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Abstract On-chip spectrometers have the potential to offer dramatic size, weight, and power advantages over conventional benchtop instruments for many applications such as spectroscopic sensing, optical network performance monitoring, hyperspectral imaging, and radio-frequency spectrum analysis. Existing on-chip spectrometer designs, however, are limited in spectral channel count and signal-to-noise ratio. Here we demonstrate a transformative on-chip digital Fourier transform spectrometer that acquires high-resolution spectra via time-domain modulation of a reconfigurable Mach-Zehnder interferometer. The device, fabricated and packaged using industry-standard silicon photonics technology, claims the multiplex advantage to dramatically boost the signal-to-noise ratio and unprecedented scalability capable of addressing exponentially increasing numbers of spectral channels. We further explore and implement machine learning regularization techniques to spectrum reconstruction. Using an ‘elastic-D1’ regularized regression method that we develop, we achieved significant noise suppression for both broad (>600 GHz) and narrow (<25 GHz) spectral features, as well as spectral resolution enhancement beyond the classical Rayleigh criterion.
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Phase transitions of spectral initialization for high-dimensional non-convex estimation
Abstract We study a spectral initialization method that serves a key role in recent work on estimating signals in non-convex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In this paper, we consider arbitrary generalized linear sensing models and present a precise asymptotic characterization of the performance of the method in the high-dimensional limit. Our analysis also reveals a phase transition phenomenon that depends on the ratio between the number of samples and the signal dimension. When the ratio is below a minimum threshold, the estimates given by the spectral method are no better than random guesses drawn from a uniform distribution on the hypersphere, thus carrying no information; above a maximum threshold, the estimates become increasingly aligned with the target signal. The computational complexity of the method, as measured by the spectral gap, is also markedly different in the two phases. Worked examples and numerical results are provided to illustrate and verify the analytical predictions. In particular, simulations show that our asymptotic formulas provide accurate predictions for the actual performance of the spectral method even at moderate signal dimensions.
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- Award ID(s):
- 1718698
- PAR ID:
- 10125407
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Information and Inference: A Journal of the IMA
- ISSN:
- 2049-8772
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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