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Quantized Information in Spectral Cyberspace

The constant-Q Gabor atom is developed for spectral power, information, and uncertainty quantification from time–frequency representations. Stable multiresolution spectral entropy algorithms are constructed with continuous wavelet and Stockwell transforms. The recommended processing and scaling method will depend on the signature of interest, the desired information, and the acceptable levels of uncertainty of signal and noise features. Selected Lamb wave signatures and information spectra from the 2022 Tonga eruption are presented as representative case studies. Resilient transformations from physical to information metrics are provided for sensor-agnostic signal processing, pattern recognition, and machine learning applications.

74 ATOMIC AND MOLECULAR PHYSICS↗

ICER-3D Hyperspectral Image Compression Software

Software has been developed to implement the ICER-3D algorithm. ICER-3D effects progressive, three-dimensional (3D), wavelet-based compression of hyperspectral images. If a compressed data stream is truncated, the progressive nature of the algorithm enables reconstruction of hyperspectral data at fidelity commensurate with the given data volume. The ICER-3D software is capable of providing either lossless or lossy compression, and incorporates an error-containment scheme to limit the effects of data loss during transmission. The compression algorithm, which was derived from the ICER image compression algorithm, includes wavelet-transform, context-modeling, and entropy coding subalgorithms. The 3D wavelet decomposition structure used by ICER-3D exploits correlations in all three dimensions of sets of hyperspectral image data, while facilitating elimination of spectral ringing artifacts, using a technique summarized in "Improving 3D Wavelet-Based Compression of Spectral Images" (NPO-41381), NASA Tech Briefs, Vol. 33, No. 3 (March 2009), page 7a. Correlation is further exploited by a context-modeling subalgorithm, which exploits spectral dependencies in the wavelet-transformed hyperspectral data, using an algorithm that is summarized in "Context Modeler for Wavelet Compression of Hyperspectral Images" (NPO-43239), which follows this article. An important feature of ICER-3D is a scheme for limiting the adverse effects of loss of data during transmission. In this scheme, as in the similar scheme used by ICER, the spatial-frequency domain is partitioned into rectangular error-containment regions. In ICER-3D, the partitions extend through all the wavelength bands. The data in each partition are compressed independently of those in the other partitions, so that loss or corruption of data from any partition does not affect the other partitions. Furthermore, because compression is progressive within each partition, when data are lost, any data from that partition received prior to the loss can be used to reconstruct that partition at lower fidelity. By virtue of the compression improvement it achieves relative to previous means of onboard data compression, this software enables (1) increased return of hyperspectral scientific data in the presence of limits on the rates of transmission of data from spacecraft to Earth via radio communication links and/or (2) reduction in spacecraft radio-communication power and/or cost through reduction in the amounts of data required to be downlinked and stored onboard prior to downlink. The software is also suitable for compressing hyperspectral images for ground storage or archival purposes.

Xie, Hua↗

Lightning and Other Influences On Tropical Tropospheric Ozone: Empirical Studies of Covariation

Tropical and subtropical tropospheric ozone are important radiatively active species, with particularly large effects in the upper third of the troposphere. Temporal variability of O3 has proved difficult to simulate day by day in process models. Thus, individual roles of lightning, biomass burning, and other pollution in providing precursor NO(x), radicals, and chain carriers (CO, hydrocarbons) remain unquantified by simulation, and it is theoretically reasonable that individual roles are magnified by a joint synergy. We use wavelet analysis and Burg-algorithm maximum entropy spectral analyses to describe time-scales and correlation of ozone with proxies for processes controlling its concentration. Our empirical studies link time variations apparent in several datasets: the SHADOZ (Southern Hemisphere Additional Ozonesondes) network stations (Nairobi, Fiji), and auxiliary series with power to explain ozone-determining processes, with some interpretation based on the TTO (Tropical Tropospheric Ozone) product derived from TOMS (the Total Ozone Mapping Spectrometer). The auxiliary series are The OTD/LIS(Optical Transient Detector/Lightning Imaging Sensor) measurements of the lightning NO(x) source, the OLR (Outgoing Longwave Radiation)measurement of high-topped clouds, and standard meteorological variables from the United States NCEP (National Centers for Environmental Prediction) and Data Assimilation Office analyses. Concentrating on equatorial ozone, we compare the statistical evidence on the variability of tropospheric ozone. Important variations occur on approximately two-week, two-month (Madden-Julian Oscillation) and annual scales, and relations with OLR suggest controls associated with continental clouds. Hence we are now using the Lightning Imaging Sensor data set to indicate NO(x) sources. We report initial results defining relative roles of the process mentioned affecting O3 using their covariance properties.

