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NASA NTRS1998

Feature Extraction of Event-Related Potentials Using Wavelets: An Application to Human Performance Monitoring

This report describes the development and evaluation of mathematical models for predicting human performance from discrete wavelet transforms (DWT) of event-related potentials (ERP) elicited by task-relevant stimuli. The DWT was compared to principal components analysis (PCA) for representation of ERPs in linear regression and neural network models developed to predict a composite measure of human signal detection performance. Linear regression models based on coefficients of the decimated DWT predicted signal detection performance with half as many f ree parameters as comparable models based on PCA scores. In addition, the DWT-based models were more resistant to model degradation due to over-fitting than PCA-based models. Feed-forward neural networks were trained using the backpropagation,-, algorithm to predict signal detection performance based on raw ERPs, PCA scores, or high-power coefficients of the DWT. Neural networks based on high-power DWT coefficients trained with fewer iterations, generalized to new data better, and were more resistant to overfitting than networks based on raw ERPs. Networks based on PCA scores did not generalize to new data as well as either the DWT network or the raw ERP network. The results show that wavelet expansions represent the ERP efficiently and extract behaviorally important features for use in linear regression or neural network models of human performance. The efficiency of the DWT is discussed in terms of its decorrelation and energy compaction properties. In addition, the DWT models provided evidence that a pattern of low-frequency activity (1 to 3.5 Hz) occurring at specific times and scalp locations is a reliable correlate of human signal detection performance.

Trejo, Leonard J.↗

NASA NTRS1999

Feature extraction of event-related potentials using wavelets: an application to human performance monitoring

This report describes the development and evaluation of mathematical models for predicting human performance from discrete wavelet transforms (DWT) of event-related potentials (ERP) elicited by task-relevant stimuli. The DWT was compared to principal components analysis (PCA) for representation of ERPs in linear regression and neural network models developed to predict a composite measure of human signal detection performance. Linear regression models based on coefficients of the decimated DWT predicted signal detection performance with half as many free parameters as comparable models based on PCA scores. In addition, the DWT-based models were more resistant to model degradation due to over-fitting than PCA-based models. Feed-forward neural networks were trained using the backpropagation algorithm to predict signal detection performance based on raw ERPs, PCA scores, or high-power coefficients of the DWT. Neural networks based on high-power DWT coefficients trained with fewer iterations, generalized to new data better, and were more resistant to overfitting than networks based on raw ERPs. Networks based on PCA scores did not generalize to new data as well as either the DWT network or the raw ERP network. The results show that wavelet expansions represent the ERP efficiently and extract behaviorally important features for use in linear regression or neural network models of human performance. The efficiency of the DWT is discussed in terms of its decorrelation and energy compaction properties. In addition, the DWT models provided evidence that a pattern of low-frequency activity (1 to 3.5 Hz) occurring at specific times and scalp locations is a reliable correlate of human signal detection performance. Copyright 1999 Academic Press.

Evoked Potentials↗

NASA NTRS1996

Perceptually Lossless Wavelet Compression

The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp -1), where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We propose a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a 'perceptually lossless' quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.

Watson, Andrew B.↗

NASA NTRS1995

Visibility of Wavelet Quantization Noise

The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp)-L , where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We describe a mathematical model to predict DWT noise detection thresholds as a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.

Watson, Andrew B.↗

NASA NTRS1997

Visibility of wavelet quantization noise

The discrete wavelet transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that we call DWT uniform quantization noise; it is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2-lambda, where r is display visual resolution in pixels/degree, and lambda is the wavelet level. Thresholds increase rapidly with wavelet spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from lowpass to horizontal/vertical to diagonal. We construct a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.

NASA Center ARC↗

NASA NTRS1987

Utilization of potatoes for life support systems in space. III - Productivity at successive harvest dates under 12-h and 24-h photoperiods

Efficient crop production for controlled ecological life support systems requires near-optimal growing conditions with harvests taken when production per unit area per unit time is maximum. This maximum for potato was determined using data on Norland plants which were grown in walk-in growth rooms under 12-h and 24-h photoperiods at 16 C. Results show that high tuber production can be obtained from potatoes grown under a continuous light regime. The dry weights (dwt) of tuber and of the entire plants were found to increase under both photoperiods until the final harvest date (148 days), reaching 5732 g tuber dwt and 704 g total dwt under 12-h, and 791 g tuber dwt and 972 g total dwt under 24-h.

Wheeler, Raymond M.↗

NASA NTRS2013

Dry wind tunnel system

This invention is a ground flutter testing system without a wind tunnel, called Dry Wind Tunnel (DWT) System. The DWT system consists of a Ground Vibration Test (GVT) hardware system, a multiple input multiple output (MIMO) force controller software, and a real-time unsteady aerodynamic force generation software, that is developed from an aerodynamic reduced order model (ROM). The ground flutter test using the DWT System operates on a real structural model, therefore no scaled-down structural model, which is required by the conventional wind tunnel flutter test, is involved. Furthermore, the impact of the structural nonlinearities on the aeroelastic stability can be included automatically. Moreover, the aeroservoelastic characteristics of the aircraft can be easily measured by simply including the flight control system in-the-loop. In addition, the unsteady aerodynamics generated computationally is interference-free from the wind tunnel walls. Finally, the DWT System can be conveniently and inexpensively carried out as a post GVT test with the same hardware, only with some possible rearrangement of the shakers and the inclusion of additional sensors.

