有限框架冗余度的一个定量概念
A quantitative notion of redundancy for finite frames
摘要：
本文的目的是改进冗余的习惯定义，提供定量的措施，在其位置上，我们硬币上，下冗余，更好地匹配与直观的理解冗余的有限框架在希尔伯特空间。这就激发了一个精心选择的列表，上面和下面的冗余所需的属性。实现这些特性的方法是考虑冗余函数的最大值和最小值，这本身就很有趣。冗余函数定义在希尔伯特空间的球面上，并测量每个点周围的帧向量的集中度。给出了球面上与某个标架上的冗余函数重合的函数的一个完整刻画。从这个功能得到的上，下冗余度示出，以满足所有的直观所需的属性。此外，它们假定的值的值域被表征。
英文摘要：
The objective of this paper is to improve the customary definition of redundancy by providing quantitative measures in its place, which we coin upper and lower redundancies, that match better with an intuitive understanding of redundancy for finite frames in a Hilbert space. This motivates a carefully chosen list of desired properties for upper and lower redundancies. The means to achieve these properties is to consider the maximum and minimum of a redundancy function, which is interesting in itself. The redundancy function is defined on the sphere of the Hilbert space and measures the concentration of frame vectors around each point. A complete characterization of functions on the sphere which coincide with a redundancy function for some frame is given. The upper and lower redundancies obtained from this function are shown to satisfy all of the intuitively desirable properties. In addition, the range of values they assume is characterized.
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