54,916 research outputs found
Visible-light Phase Curves from the Second Year of the TESS Primary Mission
We carried out a systematic study of full-orbit phase curves for known transiting systems in the northern ecliptic sky that were observed during Year 2 of the TESS primary mission. We applied the same methodology for target selection, data processing, and light-curve fitting as we did in our Year 1 study. Out of the 15 transiting systems selected for analysis, seven—HAT-P-7, KELT-1, KELT-9, KELT-16, KELT-20, Kepler-13A, and WASP-12—show statistically significant secondary eclipses and day–night atmospheric brightness modulations. Small eastward dayside hot-spot offsets were measured for KELT-9b and WASP-12b. KELT-1, Kepler-13A, and WASP-12 show additional phase-curve variability attributed to the tidal distortion of the host star; the amplitudes of these signals are consistent with theoretical predictions. We combined occultation measurements from TESS and Spitzer to compute dayside brightness temperatures, TESS-band geometric albedos, Bond albedos, and phase integrals for several systems. The new albedo values solidify the previously reported trend between dayside temperature and geometric albedo for planets with 1500 K < Tday < 3000 K. For Kepler-13Ab, we carried out an atmospheric retrieval of the full secondary eclipse spectrum, which revealed a noninverted temperature–pressure profile, significant H2O and K absorption in the near-infrared, evidence for strong optical atmospheric opacity due to sodium, and a confirmation of the high geometric albedo inferred from our simpler analysis. We explore the implications of the phase integrals (ratios of Bond to geometric albedos) for understanding exoplanet clouds. We also report updated transit ephemerides for all of the systems studied in this work
A non-linear optimal estimation inverse method for radio occultation measurements of temperature, humidity and surface pressure
An optimal estimation inverse method is presented which can be used to
retrieve simultaneously vertical profiles of temperature and specific humidity,
in addition to surface pressure, from satellite-to-satellite radio occultation
observations of the Earth's atmosphere. The method is a non-linear, maximum
{\it a posteriori} technique which can accommodate most aspects of the real
radio occultation problem and is found to be stable and to converge rapidly in
most cases. The optimal estimation inverse method has two distinct advantages
over the analytic inverse method in that it accounts for some of the effects of
horizontal gradients and is able to retrieve optimally temperature and humidity
simultaneously from the observations. It is also able to account for
observation noise and other sources of error. Combined, these advantages ensure
a realistic retrieval of atmospheric quantities.
A complete error analysis emerges naturally from the optimal estimation
theory, allowing a full characterisation of the solution. Using this analysis a
quality control scheme is implemented which allows anomalous retrieval
conditions to be recognised and removed, thus preventing gross retrieval
errors.
The inverse method presented in this paper has been implemented for bending
angle measurements derived from GPS/MET radio occultation observations of the
Earth. Preliminary results from simulated data suggest that these observations
have the potential to improve NWP model analyses significantly throughout their
vertical range.Comment: 18 (jgr journal) pages, 7 figure
Non-Convex Phase Retrieval from STFT Measurements
The problem of recovering a one-dimensional signal from its Fourier transform
magnitude, called Fourier phase retrieval, is ill-posed in most cases. We
consider the closely-related problem of recovering a signal from its phaseless
short-time Fourier transform (STFT) measurements. This problem arises naturally
in several applications, such as ultra-short laser pulse characterization and
ptychography. The redundancy offered by the STFT enables unique recovery under
mild conditions. We show that in some cases the unique solution can be obtained
by the principal eigenvector of a matrix, constructed as the solution of a
simple least-squares problem. When these conditions are not met, we suggest
using the principal eigenvector of this matrix to initialize non-convex local
optimization algorithms and propose two such methods. The first is based on
minimizing the empirical risk loss function, while the second maximizes a
quadratic function on the manifold of phases. We prove that under appropriate
conditions, the proposed initialization is close to the underlying signal. We
then analyze the geometry of the empirical risk loss function and show
numerically that both gradient algorithms converge to the underlying signal
even with small redundancy in the measurements. In addition, the algorithms are
robust to noise
A Deterministic Theory for Exact Non-Convex Phase Retrieval
In this paper, we analyze the non-convex framework of Wirtinger Flow (WF) for
phase retrieval and identify a novel sufficient condition for universal exact
recovery through the lens of low rank matrix recovery theory. Via a perspective
in the lifted domain, we show that the convergence of the WF iterates to a true
solution is attained geometrically under a single condition on the lifted
forward model. As a result, a deterministic relationship between the accuracy
of spectral initialization and the validity of {the regularity condition} is
derived. In particular, we determine that a certain concentration property on
the spectral matrix must hold uniformly with a sufficiently tight constant.
This culminates into a sufficient condition that is equivalent to a restricted
isometry-type property over rank-1, positive semi-definite matrices, and
amounts to a less stringent requirement on the lifted forward model than those
of prominent low-rank-matrix-recovery methods in the literature. We
characterize the performance limits of our framework in terms of the tightness
of the concentration property via novel bounds on the convergence rate and on
the signal-to-noise ratio such that the theoretical guarantees are valid using
the spectral initialization at the proper sample complexity.Comment: In Revision for IEEE Transactions on Signal Processin
Component Evolution Analysis in Descriptor Graphs for Descriptor Ranking
This paper presents a method based on graph behaviour analysis for the evaluation
of descriptor graphs (applied to image/video datasets) for descriptor performance
analysis and ranking. Starting from the Erd˝os-R´enyi model on uniform random
graphs, the paper presents results of investigating random geometric graph behaviour
in relation with the appearance of the giant component as a basis for
ranking descriptors based on their clustering properties. We analyse the phase
transition and the evolution of components in such graphs, and based on their
behaviour, the corresponding descriptors are compared, ranked, and validated in
retrieval tests. The goal is to build an evaluation framework where descriptors can
be analysed for automatic feature selection
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