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 (T 1-weighted, T 2-weighted, fluid-attenuated inversion recovery, and T 1-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 parallelimaging-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 | 3257 YI et al.

Accelerated calibrationless parallel transmit mapping using joint transmit and receive low‐rank tensor completion

“…While this paper was under review, a method for multi-contrast Hankel tensor completion was published, which also leveraged a low-rank Hankel-structed tensor model for undersampled image recovery. 30 In agreement with our work, they found improved reconstruction fidelity when multiple acquisitions are jointly reconstructed in a low-rank tensor framework by enforcing low-rankness on different tensor unfoldings simultaneously. However, there are several differences in the 2 approaches.…”

Improving robustness of 3D multi-shot EPI by structured low-rank reconstruction of segmented CAIPI sampling for fMRI at 7T

“…The moderate phase variations in fMRI typically do not lead to visible artifacts in the calculated coil sensitivities. However, in the worst case scenario when high fidelity coil sensitivity maps cannot be obtained from the multi-shot calibration data, alternative approaches can be used, such as employing the low-rank tensor representation (Hess et al, 2021; Liu et al, 2021; Yi et al, 2021) of multi-channel k-space for a calibration-less reconstruction without explicit use of coil sensitivity maps, or using a calibration consistency constraint that jointly identifies a coilnullspace from the imaging and calibration data, without trusting either dataset completely (Lobos et al, 2021). In addition, we did not use partial Fourier sampling in this work, which is also compatible with the seg-CAIPI trajectory.…”

“…The proposed approach is based on MUSSELS (Mani et al, 2017), a method using Hankel structured low-rank matrix completion to reconstruct multi-shot diffusion weighted images. The idea of structured low-rank matrix completion has also been successfully employed in some other applications such as calibration-less parallel imaging reconstruction (Liu et al, 2021;Shin et al, 2014;Yi et al, 2021), EPI Nyquist ghost correction (Haldar and Zhuo, 2016;Lee et al, 2016b;Lobos et al, 2021), and trajectory error correction (Mani et al, 2018).The inherent linear dependency of the phase-corrupted multi-shot data has enabled us to leverage the low-rank constraint on its Hankel matrix representation, assuming image phase fluctuations driven by respiration are relatively spatially smooth, an assumption which has been employed in other work (Wallace et al, 2020). The reconstruction strategy employed here empirically estimated hyperparameters by optimizing for resulting tSNR, which provides a useful heuristic for hyperparameter tuning without requiring any additional training data or prior knowledge.…”

Deep Learning‐Based Diffusion‐Weighted Magnetic Resonance Imaging in the Diagnosis of Ischemic Penumbra in Early Cerebral Infarction

“…Therefore, the deep learning algorithm is applied to image denoising of DWI [ 10 ]. MR image denoising algorithm based on higher-order singular value decomposition (HOSVD) [ 11 ] has a good denoising effect, especially in T1-weighted (T1w), T2-weighted (T2w), and proton density-weighted (PDw) image noise processing [ 12 – 14 ]. However, compared with conventional MR, there is more redundant information in DWI images.…”