基于量子测量理论的框架构造方法

Frame Construction Based on Theory of Quantum Measurement

紧框架是一类具有良好特性的框架,它在图像及视频编码传输等实际应用中经常被采用。首先引入框架和量子测量的基本知识,再利用量子测量与框架之间存在的紧密联系,即量子测量系统所依赖的子空间中的规范紧框架正好是该空间中的一阶广义测量,推导出了基于量子测量理论的紧框架的构造方法。通过设计出具体的实例,并将其与传统的框架构造方法进行比较。实验结果表明,在同等条件下,该文提出的方法在抗误差性能及计算复杂度等方面更优。

Tight frame ,which is the special form of frame,has lots of good properties,so it is always used in the practical applications. Firstly, some basic knowledge of frames is described in the paper, and then some concepts of quantum measurement are introduced. Using the compact relationship between quantum measurement and frames,that is, the family of normalized fight frames for the space in which a quantum -mechanical system lies is precisely the family of rank -one generalized quantum measurements on that space, we get the tight frame construction based on theory of quantum measurement. The concrete example shows that compared with the traditional construction methods, frame construction based on theory of quantum measurement has a lot of advantages in anti - error performance and computational complexity.