College of Computer Science and Engineering, Northeastern University, Shenyang, Liaoning Province, 110819, China; Key Laboratory of Intelligent Computing in Medical Image, Ministry of Education, Northeastern University, Shenyang, Liaoning Province, 110819, China.
College of Computer Science and Engineering, Northeastern University, Shenyang, Liaoning Province, 110819, China.
Comput Biol Med. 2023 May;157:106780. doi: 10.1016/j.compbiomed.2023.106780. Epub 2023 Mar 11.
Compressed sensing magnetic resonance imaging (CS-MRI) has exhibited great potential to accelerate magnetic resonance imaging if an image can be sparsely represented. How to sparsify the image significantly affects the reconstruction quality of images. In this paper, a spectral graph wavelet transform (SGWT) is introduced to sparsely represent magnetic resonance images in iterative image reconstructions. The SGWT is achieved by extending the traditional wavelets transform to the signal defined on the vertices of the weighted graph, i.e. the spectral graph domain. This SGWT uses only the connectivity information encoded in the edge weights, and does not rely on any other attributes of the vertices. Therefore, SGWT can be defined and calculated for any domain where the underlying relations between data locations can be represented by a weighted graph. Furthermore, we present a Chebyshev polynomial approximation algorithm for fast computing this SGWT transform. The l norm regularized CS-MRI reconstruction model is introduced and solved by the projected iterative soft-thresholding algorithm to verify its feasibility. Numerical experiment results demonstrate that our proposed method outperforms several state-of-the-art sparsify transforms in terms of suppressing artifacts and achieving lower reconstruction errors on the tested datasets.
压缩感知磁共振成像（CS-MRI）如果能够对图像进行稀疏表示，则表现出了很大的加速磁共振成像的潜力。如何显著地稀疏化图像，会极大地影响图像的重建质量。在本文中，我们引入了谱图小波变换（SGWT），以便在迭代图像重建中稀疏地表示磁共振图像。通过将传统的小波变换扩展到定义在加权图顶点上的信号上，即谱图域，就可以实现 SGWT。这种 SGWT 仅使用边缘权重中编码的连接信息，而不依赖于顶点的任何其他属性。因此，SGWT 可以为任何可以通过加权图表示数据位置之间的基本关系的域定义和计算。此外，我们还提出了一种 Chebyshev 多项式逼近算法，用于快速计算这种 SGWT 变换。引入了 l 范数正则化 CS-MRI 重建模型，并通过投影迭代软阈值算法进行求解，以验证其可行性。数值实验结果表明，在测试数据集上，我们提出的方法在抑制伪影和实现更低的重建误差方面，优于几种最先进的稀疏化变换。
