基于压缩感知的核磁共振图像重建的Bregman方法

摘要

Because information such as boundaries of organs is very sparse in most MR images,compressed 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 nonsmooth functions on large data sets.To handle this,we propose an efficient algorithm that It has overcome the computational complexity of solving the l1 problem,this paper puts forward β norm approximation l1 norm thought,because β norm with slickness,one can use Bregman iterative regularization method to solve this problem.The numerical experiments demonstrate that original MR images can be reconstructed exactly from the mere 40 percent of the complete set of measurements by our approach.%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,我们给出了一个有效算法,它克服以往求解l1问题的计算复杂性,提出β范数近似逼近l1范数的思想,由于β范数具有光滑性,可采用Bregman迭代正则化方法进行求解。数值实验证明,核磁共振图像可以从全部数据的40%抽样中几乎精确重构。