5D image reconstruction exploiting space-motion-echo sparsity for accelerated free-breathing quantitative liver MRI

Recent advances in 3D non-Cartesian multi-echo gradient-echo (mGRE) imaging and compressed sensing (CS)-based 4D (3D image space + 1D respiratory motion) motion-resolved image reconstruction, which applies temporal total variation to the respiratory motion dimension, have enabled free-breathing liver tissue MR parameter mapping. This technology now allows for robust reconstruction of high-resolution proton density fat fraction (PDFF), R${}_2^{\ast }$, and quantitative susceptibility mapping (QSM), previously unattainable with conventional Cartesian mGRE imaging. However, long scan times remain a persistent challenge in free-breathing 3D non-Cartesian mGRE imaging. Recognizing that the underlying dimension of the imaging data is essentially 5D (4D + 1D echo signal evolution), we propose a CS-based 5D motion-resolved mGRE image reconstruction method to further accelerate the acquisition. Our approach integrates discrete wavelet transforms along the echo and spatial dimensions into a CS-based reconstruction model and devises a solution algorithm capable of handling such a 5D complex-valued array. Through phantom and in vivo human subject studies, we evaluated the effectiveness of leveraging unexplored correlations by comparing the proposed 5D reconstruction with the 4D reconstruction (i.e., motion-resolved reconstruction with temporal total variation) across a wide range of acceleration factors. The 5D reconstruction produced more reliable and consistent measurements of PDFF, R${}_2^{\ast }$, and QSM compared to the 4D reconstruction. In conclusion, the proposed 5D motion-resolved image reconstruction demonstrates the feasibility of achieving accelerated, reliable, and free-breathing liver mGRE imaging for the measurement of PDFF, R${}_2^{\ast }$, and QSM.