Low-Rank Tensor Models for Improved Multi-Dimensional MRI: Application to Dynamic Cardiac T 1 Mapping.

Multi-dimensional, multi-contrast magnetic resonance imaging (MRI) has become increasingly available for comprehensive and time-efficient evaluation of various pathologies, providing large amounts of data and offering new opportunities for improved image reconstructions. Recently, a cardiac phase-resolved myocardial T 1 mapping method has been introduced to provide dynamic information on tissue viability. Improved spatio-temporal resolution in clinically acceptable scan times is highly desirable but requires high acceleration factors. Tensors are well-suited to describe inter-dimensional hidden structures in such multi-dimensional datasets. In this study, we sought to utilize and compare different tensor decomposition methods, without the use of auxiliary navigator data. We explored multiple processing approaches in order to enable high-resolution cardiac phase-resolved myocardial T 1 mapping. Eight different low-rank tensor approximation and processing approaches were evaluated using quantitative analysis of accuracy and precision in T 1 maps acquired in six healthy volunteers. All methods provided comparable T 1 values. However, the precision was significantly improved using local processing, as well as a direct tensor rank approximation. Low-rank tensor approximation approaches are well-suited to enable dynamic T 1 mapping at high spatio-temporal resolutions.

Locally Low-Rank Tensor Regularization for High-Resolution Quantitative Dynamic MRI.

Quantitative dynamic MRI acquisitions have the potential to diagnose diffuse diseases in conjunction with functional abnormalities. However, their resolutions are limited due to the long acquisition time. Such datasets are multi-dimensional, exhibiting interactions between ≥ 4 dimensions, which cannot be easily identified using sparsity or low-rank matrix methods. Hence, low-rank tensors are a natural fit to model such data. But in the presence of multitude of different tissue types in the field-of-view, it is difficult to find an appropriate value of tensor rank, which avoids under- or over-regularization. In this work, we propose a locally low-rank tensor regularization approach to enable high-resolution quantitative dynamic MRI. We show this approach successfully enables dynamic T 1 mapping at high spatio-temporal resolutions.