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Phase Retrieval of Bandlimited Signals Using a Morlet Wavelet and an Admissible Companion

  • Bei Liu
  • Meng Ning
  • Liping Wu
  • Qingyue Zhang
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Abstract

In this paper, we demonstrate that complex bandlimited signals can be uniquely recovered (up to a global phase factor) from two families of wavelet transform magnitudes, sampled at twice the Nyquist rate in two frequency bins. These families come from translations of the fixed dilated Morlet wavelet and a fixed companion wavelet. The companion wavelet admits an augmented Morlet--Gaussian representation. We rewrite the two families as two modulated Gaussian convolution measurements of an auxiliary bandlimited signal. Using a Gaussian convolution uniqueness result, we prove that samples on (4B)−1ℤ determine every signal in PWB2 (up to a global phase factor). Compared with earlier wavelet phase retrieval results, our approach requires significantly fewer sampling points.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026phase,
  title = {{Phase Retrieval of Bandlimited Signals Using a Morlet Wavelet and an Admissible Companion}},
  author = {Bei Liu and Meng Ning and Liping Wu and Qingyue Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39145},
  eprint = {2610.39145},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39145},
}
RIS
TY  - UNPB
TI  - Phase Retrieval of Bandlimited Signals Using a Morlet Wavelet and an Admissible Companion
AU  - Bei Liu
AU  - Meng Ning
AU  - Liping Wu
AU  - Qingyue Zhang
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39145
UR  - https://arxiv.org/abs/2610.39145
AB  - In this paper, we demonstrate that complex bandlimited signals can be uniquely recovered (up to a global phase factor) from two families of wavelet transform magnitudes, sampled at twice the Nyquist rate in two frequency bins. These families come from translations of the fixed dilated Morlet wavelet and a fixed companion wavelet. The companion wavelet admits an augmented Morlet--Gaussian representation. We rewrite the two families as two modulated Gaussian convolution measurements of an auxiliary bandlimited signal. Using a Gaussian convolution uniqueness result, we prove that samples on (4B)^−1ℤ determine every signal in PW_B^2 (up to a global phase factor). Compared with earlier wavelet phase retrieval results, our approach requires significantly fewer sampling points.
ER  -