Chatfield, Robert B.↗

Reconfigurable Hardware for Compressing Hyperspectral Image Data

High-speed, low-power, reconfigurable electronic hardware has been developed to implement ICER-3D, an algorithm for compressing hyperspectral-image data. The algorithm and parts thereof have been the topics of several NASA Tech Briefs articles, including Context Modeler for Wavelet Compression of Hyperspectral Images (NPO-43239) and ICER-3D Hyperspectral Image Compression Software (NPO-43238), which appear elsewhere in this issue of NASA Tech Briefs. As described in more detail in those articles, the algorithm includes three main subalgorithms: one for computing wavelet transforms, one for context modeling, and one for entropy encoding. For the purpose of designing the hardware, these subalgorithms are treated as modules to be implemented efficiently in field-programmable gate arrays (FPGAs). The design takes advantage of industry- standard, commercially available FPGAs. The implementation targets the Xilinx Virtex II pro architecture, which has embedded PowerPC processor cores with flexible on-chip bus architecture. It incorporates an efficient parallel and pipelined architecture to compress the three-dimensional image data. The design provides for internal buffering to minimize intensive input/output operations while making efficient use of offchip memory. The design is scalable in that the subalgorithms are implemented as independent hardware modules that can be combined in parallel to increase throughput. The on-chip processor manages the overall operation of the compression system, including execution of the top-level control functions as well as scheduling, initiating, and monitoring processes. The design prototype has been demonstrated to be capable of compressing hyperspectral data at a rate of 4.5 megasamples per second at a conservative clock frequency of 50 MHz, with a potential for substantially greater throughput at a higher clock frequency. The power consumption of the prototype is less than 6.5 W. The reconfigurability (by means of reprogramming) of the FPGAs makes it possible to effectively alter the design to some extent to satisfy different requirements without adding hardware. The implementation could be easily propagated to future FPGA generations and/or to custom application-specific integrated circuits.

Aranki, Nazeeh↗

Wavelet compression techniques for hyperspectral data

Hyperspectral sensors are electro-optic sensors which typically operate in visible and near infrared bands. Their characteristic property is the ability to resolve a relatively large number (i.e., tens to hundreds) of contiguous spectral bands to produce a detailed profile of the electromagnetic spectrum. In contrast, multispectral sensors measure relatively few non-contiguous spectral bands. Like multispectral sensors, hyperspectral sensors are often also imaging sensors, measuring spectra over an array of spatial resolution cells. The data produced may thus be viewed as a three dimensional array of samples in which two dimensions correspond to spatial position and the third to wavelength. Because they multiply the already large storage/transmission bandwidth requirements of conventional digital images, hyperspectral sensors generate formidable torrents of data. Their fine spectral resolution typically results in high redundancy in the spectral dimension, so that hyperspectral data sets are excellent candidates for compression. Although there have been a number of studies of compression algorithms for multispectral data, we are not aware of any published results for hyperspectral data. Three algorithms for hyperspectral data compression are compared. They were selected as representatives of three major approaches for extending conventional lossy image compression techniques to hyperspectral data. The simplest approach treats the data as an ensemble of images and compresses each image independently, ignoring the correlation between spectral bands. The second approach transforms the data to decorrelate the spectral bands, and then compresses the transformed data as a set of independent images. The third approach directly generalizes two-dimensional transform coding by applying a three-dimensional transform as part of the usual transform-quantize-entropy code procedure. The algorithms studied all use the discrete wavelet transform. In the first two cases, a wavelet transform coder was used for the two-dimensional compression. The third case used a three dimensional extension of this same algorithm.

