Generalized Approximate Survey Propagation for High-Dimensional Estimation

In Generalized Linear Estimation (GLE) problems, we seek to estimate a signal that is observed through a linear transform followed by a component-wise, possibly nonlinear and noisy, channel. In the Bayesian optimal setting, Generalized Approximate Message Passing (GAMP) is known to achieve optimal performance for GLE. However, its performance can significantly degrade whenever there is a mismatch between the assumed and the true generative model, a situation frequently encountered in practice. In this paper, we propose a new algorithm, named Generalized Approximate Survey Propagation (GASP), for solving GLE in the presence of prior or model mis-specifications. As a prototypical example, we consider the phase retrieval problem, where we show that GASP outperforms the corresponding GAMP, reducing the reconstruction threshold and, for certain choices of its parameters, approaching Bayesian optimal performance. Furthermore, we present a set of State Evolution equations that exactly characterize the dynamics of GASP in the high-dimensional limit

NASA Global Atmospheric Sampling Program (GASP). Data report for tape VL0001

Atmospheric trace constituents in the upper troposphere and lower stratosphere are now being measured as part of the NASA Global Atmospheric Sampling Program (GASP), using fully automated air sampling systems on board commercial 747 aircraft in routine airline service. Measurements of atmospheric ozone and related meteorological and flight information obtained during several GASP flights in March 1975 are now available from the National Climatic Center, Asheville, North Carolina. In addition to the data from the aircraft, tropopause pressure data obtained from the National Meteorological Center (NMC) archives for the dates of the flights are included. This report is the first of a series of reports which describes the data currently available from GASP, including flight routes and dates, instrumentation, the data processing procedure used, and data tape specifications

Decomposition theorem and Riesz basis for axisymmetric potenials in the right hal-plane

The Weinstein equation with complex coefficients is the equation governing generalized axisymmetric potentials (GASP) which can be written as $L_m[u]=\Delta u+\left(m/x\right)\partial_x u =0$, where $m\in\mathbb{C}$. We generalize results known for $m\in\mathbb{R}$ to $m\in\mathbb{C}$. We give explicit expressions of fundamental solutions for Weinstein operators and their estimates near singularities, then we prove a Green's formula for GASP in the right half-plane $\mathbb{H}^+$ for Re $m<1$. We establish a new decomposition theorem for the GASP in any annular domains for $m\in\mathbb{C}$, which is in fact a generalization of the B\^ocher's decomposition theorem. In particular, using bipolar coordinates, we prove for annuli that a family of solutions for GASP equation in terms of associated Legendre functions of first and second kind is complete. For $m\in\mathbb{C}$, we show that this family is even a Riesz basis in some non-concentric circular annulus

NASA Global Atmospheric Sampling Program (GASP) data report for tapes VL0007 and VL0008

The Global Atmospheric Sampling Program (GASP) is obtaining measurements of atmospheric trace constituents in the upper troposphere and lower stratosphere using fully automated air sampling systems on board the NASA CV-990 research aircraft and four commerical B-747 aircraft in routine airline service. In-situ measurements of atmospheric ozone and water vapor, data from laboratory analysis of filters exposed in flight, and related flight and meteorological data obtained from September 1976 through January 1977 are reported. These data are now available on GASP tapes VL0007 & VL0008 from the National Climatic Center, Asheville, North Carolina. In addition to the GASP data, tropopause pressure fields obtained from NMC archives for the dates of the GASP flights are included on the data tape. Flight routes and dates, instrumentation, data processing procedures, and data tape specifications are described

Ozone contamination in aircraft cabins: Results from GASP data and analyses

The global atmospheric sampling program pertaining to the problem of ozone contamination in commercial airplane cabins is described. Specifically, analyses of GASP data have: confirmed the occurrence of high ozone levels in aircraft cabins and documented the ratio of ozone inside and outside the cabins of two B747 airliners, including the effects of air conditioning modifications on that ratio; defined ambient ozone climatology at commercial airplane cruise altitudes, including tabulation of encounter frequency data which were not available before GASP; and outlined procedures for estimating the frequency of flights encountering high cabin ozone levels using climatological ambient ozone data, and verified these procedures against cabin measurements

NASA Global Atmospheric Sampling Program (GASP) data report for tapes VL0010 and VL0012

The GASP atmospheric trace constituent data currently available are considered. Included on tapes are in-situ measurements of atmospheric ozone, carbon monoxide, water vapor, and clouds, data from laboratory analysis of filters exposed in flight, and related flight and meteorological data. Measurements of ozone levels within the first class cabin of these aircraft are also reported. In addition to the GASP data, tropopause pressures obtained from time and space interpolation of NMC archived data for the dates of the flights are included. Reported herein are the flight routes and dates, instrumentation, data processing procedures, data tape specifications, and analyses of the cabin ozone measurements