Compressed Sensing Based Dynamic MR Image Reconstruction By Using 3D-Total Generalized Variation and Tensor Decomposition: k-t TGV-TD

Purpose: Compressed Sensing Magnetic Resonance Imaging (CS-MRI) is a promising technique to accelerate dynamic cardiac MR imaging (DCMRI). For DCMRI, the CS-MRI usually exploits image signal sparsity and low-rank property to reconstruct dynamic images from the undersampled k-space data. In this paper, a novel CS algorithm is investigated to improve dynamic cardiac MR image reconstruction quality under the condition of minimizing the k-space recording.Methods: The sparse representation of 3D cardiac magnetic resonance data is implemented by synergistically integrating 3D TGV algorithm and high order singular value decomposition (HOSVD) based Tensor Decomposition, termed as k-t TGV-TD method. In the proposed method, the low rank structure of the 3D dynamic cardiac MR data is performed by the HOSVD method, and the localized image sparsity is achieved by the 3D TGV method. Moreover, the Fast Composite Splitting Algorithm (FCSA) method, combining the variable splitting with operator splitting techniques, is employed to solve the low-rank and sparse problem. Two different cardiac MR datasets (cardiac cine and cardiac perfusion MR data) are used to evaluate the performance of the proposed method.Results: Compared with the state-of-art methods, such as the k-t SLR method, 3D TGV method and HOSVD based tensor decomposition method, the proposed method can offer improved reconstruction accuracy in terms of higher signal-to-error ratio (SER).Conclusions: This work proved that the k-t TGV-TD method was an effective sparse representation way for DC-MRI, which was capable of significantly improving the reconstruction accuracy with different reduction factor.