Spectral Initialization for High-Dimensional Phase Retrieval with Biased Spatial Directions
| Autor: | Bousseyroux, Pierre, Potters, Marc |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We explore a spectral initialization method that plays a central role in contemporary research on signal estimation in nonconvex scenarios. In a noiseless phase retrieval framework, we precisely analyze the method's performance in the high-dimensional limit when sensing vectors follow a multivariate Gaussian distribution for two rotationally invariant models of the covariance matrix C. In the first model C is a projector on a lower dimensional space while in the second it is a Wishart matrix. Our analytical results extend the well-established case when C is the identity matrix. Our examination shows that the introduction of biased spatial directions leads to a substantial improvement in the spectral method's effectiveness, particularly when the number of measurements is less than the signal's dimension. This extension also consistently reveals a phase transition phenomenon dependent on the ratio between sample size and signal dimension. Surprisingly, both of these models share the same threshold value. Comment: 13 pages, 4 figures |
| Databáze: | arXiv |
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