Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples

This paper presents a novel power spectral density estimation technique for band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The technique employs multi-coset sampling and incorporates the advantages of compressed sensing (CS) when the power spectrum is sparse, but applies to sparse and nonsparse power spectra alike. The estimates are consistent piecewise constant approximations whose resolutions (width of the piecewise constant segments) are controlled by the periodicity of the multi-coset sampling. We show that compressive estimates exhibit better tradeoffs among the estimator's resolution, system complexity, and average sampling rate compared to their noncompressive counterparts. For suitable sampling patterns, noncompressive estimates are obtained as least squares solutions. Because of the non-negativity of power spectra, compressive estimates can be computed by seeking non-negative least squares solutions (provided appropriate sampling patterns exist) instead of using standard CS recovery algorithms. This flexibility suggests a reduction in computational overhead for systems estimating both sparse and nonsparse power spectra because one algorithm can be used to compute both compressive and noncompressive estimates.Comment: 26 pages, single spaced, 9 figure

Visualization of and Access to CloudSat Vertical Data through Google Earth

Online tools, pioneered by the Google Earth (GE), are facilitating the way in which scientists and general public interact with geospatial data in real three dimensions. However, even in Google Earth, there is no method for depicting vertical geospatial data derived from remote sensing satellites as an orbit curtain seen from above. Here, an effective solution is proposed to automatically render the vertical atmospheric data on Google Earth. The data are first processed through the Giovanni system, then, processed to be 15-second vertical data images. A generalized COLLADA model is devised based on the 15-second vertical data profile. Using the designed COLLADA models and satellite orbit coordinates, a satellite orbit model is designed and implemented in KML format to render the vertical atmospheric data in spatial and temporal ranges vividly. The whole orbit model consists of repeated model slices. The model slices, each representing 15 seconds of vertical data, are placed on the CloudSat orbit based on the size, scale, and angle with the longitude line that are precisely and separately calculated on the fly for each slice according to the CloudSat orbit coordinates. The resulting vertical scientific data can be viewed transparently or opaquely on Google Earth. Not only is the research bridged the science and data with scientists and the general public in the most popular way, but simultaneous visualization and efficient exploration of the relationships among quantitative geospatial data, e.g. comparing the vertical data profiles with MODIS and AIRS precipitation data, becomes possible

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Peer reviewedPublisher PD

VIOLA - A multi-purpose and web-based visualization tool for neuronal-network simulation output

Neuronal network models and corresponding computer simulations are invaluable tools to aid the interpretation of the relationship between neuron properties, connectivity and measured activity in cortical tissue. Spatiotemporal patterns of activity propagating across the cortical surface as observed experimentally can for example be described by neuronal network models with layered geometry and distance-dependent connectivity. The interpretation of the resulting stream of multi-modal and multi-dimensional simulation data calls for integrating interactive visualization steps into existing simulation-analysis workflows. Here, we present a set of interactive visualization concepts called views for the visual analysis of activity data in topological network models, and a corresponding reference implementation VIOLA (VIsualization Of Layer Activity). The software is a lightweight, open-source, web-based and platform-independent application combining and adapting modern interactive visualization paradigms, such as coordinated multiple views, for massively parallel neurophysiological data. For a use-case demonstration we consider spiking activity data of a two-population, layered point-neuron network model subject to a spatially confined excitation originating from an external population. With the multiple coordinated views, an explorative and qualitative assessment of the spatiotemporal features of neuronal activity can be performed upfront of a detailed quantitative data analysis of specific aspects of the data. Furthermore, ongoing efforts including the European Human Brain Project aim at providing online user portals for integrated model development, simulation, analysis and provenance tracking, wherein interactive visual analysis tools are one component. Browser-compatible, web-technology based solutions are therefore required. Within this scope, with VIOLA we provide a first prototype.Comment: 38 pages, 10 figures, 3 table

Organization of the magnetosphere during substorms

The change in degree of organization of the magnetosphere during substorms is investigated by analyzing various geomagnetic indices, as well as interplanetary magnetic field z-component and solar wind flow speed. We conclude that the magnetosphere self-organizes globally during substorms, but neither the magnetosphere nor the solar wind become more predictable in the course of a substorm. This conclusion is based on analysis of five hundred substorms in the period from 2000 to 2002. A minimal dynamic-stochastic model of the driven magnetosphere that reproduces many statistical features of substorm indices is discussed

A sub-Nyquist co-prime sampling music spectral approach for natural frequency identification of white-noise excited structures

Motivated by practical needs to reduce data transmission payloads in wireless sensors for vibration-based monitoring of civil engineering structures, this paper proposes a novel approach for identifying resonant frequencies of white-noise excited structures using acceleration measurements acquired at rates significantly below the Nyquist rate. The approach adopts the deterministic co-prime sub-Nyquist sampling scheme, originally developed to facilitate telecommunication applications, to estimate the autocorrelation function of response acceleration time-histories of low-amplitude white-noise excited structures treated as realizations of a stationary stochastic process. This is achieved without posing any sparsity conditions to the signals. Next, the standard MUSIC algorithm is applied to the estimated autocorrelation function to derive a denoised super-resolution pseudo-spectrum in which natural frequencies are marked by prominent spikes. The accuracy and applicability of the proposed approach is numerically assessed using computer-generated noise-corrupted acceleration time-history data obtained by a simulation-based framework pertaining to a white-noise excited structural system with two closely-spaced modes of vibration carrying the same amount of energy, and a third isolated weakly excited vibrating mode. All three natural frequencies are accurately identified by sampling at as low as 78% below Nyquist rate for signal to noise ratio as low as 0dB (i.e., energy of additive white noise equal to the signal energy), suggesting that the proposed approach is robust and noise-immune while it can reduce data transmission requirements in acceleration wireless sensors for natural frequency identification of engineering structures