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Iterative image reconstruction (IIR) with sparsity-exploiting methods, suchas total variation (TV) minimization, investigated in compressive sensing (CS)claim potentially large reductions in sampling requirements. Quantifying thisclaim for computed tomography (CT) is non-trivial, because both full samplingin the discrete-to-discrete imaging model and the reduction in samplingadmitted by sparsity-exploiting methods are ill-defined. The present articleproposes definitions of full sampling by introducing four sufficient-samplingconditions (SSCs). The SSCs are based on the condition number of the systemmatrix of a linear imaging model and address invertibility and stability. Inthe example application of breast CT, the SSCs are used as reference points offull sampling for quantifying the undersampling admitted by reconstructionthrough TV-minimization. In numerical simulations, factors affecting admissibleundersampling are studied. Differences between few-view and few-detector binreconstruction as well as a relation between object sparsity and admittedundersampling are quantified.

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