FROG-measurement based phase retrieval for analytic signals

Li, Youfa; Ma, Yaoshuai; Han, Deguang

doi:10.1016/j.acha.2021.05.005

Cited by 6 publications

(5 citation statements)

References 43 publications

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“…The STFT-PR in this paper is different from FROG-PR since the window here is known and independent of the signal. The following tells us some other essential differences between Theorem 1.1 and the results in [31]. (1) The main result in [31] only applies to the case when N is even and the separation parameter 0 < L < N is odd with the property that N/L ≥ 5.…”

Section: Remark 12mentioning

confidence: 95%

“…The following tells us some other essential differences between Theorem 1.1 and the results in [31]. (1) The main result in [31] only applies to the case when N is even and the separation parameter 0 < L < N is odd with the property that N/L ≥ 5. However, Theorem 1.1 only requires N/L ≥ 3 in this case.…”

Section: Remark 12mentioning

confidence: 95%

“…The number of measurement is reduced to ( 3N 2 − 1) in Theorem 1.1. (3) The ambiguity for FROG-PR in [31] is different from that in Theorem 1.1 since it additionally contains shift and reflection. Consequently, the IFs of only a few analytic signals can be extracted from FROG-PR ([31, section 4]).…”

Section: Remark 12mentioning

confidence: 99%

“…[7]). The FROG-PR for analytic signals was addressed in [31]. The STFT-PR in this paper is different from FROG-PR since the window here is known and independent of the signal.…”

Section: Remark 12mentioning

confidence: 99%

“…However, Theorem 1.1 only requires N/L ≥ 3 in this case. (2) Similarly, ( 3N 2 + 1) FROG measurements are required in [31] for the even length case. The number of measurement is reduced to ( 3N 2 − 1) in Theorem 1.1.…”

Section: Remark 12mentioning

confidence: 99%

See 4 more Smart Citations

Phase retrieval of analytic signals from short-time Fourier transform measurements

Li¹,

Wang²,

Han³

2022

Preprint

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Analytic signals belong to a widely applied class of signals especially for extracting instantaneous frequency (IF) or phase derivative which is very helpful in the characterization of ultrashort laser pulse. In this paper we investigate the phase retrieval (PR) problem for analytic signals in C N by their short-time Fourier transform (STFT) measurements. When the window is bandlimited, it was found that the corresponding STFT of an analytic signal enjoys nice structures. Exploiting such structures, our main results state that the STFT-PR of generic analytic signals can be achieved by their (3 N 2 + 1) measurements. Note that the generic analytic signals are ( N 2 + 1)-sparse in Fourier domain. Such a number of measurements is lower than 4N +O(1) and O(k 3 ) which are required in the literature for STFT-PR of signals in C N and of k-sparse (in Fourier domain) signals, respectively. Furthermore, if the length N is even and the windows are also analytic then the number of measurements can be reduced to ( 3N 2 − 1). PR approaches are established for different cases of window bandlimit. As an application, the IF of a generic analytic signal can be exactly recovered from the PR results. Several examples are provided to demonstrate the main results and their applications.

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Section: Remark 12mentioning

confidence: 95%

Section: Remark 12mentioning

confidence: 95%

Section: Remark 12mentioning

confidence: 99%

“…[7]). The FROG-PR for analytic signals was addressed in [31]. The STFT-PR in this paper is different from FROG-PR since the window here is known and independent of the signal.…”

Section: Remark 12mentioning

confidence: 99%

Section: Remark 12mentioning

confidence: 99%

See 3 more Smart Citations

Phase retrieval of analytic signals from short-time Fourier transform measurements

Li¹,

Wang²,

Han³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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Generalized phase retrieval in quaternion Euclidean spaces

Yang,

2024

Math Methods in App Sciences

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Recently, quaternionic Fourier analysis has received increasing attention due to its applications in signal analysis and image processing. This paper addresses quaternionic generalized phase retrieval (QGPR) problem in quaternion Euclidean spaces . We introduce the concept of QGPR which aims to reconstruct a signal in from the quadratic measurements , where each is an self‐adjoint quaternion matrix. We characterize QGPR sequences in terms of their real Jacobian matrices, prove that the set of QGPR sequences is an open set in some sense, and present some phaselift‐based sufficient conditions on QGPR which gives a method to construct QGPR sequences.

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