[Compressed sensing magnetic resonance image reconstruction based on double sparse model]

Abstract

The medical magnetic resonance (MR) image reconstruction is one of the key technologies in the field of magnetic resonance imaging (MRI). The compressed sensing (CS) theory indicates that the image can be reconstructed accurately from highly undersampled measurements by using the sparsity of the MR image. However, how to improve the image reconstruction quality by employing more sparse priors of the image becomes a crucial issue for MRI. In this paper, an adaptive image reconstruction model fusing the double dictionary learning is proposed by exploiting sparse priors of the MR image in the image domain and transform domain. The double sparse model which combines synthesis sparse model with sparse transform model is applied to the CS MR image reconstruction according to the complementarity of synthesis sparse and sparse transform model. Making full use of the two sparse priors of the image under the synthesis dictionary and transform dictionary learning, the proposed model is tackled in stages by the iterative alternating minimization algorithm. The solution procedure needs to utilize the synthesis and transform K-singular value decomposition (K-SVD) algorithms. Compared with the existing MRI models, the experimental results show that the proposed model can more efficiently improve the quality of the image reconstruction, and has faster convergence speed and better robustness to noise.

Keywords: compressed sensing; image reconstruction; magnetic resonance image; sparse transform model; synthesis sparse model.

图 1

MR test images MR 测试图像

图 2

PSNR and HFEN changing curves of Brain image along with iterations Brain 图像的 PSNR 与 HFEN 随迭代次数的变化曲线

图 3

Reconstruction results of the local Brain image (the original part is the region which is in the white rectangle of Fig.1b) by 2D variable density random sampling 2D 变密度随机采样下 Brain 图像的局部（图 1b 中白框标注区域为本图的原图）重构结果放大图

图 4

The t2axialbrain image reconstruction results and errors of different models under pseudo radial sampling 伪射线采样下 t2axialbrain 图像的不同模型重构结果及重构误差图