Magnetic resonance imaging serves as an essential tool for clinical diagnosis. However, it suffers from a long acquisition time. The utilization of deep learning, especially the deep generative models, offers aggressive acceleration and better reconstruction in magnetic resonance imaging. Nevertheless, learning the data distribution as prior knowledge and reconstructing the image from limited data remains challenging. In this work, we propose a novel Hankel-k-space generative model (HKGM), which can generate samples from a training set of as little as one k-space data. At the prior learning stage, we first construct a large Hankel matrix from k-space data, then extract multiple structured k-space patches from the large Hankel matrix to capture the internal distribution among different patches. Extracting patches from a Hankel matrix enables the generative model to be learned from redundant and low-rank data space. At the iterative reconstruction stage, it is observed that the desired solution obeys the learned prior knowledge. The intermediate reconstruction solution is updated by taking it as the input of the generative model. The updated result is then alternatively operated by imposing low-rank penalty on its Hankel matrix and data consistency con-strain on the measurement data. Experimental results confirmed that the internal statistics of patches within a single k-space data carry enough information for learning a powerful generative model and provide state-of-the-art reconstruction.
翻译:磁共振成像(HKGM)是临床诊断的基本工具。然而,它却在很长的学习时间里成为临床诊断的基本工具。利用深层次的学习,特别是深层次的基因模型,在磁共振成像中进行积极的加速和更好的重建。然而,将数据传播作为先前的知识学习,从有限的数据中重建图像,仍然具有挑战性。在这项工作中,我们提出一个新的Hankel-k-space基因化模型(HKGM),它能够从一个小于一个k-空间数据的培训中产生样本。在以前的学习阶段,我们首先从 k-空间数据中建立一个大型的Hankel矩阵,然后从大型的Hankel矩阵中提取多个结构化的 k-space补丁,以捕捉到不同部分的内部分布。从Hankel 矩阵中提取补丁,使基因化模型能够从多余和低层数据中学习。在迭接阶段,发现理想的解决方案符合所学知识。中间重建解决方案通过将它作为基因化模型的输入来更新。随后,更新的结果是通过对它的Hankel 矩阵矩阵矩阵矩阵矩阵和数据一致性化模型进行操作操作,同时对它内部的模型进行低的测试,对数据库进行测试,对数据库化数据进行充分进行数据进行测试,对数据库进行测试,对数据库进行测试,对数据库进行测试,对数据进行测试,对数据进行测试,对数据进行测试,对数据进行测试,对数据进行测试,对数据进行测试,对数据进行测试,对数据进行测试,对数据进行测试后进行测试后进行数据进行数据进行测试,对数据进行测试,对数据进行测试,对数据进行数据进行测试,对数据进行测试,对数据进行测试后进行测试后进行数据采集数据进行数据进行测试后进行数据采集数据采集数据采集数据进行数据进行测试,对数据进行测试,对数据采集数据采集数据进行数据进行数据采集数据采集。