A divide-and-conquer approach to compressed sensing MRI.Magn Reson Imaging 2019; 63:37-48MR
Compressed sensing (CS) theory assures us that we can accurately reconstruct magnetic resonance images using fewer k-space measurements than the Nyquist sampling rate requires. In traditional CS-MRI inversion methods, the fact that the energy within the Fourier measurement domain is distributed non-uniformly is often neglected during reconstruction. As a result, more densely sampled low frequency information tends to dominate penalization schemes for reconstructing MRI at the expense of high frequency details. In this paper, we propose a new framework for CS-MRI inversion in which we decompose the observed k-space data into "subspaces" via sets of filters in a lossless way, and reconstruct the images in these various spaces individually using off-the-shelf algorithms. We then fuse the results to obtain the final reconstruction. In this way, we are able to focus reconstruction on frequency information within the entire k-space more equally, preserving both high and low frequency details. We demonstrate that the proposed framework is competitive with state-of-the-art methods in CS-MRI in terms of quantitative performance, and often improves an algorithm's results qualitatively compared with its direct application to k-space.