Iterative image reconstruction (IIR) with sparsity-exploiting methods, such
as total variation (TV) minimization, investigated in compressive sensing (CS)
claim potentially large reductions in sampling requirements. Quantifying this
claim for computed tomography (CT) is non-trivial, 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.Comment: Revised version that was submitted to IEEE Transactions on Medical
Imaging on 8/16/201
