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.