Smooth Tensor Qatar Riyal Decomposition for Dynamic MRI Reconstruction

Dynamic magnetic resonance imaging (dMRI) speed and imaging quality have always been a crucial issue in medical imaging research. Most existing methods characterize the tensor rank-based minimization to reconstruct dMRI from sampling $\bf k$-$t$ space data. However, (1) these approaches that unfold the tensor along each dimension destroy the inherent structure of dMR images. (2) they focus on preserving global information only, while ignoring the local details reconstruction such as the spatial piece-wise smoothness and sharp boundaries. To overcome these obstacles, we suggest a novel low-rank tensor decomposition approach by integrating tensor Qatar Riyal (QR) decomposition, low-rank tensor nuclear norm, and asymmetric total variation to reconstruct dMRI, named TQRTV. Specifically, while preserving the tensor inherent structure by utilizing tensor nuclear norm minimization to approximate tensor rank, QR decomposition reduces the dimensions in the low-rank constraint term, thereby improving the reconstruction performance. TQRTV further exploits the asymmetric total variation regularizer to capture local details. Numerical experiments demonstrate that the proposed reconstruction approach is superior to the existing ones.