A Quantitative Criterion for Selecting the Optimal Sparse Representation of Dynamic Cardiac Data in Compressed Mri

One of the important performance factors in compressed sensing (CS) reconstructions is the level of sparsity in sparse representation of the signal. The goal in CS is to find the sparsest representation of the underlying signal or image. However, for compressible or nearly sparse signals such as dynamic cardiac MR data, the quantification of sparsity is quite subjective due to issues such as dropped SNR or low contrast to noise ratio (CNR) in sparse domains such as x-f space or temporal difference domains. Hence, we need a criterion to compare different sparse representations of compressible signals. In this paper, we define a model that can fit the decay of practical compressible signals and as an application; we verify that this model can be used as a basis for selecting the optimal sparse representation of dynamic cardiac MR data.