Fast Multiclass Dictionaries Learning with Geometrical Directions in Sparse Image Reconstruction

欠采样磁共振成像方法通过减少采集数据量来加速成像，并利用图像重建方法得到完整的磁共振图像。这类方法在抑制心脏和腹部等成像运动伪影上具有良好的应用前景，其中利用图像稀疏性的压缩感知方法是磁共振成像的研究热点之一。在图像稀疏重建中，图像稀疏表示的前向逼近误差是图像重建反问题中的重建误差的上限。因此，如何设计稀疏变换来降低图像表示误差进而提高重建图像质量有着重要意义。诸如小波变换只能普适地表示各种图像，而对某一特定重建目标图像的稀疏表示能力有限。因此，近几年学者重点关注图像的自适应稀疏表示，并发现自适应稀疏变换重建的图像质量明显优于典型的非自适应稀疏变换。但是，诸如K-SVD等自适应训练图像表示的方...Compressed sensing magnetic resonance imaging has shown great capability to accelerate data acquisition by exploiting sparsity of images under a certain transform or dictionary. Sparser representations usually lead to lower reconstruction errors, thus enduring efforts have been made to find dictionaries that provide sparser representation of magnetic resonance images. Previously, adaptive sparse r...学位：工程硕士院系专业：物理科学与技术学院_工程硕士(电子与通信工程)学号：3332014115283

A Theoretically Guaranteed Deep Optimization Framework for Robust Compressive Sensing MRI

Magnetic Resonance Imaging (MRI) is one of the most dynamic and safe imaging techniques available for clinical applications. However, the rather slow speed of MRI acquisitions limits the patient throughput and potential indi cations. Compressive Sensing (CS) has proven to be an efficient technique for accelerating MRI acquisition. The most widely used CS-MRI model, founded on the premise of reconstructing an image from an incompletely filled k-space, leads to an ill-posed inverse problem. In the past years, lots of efforts have been made to efficiently optimize the CS-MRI model. Inspired by deep learning techniques, some preliminary works have tried to incorporate deep architectures into CS-MRI process. Unfortunately, the convergence issues (due to the experience-based networks) and the robustness (i.e., lack real-world noise modeling) of these deeply trained optimization methods are still missing. In this work, we develop a new paradigm to integrate designed numerical solvers and the data-driven architectures for CS-MRI. By introducing an optimal condition checking mechanism, we can successfully prove the convergence of our established deep CS-MRI optimization scheme. Furthermore, we explicitly formulate the Rician noise distributions within our framework and obtain an extended CS-MRI network to handle the real-world nosies in the MRI process. Extensive experimental results verify that the proposed paradigm outperforms the existing state-of-the-art techniques both in reconstruction accuracy and efficiency as well as robustness to noises in real scene