Joint calibrationless reconstruction of highly undersampled multicontrast MR datasets using a low-rank Hankel tensor completion framework

Abstract

Purpose: To jointly reconstruct highly undersampled multicontrast two-dimensional (2D) datasets through a low-rank Hankel tensor completion framework. Methods: A multicontrast Hankel tensor completion (MC-HTC) framework is proposed to exploit the shareable information in multicontrast datasets with respect to their highly correlated image structure, common spatial support, and shared coil sensitivity for joint reconstruction. This is achieved by first organizing multicontrast k-space datasets into a single block-wise Hankel tensor. Subsequent low-rank tensor approximation via higher-order singular value decomposition (HOSVD) uses the image structural correlation by considering different contrasts as virtual channels. Meanwhile, the HOSVD imposes common spatial support and shared coil sensitivity by treating data from different contrasts as from additional k-space kernels. The missing k-space data are then recovered by iteratively performing such low-rank approximation and enforcing data consistency. This joint reconstruction framework was evaluated using multicontrast multichannel 2D human brain datasets (T1-weighted, T2-weighted, fluid-attenuated inversion recovery, and T1-weighted-inversion recovery) of identical image geometry with random and uniform undersampling schemes. Results: The proposed method offered high acceleration, exhibiting significantly less residual errors when compared with both single-contrast SAKE (simultaneous autocalibrating and k-space estimation) and multicontrast J-LORAKS (joint parallel-imaging–low-rank matrix modeling of local k-space neighborhoods) low-rank reconstruction. Furthermore, the MC-HTC framework was applied uniquely to Cartesian uniform undersampling by incorporating a novel complementary k-space sampling strategy where the phase-encoding direction among different contrasts is orthogonally alternated. Conclusion: The proposed MC-HTC approach presents an effective tensor completion framework to jointly reconstruct highly undersampled multicontrast 2D datasets without coil-sensitivity calibration.