Phase-regularized and displacement-regularized compressed sensing for fast magnetic resonance elastography

Liver magnetic resonance elastography (MRE) is a noninvasive stiffness measurement technique that captures the tissue displacement in the phase of the signal. To limit the scanning time to a single breath-hold, liver MRE usually involves advanced readout techniques such as simultaneous multislice (SMS) or multishot methods. Furthermore, all these readout techniques require additional in-plane acceleration using either parallel imaging capabilities, such as sensitivity encoding (SENSE), or $$ -space undersampling, such as compressed sensing (CS). However, these methods apply a single regularization function on the complex image. This study aims to design and evaluate methods that use separate regularization on the magnitude and phase of MRE to exploit their distinct spatiotemporal characteristics. Specifically, we introduce two compressed sensing methods. The first method, termed phase-regularized compressed sensing (PRCS), applies a two-dimensional total variation (TV) prior to the magnitude and two-dimensional wavelet regularization to the phase. The second method, termed displacement-regularized compressed sensing (DRCS), exploits the spatiotemporal redundancy using 3D total variation on the magnitude. Additionally, DRCS includes a displacement fitting function to apply wavelet regularization to the displacement phasor. Both DRCS and PRCS were evaluated with different levels of compression factors in three datasets: an in silico abdomen dataset, an in vitro tissue-mimicking phantom, and an in vivo liver dataset. The reconstructed images were compared with the full sampled reconstruction, zero-filling reconstruction, wavelet-regularized compressed sensing, and a low rank plus sparse reconstruction. The metrics used for quantitative evaluation were the structural similarity index (SSIM) of magnitude (M-SSIM), displacement (D-SSIM), and shear modulus (S-SSIM), and mean shear modulus. Results from highly undersampled in silico and in vitro datasets demonstrate that the DRCS method provides higher reconstruction quality than the conventional compressed sensing method for a wide range of stiffness values. Notably, DRCS provides 24% and 22% increase in D-SSIM compared with CS for the in silico and in vitro datasets, respectively. Comparison with liver stiffness measured from full sampled data and highly undersampled data (CR=4) demonstrates that the DRCS method provided the strongest correlation ( $$ =0.95), second-lowest mean bias (-0.18 kPa, lowest for CS with -0.16 kPa), and lowest coefficient of variation (CV=3.6%). Our results demonstrate the potential of using DRCS to improve the reconstruction quality of accelerated MRE.