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

Yair Censor, Dan Gordon, Rachel Gordon

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)1050-1060
Number of pages11
JournalIEEE Transactions on Medical Imaging
Issue number10
StatePublished - 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:


  • 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


Dive into the research topics of 'BICAV: A block-iterative parallel algorithm for sparse systems with pixel-related weighting'. Together they form a unique fingerprint.

Cite this