Dimensionality Collapse: Optimal Measurement Selection for Low-Error Infinite-Horizon Forecasting

This work introduces a method to select linear functional measurements of a vector-valued time series optimized for forecasting distant time-horizons. By formulating and solving the problem of sequential linear measurement design as an infinite-horizon problem with the time-averaged trace of the Cram\'{e}r-Rao lower bound (CRLB) for forecasting as the cost, the most informative data can be collected irrespective of the eventual forecasting algorithm. By introducing theoretical results regarding measurements under additive noise from natural exponential families, we construct an equivalent problem from which a local dimensionality reduction can be derived. This alternative formulation is based on the future collapse of dimensionality inherent in the limiting behavior of many differential equations and can be directly observed in the low-rank structure of the CRLB for forecasting. Implementations of both an approximate dynamic programming formulation and the proposed alternative are illustrated using an extended Kalman filter for state estimation, with results on simulated systems with limit cycles and chaotic behavior demonstrating a linear improvement in the CRLB as a function of the number of collapsing dimensions of the system.Comment: 33 Pages, 9 Figures, To appear in Proceedings of the 26th International Conference on Artificial Intelligence and Statistics (AISTATS) 202

Tomographic Imaging of Airglow from Airborne Spectroscopic Measurements

A description is given of the methodology based on a single, aircraft-mounted spectroscopic imager to tomographically reconstruct airglow perturbations induced by atmospheric gravity waves. In this configuration, the imager passes under the airglow structure to gather multiple-angle views of the wave structure in a relatively short amount of time. Under the assumption that the airglow structure does not change significantly during the acquisition interval, the data can be tomographically inverted to estimate the 2D (horizontal–vertical) airglow structure. We develop an inversion strategy for this image formation task and illustrate its applicability by inverting time-sequential imaging data taken from different vantage points during the ALOHA-93 campaign to reconstruct atmospheric gravity wave structures

A phase field method for tomographic reconstruction from limited data.

Classical tomographic reconstruction methods fail for problems in which there is extreme temporal and spatial sparsity in the measured data. Reconstruction of coronal mass ejections (CMEs), a space weather phenomenon with potential negative effects on the Earth, is one such problem. However, the topological complexity of CMEs renders recent limited data reconstruction methods inapplicable. We propose an energy function, based on a phase field level set framework, for the joint segmentation and tomographic reconstruction of CMEs from measurements acquired by coronagraphs, a type of solar telescope. Our phase field model deals easily with complex topologies, and is more robust than classical methods when the data are very sparse. We use a fast variational algorithm that combines the finite element method with a trust region variant of Newton’s method to minimize the energy. We compare the results obtained with our model to classical regularized tomography for synthetic CME-like images

On the Variability of Mesospheric OH Emission Profiles

Mesospheric OH radiance limb profiles measured by the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument aboard the Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) spacecraft were inverted to yield altitude profiles of OH volume emission rates. The Abel inversion results of two months of data (from 1 June to 31 July 2004) were analyzed for the layer mean and standard deviation as a function of latitude and local time. Statistical analysis of SABER data shows that the global difference between the mean and standard deviation profiles for the OH(vu = 7, 8, 9; ∆v = 2) emission (at 2.0 µm) is approximately 2.8 km, very similar to the theoretical model prediction by Liu and Swenson (2003). This agreement is an indication that these variations from the mean are likely caused by atmospheric tides and gravity waves

High-resolution Multi-spectral Imaging with Diffractive Lenses and Learned Reconstruction

Spectral imaging is a fundamental diagnostic technique with widespread application. Conventional spectral imaging approaches have intrinsic limitations on spatial and spectral resolutions due to the physical components they rely on. To overcome these physical limitations, in this paper, we develop a novel multi-spectral imaging modality that enables higher spatial and spectral resolutions. In the developed computational imaging modality, we exploit a diffractive lens, such as a photon sieve, for both dispersing and focusing the optical field, and achieve measurement diversity by changing the focusing behavior of this lens. Because the focal length of a diffractive lens is wavelength-dependent, each measurement is a superposition of differently blurred spectral components. To reconstruct the individual spectral images from these superimposed and blurred measurements, model-based fast reconstruction algorithms are developed with deep and analytical priors using alternating minimization and unrolling. Finally, the effectiveness and performance of the developed technique is illustrated for an application in astrophysical imaging under various observation scenarios in the extreme ultraviolet (EUV) regime. The results demonstrate that the technique provides not only diffraction-limited high spatial resolution, as enabled by diffractive lenses, but also the capability of resolving close-by spectral sources that would not otherwise be possible with the existing techniques. This work enables high resolution multi-spectral imaging with low cost designs for a variety of applications and spectral regimes.Comment: accepted for publication in IEEE Transactions on Computational Imaging, see DOI belo

Estimation of Gravity Wave Momentum Flux with Spectroscopic Imaging

Atmospheric gravity waves play a significant role in the dynamics and thermal balance of the upper atmosphere. In this paper, we present a novel technique for automated and robust calculation of momentum flux of high-frequency quasi-monochromatic wave components from spectroscopic imaging and horizontal radar wind measurements. Our approach uses the two-dimensional (2-D) cross periodogram of two consecutive Doppler-shifted time-differenced (TD) images to identify wave components and estimate intrinsic wave parameters. Besides estimating the average perturbation of dominant waves in the whole field of view, this technique applies 2-D short-space Fourier transform to the TD images to identify localized wave events. With the wave parameters acquired, the momentum flux carried by all vertically propagating wave components is calculated using an analytical model relating the measured intensity perturbation to the wave amplitude. This model is tested by comparing wave perturbation amplitudes inferred from spectroscopic images with those from sodium lidar temperature measurements. The proposed technique enables characterization of the variations in the direction and strength of gravity waves with high temporal resolution for each clear data-taking night. The nightly results provide statistical information for investigating seasonal and geographical variations in momentum flux of gravity waves