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

在这个项目中，我们的目标是更深入的数学理解的不同最近的方法，并行磁共振成像（MRI）的基础上正则化和子空间方法。使用当前方法的基本傅立叶分析背景，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，并在傅立叶域中的自适应基中采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.