分数域深度压缩感知的磁共振图像重建理论及最优化设计研究

磁共振成像在临床诊断中具有很大优越性和应用潜力，当前面临的关键问题是如何加快成像速度和提升成像质量。本项目拟结合分数Fourier分析和深度学习最新理论，利用深度神经网络图像处理的优势，以磁共振图像重建为研究对象，深入研究深度学习的分数域压缩感知重建理论，包括利用分数Fourier变换表征磁共振信号，设计分数域磁共振图像重建方法；研究联合分数域和图像域神经网络的磁共振图像重建理论，构建级联的混合双域模型和设计训练学习方法，实现高效高质重建欠采样图像；研究分数域深度压缩感知的磁共振图像重建理论，构建融合分数域测量网络和生成器的深度压缩感知模型，针对模型效率提出一种混合下降算法快速求重建过程中非凸优化问题的全局最优解，以及元学习迭代训练测量网络和生成器，实现小样本条件下图像重建，增强医学图像处理实用性。本项目将突破现有Fourier分析磁共振成像框架的局限，完善深度学习框架下压缩感知重建理论。

MRI has great advantages and potential applications for the clinical diagnosis. The key problem is how to improve the imaging speed and quality. This project focuses on the image reconstruction of MRI. It will combine the latest theory of deep learning and fractional Fourier analysis.Taking advantages of the deep neural network for image processing, the comprehensive study of compressed sensing in fractional domains based on the deep learning is conducted. The MRI signals are represented using fractional Fourier transforms and the image reconstruction method in fractional domains is proposed. Then it considers the image reconstruction theory based on the jointed fractional domain and image domain neural network. By employing a cascaded hybrid dual-domain model and designing the corresponding training method, the effective and high quality under-sampling image reconstructions are obtained. Further more, the image reconstruction theory based on the deep compression sensing in fractional domains is discussed. The deep compression sensing model combining the fractional domains measurement network and generator is proposed. A fast hybrid descent algorithm is employing to solve the global optimal solution of the non-convex optimization problem in the process of reconstruction. As well as an iterative training of the measurement network and generator by the meta learning is implemented. It will achieve the image reconstruction under the condition of small samples and enhance the practicability of medical image processing. This project will break through the limitations of existing Fourier analysis MRI framework and improve the theory of compressed sensing under the deep learning framework.