A cosparse analysis model with combined redundant systems for MRI reconstruction

Abstract

Purpose Magnetic resonance imaging (MRI) is widely used due to its noninvasive and nonionizing properties. However, MRI requires a long scanning time. In this paper, our goal is to reconstruct a high‐quality MR image from its sampled k‐space data to accelerate the data acquisition in MRI. Methods We propose a cosparse analysis model with combined redundant systems to fully exploit the sparsity of MR images. Two fixed redundant systems are used to characterize different structures, namely, the wavelet tight frame and Gabor frame. An alternating iteration scheme is used for reconstruction with simple implementation and good performance. Results The proposed method is tested on two MR images under three sampling patterns with sampling ratios ranging from 10% to 60%. The results show that the proposed method outperforms other state‐of‐the‐art MRI reconstruction methods in terms of both subjective visual quality and objective quantitative measurement. For instance, for brain images under random sampling with a ratio of 10%, compared to the other three methods, the proposed method improves the peak signal‐to‐noise ratio (PSNR) by more than 9 dB. Conclusions To better characterize different sparsities of different structures of MRI, a cosparse analysis model combining the wavelet tight frame and Gabor frame is proposed. A partial ℓ2 norm regularization is leveraged to obtain the optimal solution in a lower dimension. Compared to other state‐of‐the‐art MRI reconstruction methods, the proposed method improves the reconstruction quality of MRI, especially highly undersampled MRI.