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

Details Quantification of admissible undersampling for sparsity-exploiting iterative image reconstruction in X-ray CT Quantification of admissible undersampling for sparsity-exploiting iterative image reconstruction in X-ray CT

2011-09-03

arxiv.org/abs/1109.0629v2

Physics

Medical Physics

Revised version that was submitted to IEEE Transaction on Medical Imaging on 2/8/2012

Scientific paper

Iterative image reconstruction (IIR) with sparsity-exploiting methods proposed in compressive sensing (CS) claim potentially large reductions in sampling requirements. Quantifying this claim for computed tomography (CT) is difficult, because both full sampling and the reduction in sampling admitted by sparsity-exploiting methods are ill-defined. CS does not provide answers, aside from designing the optimization problem, because the CT imaging model does not belong to any class of measurement matrices for which CS provides theoretical guarantees. This article addresses quantification of admissible undersampling through sparsity-exploiting methods. Four sufficient-sampling conditions (SSCs) are introduced and their use as a reference of full sampling is discussed. The derived SSCs are based only on the condition number of the system matrix. In numerical simulation studies in the setting of breast CT the SSCs are evaluated for quantifying undersampling admitted by total variation minimization. A direct connection between sparsity and admitted undersampling is found.

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