Dynamic MRI reconstruction from highly undersampled (k, t)-space data using weighted Schatten p-norm regularizer of tensor.
Combination of the low-rankness and sparsity has been successfully used to reconstruct desired dynamic magnetic resonance image (MRI) from highly-undersampled (k, t)-space data. However, nuclear norm, as a convex relaxation of the rank function, can cause the solution deviating from the original solution of low-rank problem. Moreover, equally treating different rank component is not flexible to deal with real applications. In this paper, an efficient reconstruction model is proposed to efficiently reconstruct dynamic MRI. First, we treat dynamic MRI as a 3rd-order tensor, and formulate the low-rankness via non-convex Schatten p-norm of matrices unfolded from the tensor. Secondly, we assign different weight for each rank component in Schatten p-norm. Furthermore, we combine the proposed weighted Schatten p-norm of a tensor as low-rank regularizer, and spatiotemporal total variation as sparse regularizer to formulate the reconstruction model for dynamic MRI. Thirdly, to efficiently solve the formulated reconstruction model, we derive an algorithm based on Bregman iterations with alternating direction multiplier. Over two public data sets of dynamic MRI, experiments demonstrate that the proposed method achieves much better quality.
School of Electrical Engineering and Information, Sichuan University, No.24 South Section 1, Yihuan Road, Chengdu, China.
Xiaomei
X
Yang
School of Electrical Engineering and Information, Sichuan University, No.24 South Section 1, Yihuan Road, Chengdu, China.
Yuewan
Y
Luo
School of Electrical Engineering and Information, Sichuan University, No.24 South Section 1, Yihuan Road, Chengdu, China.
Siji
S
Chen
School of Electrical Engineering and Information, Sichuan University, No.24 South Section 1, Yihuan Road, Chengdu, China.
Xiujuan
X
Zhen
School of Electrical Engineering and Information, Sichuan University, No.24 South Section 1, Yihuan Road, Chengdu, China.
Qin
Q
Yu
School of Electrical Engineering and Information, Sichuan University, No.24 South Section 1, Yihuan Road, Chengdu, China.
Kai
K
Liu
D000465:Algorithms; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008962:Models, Theoretical
Alternating direction multiplier method; Low-rankness; Spatiotemporal total variation; Tensor; Weighted Schatten p-norm