Evans, Bruce↗

Context Modeler for Wavelet Compression of Spectral Hyperspectral Images

A context-modeling sub-algorithm has been developed as part of an algorithm that effects three-dimensional (3D) wavelet-based compression of hyperspectral image data. The context-modeling subalgorithm, hereafter denoted the context modeler, provides estimates of probability distributions of wavelet-transformed data being encoded. These estimates are utilized by an entropy coding subalgorithm that is another major component of the compression algorithm. The estimates make it possible to compress the image data more effectively than would otherwise be possible. The following background discussion is prerequisite to a meaningful summary of the context modeler. This discussion is presented relative to ICER-3D, which is the name attached to a particular compression algorithm and the software that implements it. The ICER-3D software is summarized briefly in the preceding article, ICER-3D Hyperspectral Image Compression Software (NPO-43238). Some aspects of this algorithm were previously described, in a slightly more general context than the ICER-3D software, in "Improving 3D Wavelet-Based Compression of Hyperspectral Images" (NPO-41381), NASA Tech Briefs, Vol. 33, No. 3 (March 2009), page 7a. In turn, ICER-3D is a product of generalization of ICER, another previously reported algorithm and computer program that can perform both lossless and lossy wavelet-based compression and decompression of gray-scale-image data. In ICER-3D, hyperspectral image data are decomposed using a 3D discrete wavelet transform (DWT). Following wavelet decomposition, mean values are subtracted from spatial planes of spatially low-pass subbands prior to encoding. The resulting data are converted to sign-magnitude form and compressed. In ICER-3D, compression is progressive, in that compressed information is ordered so that as more of the compressed data stream is received, successive reconstructions of the hyperspectral image data are of successively higher overall fidelity.

Kiely, Aaron↗

Visual information processing; Proceedings of the Meeting, Orlando, FL, Apr. 20-22, 1992

Topics discussed in these proceedings include nonlinear processing and communications; feature extraction and recognition; image gathering, interpolation, and restoration; image coding; and wavelet transform. Papers are presented on noise reduction for signals from nonlinear systems; driving nonlinear systems with chaotic signals; edge detection and image segmentation of space scenes using fractal analyses; a vision system for telerobotic operation; a fidelity analysis of image gathering, interpolation, and restoration; restoration of images degraded by motion; and information, entropy, and fidelity in visual communication. Attention is also given to image coding methods and their assessment, hybrid JPEG/recursive block coding of images, modified wavelets that accommodate causality, modified wavelet transform for unbiased frequency representation, and continuous wavelet transform of one-dimensional signals by Fourier filtering.

Huck, Friedrich O.↗

Effects on Task Performance and Psychophysiological Measures of Performance During Normobaric Hypoxia Exposure

