基于最优低秩约束的动态心脏磁共振图像重建算法

Dynamic cardiac magnetic resonance image reconstruction algorithm based on optimal low-rank constraints

关键词:  动态磁共振成像  压缩感知  非局部低秩  加权Schatten p-范数  交替方向乘子法

Key words:  dynamic magnetic resonance imaging  compressed sensing  nonlocal low-rank  weighted Schatten p-norm  alternating direction multiplier method

摘要:

动态心脏磁共振成像(CMRI)是无创评估心血管疾病的重要工具。在动态CMRI中,常运用低秩张量恢复方法来探索动态磁共振图像的稀疏性,然而,张量的不同模态具有不同的低秩属性。研究发现,基于张量的非局部自相似性模态最能提升动态CMRI的重建质量。因此,在非局部低秩（NLR）方法的基础上,将高维图像中提取的每一组相似块视作一个矩阵,提出一种具有矩阵稀疏性的最优低秩矩阵恢复（OLRMR）模型。该模型使用加权Schatten p-范数作为秩代理函数,采用交替方向乘子法（ADMM）和快速软阈值迭代算法求解。基于心脏数据集的实验结果表明,OLRMR算法比BCS、k-t SLR和k-t LRTC算法更能有效提升重建图像的质量,更好保留图像细节与边缘轮廓信息。实验还表明,OLRMR的重建速度比k-t LRTC提升了2.6~3倍。

Abstract:

Dynamic cardiac magnetic resonance imaging (CMRI) is an important tool for noninvasive assessment of cardiovascular disease. In dynamic CMRI, a low-rank tensor recovery method is usually employed to explore the sparsity of dynamic magnetic resonance images; however, different modes along the tensor have different low-rank properties. The studies have found that the nonlocal self-similarity mode along the tensor can best improve the reconstruction quality of dynamic CMRI. Therefore, this paper proposes an optimal low-rank matrix recovery (OLRMR) model with matrix sparsity based on the nonlocal low-rank (NLR) method by treating each set of similar blocks extracted from a high-dimensional image as a matrix. The model uses the weighted Schatten p-norm as the rank proxy function and was solved using the alternating direction multiplier method (ADMM) and a fast soft-threshold iterative algorithm. Experimental results based on the cardiac dataset show that the OLRMR algorithm is more effective in improving the quality of the reconstructed image than the BCS, k-t SLR, and k-t LRTC algorithms and can better keep the detail of the image and the edge contour information intact. The experimental results also show that OLRMR improves the reconstruction speed by a factor of 2.6-3 over k-t LRTC.