Dynamic Cardiac MRI Reconstruction Using Combined Tensor Nuclear Norm and Casorati Matrix Nuclear Norm Regularizations

TL;DR

This paper introduces TMNN, a novel framework combining tensor nuclear norm and Casorati matrix nuclear norm regularizations for improved dynamic cardiac MRI reconstruction, leveraging spatial and temporal data correlations.

Contribution

The paper proposes a new combined regularization method (TMNN) for dynamic MRI reconstruction, enhancing performance over traditional methods by exploiting multiple data structures.

Findings

Improved reconstruction quality in cardiac MRI datasets.

Faster computation with the proposed algorithm under Cartesian sampling.

Demonstrated superior performance over traditional Casorati nuclear norm methods.

Abstract

Low-rank tensor models have been applied in accelerating dynamic magnetic resonance imaging (dMRI). Recently, a new tensor nuclear norm based on t-SVD has been proposed and applied to tensor completion. Inspired by the different properties of the tensor nuclear norm (TNN) and the Casorati matrix nuclear norm (MNN), we introduce a combined TNN and Casorati MNN regularizations framework to reconstruct dMRI, which we term as TMNN. The proposed method simultaneously exploits the spatial structure and the temporal correlation of the dynamic MR data. The optimization problem can be efficiently solved by the alternating direction method of multipliers (ADMM). In order to further improve the computational efficiency, we develop a fast algorithm under the Cartesian sampling scenario. Numerical experiments based on cardiac cine MRI and perfusion MRI data demonstrate the performance improvement over the traditional Casorati nuclear norm regularization method.