不动点方法及其在压缩感知核磁共振成像中的应用

摘要

由于一些器官的边界信息在大多数核磁共振图像中都是稀疏的，所以利用压缩感知从数量非常有限的观测数据集合中重构出同样的核磁共振图像并且大大减少核磁共振图像的扫描磨损成为可能。然而，为了能够做到这一点，我们必须要解决定义在大量数据集合上的非光滑函数的最小化这一困难问题。为了解决这一问题，我们应用了在BB-step和线性搜索下的不动点算法，来快速重构核磁共振图像。数值实验证明，核磁共振图像可以由不动点算法从全部数据的40%-50%抽样中几乎精确重构。%Because information such as boundaries of organs is very sparse in most MR images, compres-sive sensing makes it possible to reconstruct the same MR images from a very limited set of measurements significantly reducing the MRI scan duration. In order to do that,however, one has to solve the difficult problem of minimizing non smooth functions on large data sets. To handle this, we use the fixed point continuation algorithm, with the BB step and line search to reconstruct MR images. The numerical exper-iments demonstrate that original MR images can be reconstructed exactly from the mere 40 percent of the complete set of measurements by fixed point algorithm.