CS-MRI中评价随机欠采样矩阵的新方法

摘要

In compressed sensing magnetic resonance imaging (CS-MRI), the quality of reconstructed image is largely determined by the random undersampling matrix. It is a common practice to select the random undersampling matrix though computation of the point spread function (PSF) and the maximal artifacts possible. In this paper, we proposed to use two novel statistical parameters, mean value (MV) and standard deviation (SD), to guide the selection of random undersampling matrix. The two parameters evaluate the average amplitude and fluctuation of the possible artifacts, respectively. Experiments on mice brain and human brain were used to compare image quality of CS reconstructions of MRI data acquired with random undersampling matrices determined by different criteria. It was shown that reconstruction withMV had better performance when the sampling ratio is above four times of sparsity. It is concluded that better CS-MRI reconstruction quality can be achieved with reasonable selection of sampling ratio guided by prior knowledge of sparsity andMV as random undersampling matrix evaluation parameter.%在压缩感知-磁共振成像(CS-MRI)中，随机欠采样矩阵与重建图像质量密切相关。而选取随机欠采样矩阵一般是通过计算点扩散函数(PSF)，以可能产生的伪影的最大值为评价参数，评估欠采样对图像重建的影响，然而最大值只反应了伪影的最坏情况。该文引入了两种新的统计学评价参数平均值(MV)和标准差(SD)，其中平均值评估了伪影的平均大小，标准差可以反映伪影的波动情况。该文分别使用这3种参数对小鼠和人体脑部MRI数据以不同的采样比率进行CS图像重建，实验结果表明，当采样比率不低于4倍稀疏度时，使用平均值获得了质量更优的重建图像。因此，通过稀疏度先验知识指导合理选取采样比率，并以平均值为评价参数选取随机欠采样矩阵，能够获得更优的CS-MRI重建图像。