Low-rank and sparsity-based models in Magnetic Resonance Imaging (B03)

在这个项目中，我们的目标是对最近基于正则化和子空间方法的并行磁共振成像（MRI）的不同方法有更深的数学理解。利用当前方法的基础傅立叶分析背景，我们将开发新的高效并行MRI算法。我们将在正则化方法中以原则性的方式使用关于图像和线圈灵敏度的定性先验知识，并在傅里叶域的自适应基中使用结构矩阵的低秩近似和稀疏性。

In this project, we aim at a deeper mathematical understanding of the different recent approaches to parallel Magnetic Resonance Imaging (MRI) which are based on regularization and subspace methods. Using the underlying Fourier analysis background of the current methods, we will develop new efficient algorithms for parallel MRI. We will use qualitative prior knowledge about the image and the coil sensitivities in a principled way in the regularization methods and employ low-rank approximation of structured matrices and sparsity in adaptive bases in Fourier domain.