Impact of DFT properties on the inherent resolution of compressed sensing reconstructed images

Compressed sensing (CS) algorithms exploit sparseness properties to reconstruct high spatial resolution magnetic resonance (MR) images from k-space data acquisitions significantly under sampled to reduce imaging times. CS algorithm effectiveness is frequently shown using under-sampled k-space data from NxN simulated images. These demonstration reconstructions are near perfect with quality higher than reconstructions using under-sampled NxN experimental k-space data sets. These differences are explained in terms of the interaction between the explicit transform domain sparsity requirement employed during iterative CS reconstruction and an inherent frequency domain property of the discrete Fourier transform (DFT). We report on experiments to overcome the limitations imposed by this DFT property by modifying the CS objective function to use a sparseness transform with a resolution higher that the standard transform related to the acquired NxN data matrix size. We demonstrate the relative effectiveness and limitations of standard CS and our proposed highresolution k-space extrapolation enabled (Hi-KEE) CS reconstruction on underand fully-sampled, simulated and experimental MR k-space data.