Quantifying admissible undersampling for sparsity-exploiting iterative image reconstruction in X-ray CT

IEEE Trans Med Imaging. 2013 Feb;32(2):460-73. doi: 10.1109/TMI.2012.2230185. Epub 2012 Nov 27.

Abstract

Iterative image reconstruction with sparsity-exploiting methods, such as total variation (TV) minimization, investigated in compressive sensing claim potentially large reductions in sampling requirements. Quantifying this claim for computed tomography (CT) is nontrivial, because both full sampling in the discrete-to-discrete imaging model and the reduction in sampling admitted by sparsity-exploiting methods are ill-defined. The present article proposes definitions of full sampling by introducing four sufficient-sampling conditions (SSCs). The SSCs are based on the condition number of the system matrix of a linear imaging model and address invertibility and stability. In the example application of breast CT, the SSCs are used as reference points of full sampling for quantifying the undersampling admitted by reconstruction through TV-minimization. In numerical simulations, factors affecting admissible undersampling are studied. Differences between few-view and few-detector bin reconstruction as well as a relation between object sparsity and admitted undersampling are quantified.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms*
  • Artifacts*
  • Radiographic Image Enhancement / methods*
  • Radiographic Image Interpretation, Computer-Assisted / methods*
  • Reproducibility of Results
  • Sample Size
  • Sensitivity and Specificity
  • Signal Processing, Computer-Assisted*
  • Tomography, X-Ray Computed / methods*