experimental results with a block-iterative version of component averaging (BICAV). When BICAV is optimized for block size and relaxation parameters, its very first iterates are far superior to those of CAV, and more or less on a par with ART. Similar to CAV, BICAV is also inherently parallel. The fast convergence is demonstrated on problems of image reconstruction from projections, using the SNARK93 image reconstruction software package. Detailed plots of various measures of convergence, and reconstructed images are presented.

AB - Component averaging (CAV) was recently introduced by Censor, Gordon, and Gordon as a new iterative parallel technique suitable for large and sparse unstructured systems of linear equations. Based on earlier work of Byrne and Censor, it uses diagonal weighting matrices, with pixel-related weights determined by the sparsity of the system matrix. CAV is inherently parallel (similar to the very slowly converging Cimmino method) but its practical convergence on problems of image reconstruction from projections is similar to that of the algebraic reconstruction technique (ART). Parallel techniques are becoming more important for practical image reconstruction since they are relevant not only for supercomputers but also for the increasingly prevalent multiprocessor workstations. This paper reports on experimental results with a block-iterative version of component averaging (BICAV). When BICAV is optimized for block size and relaxation parameters, its very first iterates are far superior to those of CAV, and more or less on a par with ART. Similar to CAV, BICAV is also inherently parallel. The fast convergence is demonstrated on problems of image reconstruction from projections, using the SNARK93 image reconstruction software package. Detailed plots of various measures of convergence, and reconstructed images are presented.

KW - Block-iterative

KW - Component averaging

KW - Image reconstruction

KW - Parallel processing

KW - Pixel-related weighting

KW - Sparse systems

UR - http://www.scopus.com/inward/record.url?scp=0035487602&partnerID=8YFLogxK

U2 - 10.1109/42.959302

DO - 10.1109/42.959302

M3 - Article

C2 - 11686440

AN - SCOPUS:0035487602

SN - 0278-0062

VL - 20

SP - 1050

EP - 1060

JO - IEEE Transactions on Medical Imaging

JF - IEEE Transactions on Medical Imaging

IS - 10

ER -

BICAV: A block-iterative parallel algorithm for sparse systems with pixel-related weighting

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this