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Abstract:
Quaternion algebra H is a noncommutative associative algebra. In recent years, quaternionic Fourier analysis has received increasing attention due to its applications in signal analysis and image processing. This paper addresses conjugate phase retrieval problem in the quaternion Euclidean space H-M with M >= 2. Write C-eta = {xi : xi = xi(0) + beta eta, xi(0), beta is an element of R} for eta is an element of {i, j, k}. We remark that not only C-eta(M)-vectors cannot allow traditional conjugate phase retrieval in H-M, but also C-i(i)M boolean OR C-j(M)-complex vectors cannot allow phase retrieval in H-M . We are devoted to conjugate phase retrieval of C-i(M) boolean OR C-j(M) -complex vectors in H-M, where "conjugate" is not the traditional conjugate. We introduce the notions of conjugation, maximal commutative subset and conjugate phase retrieval. Using the phase lifting techniques, we present some sufficient conditions on complex vectors allowing conjugate phase retrieval. And some examples are also provided to illustrate the generality of our theory.
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Source :
FORUM MATHEMATICUM
ISSN: 0933-7741
Year: 2024
Issue: 6
Volume: 36
Page: 1585-1601
Cited Count:
WoS CC Cited Count: 3
SCOPUS Cited Count: 3
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 2
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