生物医学工程学杂志

生物医学工程学杂志

基于双稀疏模型的压缩感知核磁共振图像重构

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医学核磁共振图像重构技术是核磁共振成像领域的关键技术之一。压缩感知理论指出利用核磁共振图像的稀疏性能够从高度欠采样的观测值中精确重构图像。如何利用图像的稀疏性先验以及更多的先验知识来提高重构质量成为核磁共振成像的一个关键问题。本文根据综合稀疏模型和稀疏变换模型的相互补充作用,利用核磁共振图像在这两种模型下的稀疏性先验,将结合了综合稀疏模型与稀疏变换模型的双稀疏模型应用于压缩感知核磁共振图像的重构系统,提出了一种融合双字典学习的自适应图像重构模型。本文充分利用了图像在自适应综合字典学习和自适应变换字典学习下的两种稀疏先验知识,使用交替迭代最小化法对提出的模型进行分阶段求解,求解过程中引入了综合 K-奇异值分解(K-SVD)算法和变换 K-SVD 算法。通过实验验证,与目前较好的核磁共振图像重构模型对比,本文提出模型的图像重构效果更好、收敛速度更快,且具有更好的鲁棒性。

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.

关键词: 核磁共振图像; 压缩感知; 综合稀疏模型; 稀疏变换模型; 图像重构

Key words: magnetic resonance image; compressed sensing; synthesis sparse model; sparse transform model; image reconstruction

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