通过零均值张量嵌入实现低帧相干性
Low frame coherence via zero-mean tensor embeddings
摘要：
本文研究了高冗余实单位模框架的最优相干性问题。随着冗余度的增加，帧中的矢量数量变得太大，以至于不能进行等角排列。在这种情况下，需要确定其他几何最优性准则。为此，我们使用迭代的嵌入技术的康威，哈丁和斯隆。作为他们工作的结果，二次映射将等角线嵌入实欧几里得空间中的单纯形。这里，高次多项式映射将高度冗余的单位范数框架嵌入到高维欧几里得空间中的单形中。我们专注于最低程度的情况下，嵌入是四次。
英文摘要：
This paper is concerned with achieving optimal coherence for highly redundant real unit-norm frames. As the redundancy grows, the number of vectors in the frame becomes too large to admit equiangular arrangements. In this case, other geometric optimality criteria need to be identified. To this end, we use an iteration of the embedding technique by Conway, Hardin and Sloane. As a consequence of their work, a quadratic mapping embeds equiangular lines into a simplex in a real Euclidean space. Here, higher degree polynomial maps embed highly redundant unit-norm frames to simplices in high-dimensional Euclidean spaces. We focus on the lowest degree case in which the embedding is quartic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
