Exponential Spectral Pursuit: An Effective Initialization Method for Sparse Phase Retrieval

Mengchu Xu, Yuxuan Zhang, Jian Wang
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:55525-55546, 2024.

Abstract

Sparse phase retrieval aims to reconstruct an $n$-dimensional $k$-sparse signal from its phaseless measurements. For most of the existing reconstruction algorithms, their sampling complexity is known to be dominated by the initialization stage. In this paper, in order to improve the sampling complexity for initialization, we propose a novel method termed exponential spectral pursuit (ESP). Theoretically, our method offers a tighter bound of sampling complexity compared to the state-of-the-art ones, such as the truncated power method. Moreover, it empirically outperforms the existing initialization methods for sparse phase retrieval.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-xu24ah, title = {Exponential Spectral Pursuit: An Effective Initialization Method for Sparse Phase Retrieval}, author = {Xu, Mengchu and Zhang, Yuxuan and Wang, Jian}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {55525--55546}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/xu24ah/xu24ah.pdf}, url = {https://proceedings.mlr.press/v235/xu24ah.html}, abstract = {Sparse phase retrieval aims to reconstruct an $n$-dimensional $k$-sparse signal from its phaseless measurements. For most of the existing reconstruction algorithms, their sampling complexity is known to be dominated by the initialization stage. In this paper, in order to improve the sampling complexity for initialization, we propose a novel method termed exponential spectral pursuit (ESP). Theoretically, our method offers a tighter bound of sampling complexity compared to the state-of-the-art ones, such as the truncated power method. Moreover, it empirically outperforms the existing initialization methods for sparse phase retrieval.} }
Endnote
%0 Conference Paper %T Exponential Spectral Pursuit: An Effective Initialization Method for Sparse Phase Retrieval %A Mengchu Xu %A Yuxuan Zhang %A Jian Wang %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-xu24ah %I PMLR %P 55525--55546 %U https://proceedings.mlr.press/v235/xu24ah.html %V 235 %X Sparse phase retrieval aims to reconstruct an $n$-dimensional $k$-sparse signal from its phaseless measurements. For most of the existing reconstruction algorithms, their sampling complexity is known to be dominated by the initialization stage. In this paper, in order to improve the sampling complexity for initialization, we propose a novel method termed exponential spectral pursuit (ESP). Theoretically, our method offers a tighter bound of sampling complexity compared to the state-of-the-art ones, such as the truncated power method. Moreover, it empirically outperforms the existing initialization methods for sparse phase retrieval.
APA
Xu, M., Zhang, Y. & Wang, J.. (2024). Exponential Spectral Pursuit: An Effective Initialization Method for Sparse Phase Retrieval. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:55525-55546 Available from https://proceedings.mlr.press/v235/xu24ah.html.

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