A Divide-and-Conquer Approach to Compressed Sensing MRI

TL;DR

This paper introduces a divide-and-conquer framework for compressed sensing MRI that decomposes k-space data into subspaces, reconstructs each separately, and fuses results to improve preservation of high and low frequency details.

Contribution

It proposes a novel subspace decomposition approach for CS-MRI that enhances reconstruction quality by more evenly handling frequency information.

Findings

Competitive with state-of-the-art in quantitative metrics

Often improves qualitative image details

Balances high and low frequency information effectively

Abstract

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 it's direct application to k-space.