Phase Retrievable Projective Representation Frames for Finite Abelian Groups
Phase Retrievable Projective Representation Frames for Finite Abelian Groups
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DOI：
10.1007/s00041-017-9570-6
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发表时间：
2019-02
影响因子：
1.2
通讯作者：
Lan Li;Ted Juste;J. Brennan;Chuangxun Cheng;D. Han
中科院分区：
文献类型：
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作者：
Lan Li;Ted Juste;J. Brennan;Chuangxun Cheng;D. Han
我们考虑的问题，特征的投影表示，承认帧向量的最大跨度属性，属性，允许代数恢复的相位检索问题。对于有限交换群G的一个给定乘子，我们证明了G的任何不可约投射表示的表示维数恰为与之相关联的对称乘子矩阵的秩.借助于这个结果，我们证明了有限交换群G的每一个不可约投射表示都存在一个具有最大跨距性质的框架向量，并得到了所有这类框架向量的一个完整刻画.因此，任何有限阿贝尔群的任何投射酉表示的所有最大跨度框架向量的集合的补是Zurkki-闭的。这些推广了最近的一些结果相位恢复与Gabor（或STFT）测量。
We consider the problem of characterizing projective representations that admit frame vectors with the maximal span property, a property that allows for an algebraic recovering for the phase-retrieval problem. For a given multiplierof a finite abelian groupG, we show that the representation dimension of any irreducible-projective representation ofGis exactly the rank of the symmetric multiplier matrix associated with. With the help of this result we are able to prove that every irreducible-projective representation of a finite abelian groupGadmits a frame vector with the maximal span property, and obtain a complete characterization for all such frame vectors. Consequently the complement of the set of all the maximal span frame vectors for any projective unitary representation of any finite abelian group is Zariski-closed. These generalize some of the recent results about phase-retrieval with Gabor (or STFT) measurements.