Human-autonomous systems have the potential to mitigate pilot cognitive impairment and improve aviation safety. A research team at NASA Langley conducted an experiment to study the impact of mild normobaric hypoxia induction on aircraft pilot performance and psychophysiological state. A within-subjects design involved non-hypoxic and hypoxic exposures while performing three 10-minute tasks. Results indicated the effect of 15,000 feet simulated altitude did not induce significant performance decrement but did produce increase in perceived workload. Analyses of psychophysiological responses evince the potential of biomarkers for hypoxia onset. This study represents on-going work at NASA intending to add to the current knowledge of psychophysiologically-based input to automation to increase aviation safety. Analyses involving coupling across physiological systems and wavelet transforms of cortical activity revealed patterns that can discern between the simulated altitude conditions. Specifically, multivariate entropy of ECG/Respiration components were found to be significant predictors (p< 0.02) of hypoxia. Furthermore, in EEG, there was a significant decrease in mid-level beta (15.19-18.37Hz) during the hypoxic condition in thirteen of sixteen sites across the scalp. Task performance was not appreciably impacted by the effect of 15,000 feet simulated altitude. Analyses of psychophysiological responses evince the potential of biomarkers for mild hypoxia onset.The potential for identifying shifts in underlying cortical and physiological systems could serve as a means to identify the onset of deteriorated cognitive state. Enabling such assessment in future flightdecks could permit increasingly autonomous systems-supported operations. Augmenting human operator through assessment of cognitive impairment has the potential to further improve operator performance and mitigate human error in safety critical contexts. This study represents ongoing work at NASA intending to add to the current knowledge of psychophysiologically-based input to automation to increase aviation safety.

Stephens, Chad↗

Progress in the Development of a Class of Efficient Low Dissipative High Order Shock-capturing Methods

In a series of papers, Olsson (1994, 1995), Olsson & Oliger (1994), Strand (1994), Gerritsen Olsson (1996), Yee et al. (1999a,b, 2000) and Sandham & Yee (2000), the issue of nonlinear stability of the compressible Euler and Navier-Stokes Equations, including physical boundaries, and the corresponding development of the discrete analogue of nonlinear stable high order schemes, including boundary schemes, were developed, extended and evaluated for various fluid flows. High order here refers to spatial schemes that are essentially fourth-order or higher away from shock and shear regions. The objective of this paper is to give an overview of the progress of the low dissipative high order shock-capturing schemes proposed by Yee et al. (1999a,b, 2000). This class of schemes consists of simple non-dissipative high order compact or non-compact central spatial differencings and adaptive nonlinear numerical dissipation operators to minimize the use of numerical dissipation. The amount of numerical dissipation is further minimized by applying the scheme to the entropy splitting form of the inviscid flux derivatives, and by rewriting the viscous terms to minimize odd-even decoupling before the application of the central scheme (Sandham & Yee). The efficiency and accuracy of these scheme are compared with spectral, TVD and fifth- order WENO schemes. A new approach of Sjogreen & Yee (2000) utilizing non-orthogonal multi-resolution wavelet basis functions as sensors to dynamically determine the appropriate amount of numerical dissipation to be added to the non-dissipative high order spatial scheme at each grid point will be discussed. Numerical experiments of long time integration of smooth flows, shock-turbulence interactions, direct numerical simulations of a 3-D compressible turbulent plane channel flow, and various mixing layer problems indicate that these schemes are especially suitable for practical complex problems in nonlinear aeroacoustics, rotorcraft dynamics, direct numerical simulation or large eddy simulation of compressible turbulent flows at various speeds including high-speed shock-turbulence interactions, and general long time wave propagation problems. These schemes, including entropy splitting, have also been extended to freestream preserving schemes on curvilinear moving grids for a thermally perfect gas (Vinokur & Yee 2000).

Yee, H. C.↗

Science with High Spatial Resolution Far-Infrared Data

The goal of this workshop was to discuss new science and techniques relevant to high spatial resolution processing of far-infrared data, with particular focus on high resolution processing of IRAS data. Users of the maximum correlation method, maximum entropy, and other resolution enhancement algorithms applicable to far-infrared data gathered at the Infrared Processing and Analysis Center (IPAC) for two days in June 1993 to compare techniques and discuss new results. During a special session on the third day, interested astronomers were introduced to IRAS HIRES processing, which is IPAC's implementation of the maximum correlation method to the IRAS data. Topics discussed during the workshop included: (1) image reconstruction; (2) random noise; (3) imagery; (4) interacting galaxies; (5) spiral galaxies; (6) galactic dust and elliptical galaxies; (7) star formation in Seyfert galaxies; (8) wavelet analysis; and (9) supernova remnants.

Terebey, Susan↗