Applied and Computational Harmonic Analysis ( IF 2.5 ) Pub Date : 2020-08-26 , DOI: 10.1016/j.acha.2020.08.002 Meng Huang , Yi Rong , Yang Wang , Zhiqiang Xu
The aim of generalized phase retrieval is to recover from the quadratic measurements , where and or . In this paper, we study the matrix set which has the almost everywhere phase retrieval property. For the case , we show that generic matrices with prescribed ranks have almost everywhere phase retrieval property. We also extend this result to the case where are orthogonal matrices and hence establish the almost everywhere phase retrieval property for the fusion frame phase retrieval. For the case where , we obtain similar results under the assumption of . We lower the measurement number (resp. 2d) with showing that there exist (resp. ) matrices (resp. ) which have the almost everywhere phase retrieval property. Our results are an extension of almost everywhere phase retrieval from the standard phase retrieval to the general setting and the proofs are often based on some new ideas about determinant variety.
中文翻译:
几乎所有地方的广义相位检索
广义相位检索的目的是恢复 从二次测量 ,在哪里 和 要么 。在本文中,我们研究矩阵集具有几乎所有相位检索特性。对于这种情况,我们证明 具有规定等级的通用矩阵几乎在任何地方都具有相检索特性。我们还将这个结果扩展到以下情况是正交矩阵,因此为融合帧相位检索建立了几乎无处不在的相位检索特性。对于这种情况,我们在 。我们降低测量数(第2 d天)并显示存在 (分别 )矩阵 (分别 ),几乎具有无处不在的相位检索特性。我们的结果是将几乎所有相位检索从标准相位检索扩展到常规设置,并且证明常常基于关于行列式变化的一些新思想。