Accelerating cardiac diffusion tensor imaging combining local low-rank and 3D TV constraint

Objective Diffusion tensor magnetic resonance imaging (DT-MRI, or DTI) is a promising technique for invasively probing biological tissue structures. However, DTI is known to suffer from much longer acquisition time with respect to conventional MRI and the problem is worsened when dealing with in vivo acquisitions. Therefore, faster DTI for both ex vivo and in vivo scans is highly desired. Materials and methods This paper proposes a new compressed sensing (CS) reconstruction method that employs local low-rank (LLR) model and three-dimensional (3D) total variation (TV) constraint to reconstruct cardiac diffusion-weighted (DW) images from highly undersampled k-space data. The LLR model takes the set of DW images corresponding to different diffusion gradient directions as a 3D image volume and decomposes the latter into overlapping 3D blocks. Then, the 3D blocks are stacked as two-dimensional (2D) matrix. Finally, low-rank property is applied to each block matrix and the 3D TV constraint to the 3D image volume. The underlying constrained optimization problem is finally solved using the first-order fast method. The proposed method is evaluated on real ex vivo cardiac DTI data as a prerequisite to in vivo cardiac DTI applications. Results The results on real human ex vivo cardiac DTI images demonstrate that the proposed method exhibits lower reconstruction errors for DTI indices, including fractional anisotropy (FA), mean diffusivities (MD), transverse angle (TA), and helix angle (HA), compared to existing CS-based DTI image reconstruction techniques. Conclusion The proposed method provides better reconstruction quality and more accurate DTI indices in comparison with the state-of-the-art CS-based DW image reconstruction methods.