Compressed sensing MRI: a review from signal processing perspective

Abstract

Magnetic resonance imaging (MRI) is an inherently slow imaging modality, since it acquires multi-dimensional k-space data through 1-D free induction decay or echo signals. This often limits the use of MRI, especially for high resolution or dynamic imaging. Accordingly, many investigators has developed various acceleration techniques to allow fast MR imaging. For the last two decades, one of the most important breakthroughs in this direction is the introduction of compressed sensing (CS) that allows accurate reconstruction from sparsely sampled k-space data. The recent FDA approval of compressed sensing products for clinical scans clearly reflect the maturity of this technology. Therefore, this paper reviews the basic idea of CS and how this technology have been evolved for various MR imaging problems.

Keywords: MRI; compressed sensing; k-space.

Fig. 1

Various types of sparsity in MRI. (a) Sparsity from spatial domain redundancy, (b) Sparsity from temporal redundancy, and (c) sparsity from mu.ti-channel redundancy

Fig. 2

Various under-sampling patterns: (a) Cartesian undersampling, (b) radial undersampling, and (c) spiral undersampling

Fig. 3

Construction of Hankel matrix for MR parameter mapping [59]

Fig. 4

Construction of Hankel matrix for multi-channel filter data for the case of MR parameter mapping [59]