88 research outputs found
Bispectrum Inversion with Application to Multireference Alignment
We consider the problem of estimating a signal from noisy
circularly-translated versions of itself, called multireference alignment
(MRA). One natural approach to MRA could be to estimate the shifts of the
observations first, and infer the signal by aligning and averaging the data. In
contrast, we consider a method based on estimating the signal directly, using
features of the signal that are invariant under translations. Specifically, we
estimate the power spectrum and the bispectrum of the signal from the
observations. Under mild assumptions, these invariant features contain enough
information to infer the signal. In particular, the bispectrum can be used to
estimate the Fourier phases. To this end, we propose and analyze a few
algorithms. Our main methods consist of non-convex optimization over the smooth
manifold of phases. Empirically, in the absence of noise, these non-convex
algorithms appear to converge to the target signal with random initialization.
The algorithms are also robust to noise. We then suggest three additional
methods. These methods are based on frequency marching, semidefinite relaxation
and integer programming. The first two methods provably recover the phases
exactly in the absence of noise. In the high noise level regime, the invariant
features approach for MRA results in stable estimation if the number of
measurements scales like the cube of the noise variance, which is the
information-theoretic rate. Additionally, it requires only one pass over the
data which is important at low signal-to-noise ratio when the number of
observations must be large
Temperature Dependence of a Sub-wavelength Compact Graphene Plasmon-Slot Modulator
We investigate a plasmonic electro-optic modulator with an extinction ratio
exceeding 1 dB/um by engineering the optical mode to be in-plane with the
graphene layer, and show how lowering the operating temperature enables steeper
switching. We show how cooling Graphene enables steeping thus improving dynamic
energy consumption. Further, we show that multi-layer Graphene integrated with
a plasmonic slot waveguide allows for in-plane electric field components, and
3-dB device lengths as short as several hundred nanometers only. Compact
modulators approaching electronic length-scales pave a way for ultra-dense
photonic integrated circuits with smallest footprint
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