Journal article
Quantifying Admissible Undersampling for Sparsity-Exploiting Iterative Image Reconstruction in X-Ray CT
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.
Language: | English |
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Publisher: | IEEE |
Year: | 2013 |
Pages: | 460-473 |
ISSN: | 1558254x and 02780062 |
Types: | Journal article |
DOI: | 10.1109/TMI.2012.2230185 |
ORCIDs: | Jørgensen, Jakob Heide |
Algorithms Artifacts Compressed sensing (CS) Computed tomography Data models Detectors Image reconstruction Radiographic Image Enhancement Radiographic Image Interpretation, Computer-Assisted Reproducibility of Results Sample Size Sensitivity and Specificity Signal Processing, Computer-Assisted Tomography, X-Ray Computed Transforms X-ray imaging computed tomography (CT) data models image sampling iterative methods