基于部分K空间数据子空间分解的贝叶斯非参数压缩感知MRI重建方法

基于压缩感知理论（CS）由部分K空间数据重建MRI图像（CSMRI）是一种有效的加快成像速度的方法，然而现有CSMRI存在弱对比度结构易丢失、低采样率时重建图像质量差以及模型中关键参数需设定等不足，难以满足医学应用需求。项目旨在依据实际应用特点，研究将子空间分析、图像融合与贝叶斯非参数CS理论相结合的CSMRI重建方法，以提升CSMRI重建性能。具体为：1)由部分K空间数据子空间分解，获得子空间图像对应的部分K空间数据，通过子空间图像各自重建以深入挖掘K空间数据幅值、能量及稀疏度分布不均匀特性；2)由贝叶斯非参数模型重建子空间图像，解决现有CSMRI的关键参数需人为设定且难以有效将多种先验有机结合到同一模型的问题；3）采取“分而治之”与“渐进逼近”策略，并结合原始部分K空间观测数据将多子空间图像融合为待重建图像。相关研究既针对医学应用实际，又对图像处理中的各种反问题求解具有一定借鉴意义。

Compressed sensing has had a major impact on magnetic resonance imaging (MRI) since it gives a way to significantly undersample the Fourier measurement domain of MR images (called k-space), while still allowing for a high-quality image reconstruction. However, CS-MRI still has limitations in clinical applications because of the disappearance of low-contrast structure necessary for clinical diagnosis, poor performances with low sampling rate and the burdensome requirement of manually estimating key parameters. Motivated by real-world clinical applications, this proposal aims to combine subspace analysis, image fusion, and Bayesian nonparametric models in order to significantly improve the performances of CS-MRI. Using our methodology, we first propose decomposing the partial k-space data into different subspaces in order to exploit the nonuniform distribution of data magnitude, power, and sparsity in k-space to individually reconstruct images from each subspace. Second, we propose Bayesian nonparametric modeling to adaptively infer the key parameters in CS-MRI, and to combine the various priors from different subspaces using a hierarchical representation. Finally, we reconstruct the MRI by fusing images from different subspaces using the strategies of ‘divide and conquer’ and ‘progressive approximation’. As a result, the methodology of this proposal combines subspace analysis, image fusion, and Bayesian nonparametric analysis in order to significantly improve the performance of CS-MRI, providing doctors with better information for making diagnoses. We also anticipate that our approach will have broader applications outside of CS-MRI, providing a way to solve various inverse problems in image processing.