Chen, Ping-Chih↗

NASA NTRS1993

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

Cai, Wei↗

NASA NTRS2000

Low potassium enhances sodium uptake in red-beet under moderate saline conditions

Due to the discrepancy in metabolic sodium (Na) requirements between plants and animals, cycling of Na between humans and plants is limited and critical to the proper functioning of bio-regenerative life support systems, being considered for long-term human habitats in space (e.g., Martian bases). This study was conducted to determine the effects of limited potassium (K) on growth, Na uptake, photosynthesis, ionic partitioning, and water relations of red-beet (Beta vulgaris L. ssp. vulgaris) under moderate Na-saline conditions. Two cultivars, Klein Bol, and Ruby Queen were grown for 42 days in a growth chamber using a re-circulating nutrient film technique where the supplied K levels were 5.0, 1.25, 0.25, and 0.10 mM in a modified half-strength Hoagland solution salinized with 50 mM NaCl. Reducing K levels from 5.0 to 0.10 mM quadrupled the Na uptake, and lamina Na levels reached -20 g kg-1 dwt. Lamina K levels decreased from -60 g kg-1 dwt at 5.0 mM K to -4.0 g kg-1 dwt at 0.10 mM K. Ruby Queen and Klein Bol responded differently to these changes in Na and K status. Klein Bol showed a linear decline in dry matter production with a decrease in available K, whereas for cv. Ruby Queen, growth was stimulated at 1.25 mM K and relatively insensitive to a further decreases of K down to 0.10 mM. Leaf glycinebetaine levels showed no significant response to the changing K treatments. Leaf relative water content and osmotic potential were significantly higher for both cultivars at low-K treatments. Leaf chlorophyll levels were significantly decreased at low-K treatments, but leaf photosynthetic rates showed no significant difference. No substantial changes were observed in the total cation concentration of plant tissues despite major shifts in the relative Na and K uptake at various K levels. Sodium accounted for 90% of the total cation uptake at the low K levels, and thus Na was likely replacing K in osmotic functions without negatively affecting the plant water status, or growth. Our results also suggest that cv. Ruby Queen can tolerate a much higher Na tissue concentration than cv. Klein Bol before there is any growth reduction. Grant numbers: 12180.

NASA Center KSC↗

NASA NTRS1987

Analysis of a dual-wavelength surface reference radar technique

The use of the single-wavelength surface reference technique (SRT), the standard dual-wavelength technique (DWT), and dual-wavelength surface reference technique (DSRT) for measuring precipitation from space is analyzed, and the results are compared. The characteristics of the three methods are described, and the surface return powers during clear air conditions are measured. It is observed that the rain rate estimates obtained with the DWT and DSRT are identical in form, and the surface reflectance can be derived from the estimates by replacing the rain reflectivity statistics with those of the backscattering cross section of the surface. The data reveal that the DSRT is more applicable than the SRT when the wavelength correlation in the backscattering cross section of the surface is high or when the mean values of the backscattering cross section at the two wavelengths are nearly equal.

Meneghini, Robert↗

NASA NTRS1993

Applications of wavelet-based compression to multidimensional Earth science data

A data compression algorithm involving vector quantization (VQ) and the discrete wavelet transform (DWT) is applied to two different types of multidimensional digital earth-science data. The algorithms (WVQ) is optimized for each particular application through an optimization procedure that assigns VQ parameters to the wavelet transform subbands subject to constraints on compression ratio and encoding complexity. Preliminary results of compressing global ocean model data generated on a Thinking Machines CM-200 supercomputer are presented. The WVQ scheme is used in both a predictive and nonpredictive mode. Parameters generated by the optimization algorithm are reported, as are signal-to-noise (SNR) measurements of actual quantized data. The problem of extrapolating hydrodynamic variables across the continental landmasses in order to compute the DWT on a rectangular grid is discussed. Results are also presented for compressing Landsat TM 7-band data using the WVQ scheme. The formulation of the optimization problem is presented along with SNR measurements of actual quantized data. Postprocessing applications are considered in which the seven spectral bands are clustered into 256 clusters using a k-means algorithm and analyzed using the Los Alamos multispectral data analysis program, SPECTRUM, both before and after being compressed using the WVQ program.

Bradley, Jonathan N.↗

NASA NTRS2001

The Application of Time-Frequency Methods to HUMS

This paper reports the study of four time-frequency transforms applied to vibration signals and presents a new metric for comparing them for fault detection. The four methods to be described and compared are the Short Time Frequency Transform (STFT), the Choi-Williams Distribution (WV-CW), the Continuous Wavelet Transform (CWT) and the Discrete Wavelet Transform (DWT). Vibration data of bevel gear tooth fatigue cracks, under a variety of operating load levels, are analyzed using these methods. The new metric for automatic fault detection is developed and can be produced from any systematic numerical representation of the vibration signals. This new metric reveals indications of gear damage with all of the methods on this data set. Analysis with the CWT detects mechanical problems with the test rig not found with the other transforms. The WV-CW and CWT use considerably more resources than the STFT and the DWT. More testing of the new metric is needed to determine its value for automatic fault detection and to develop methods of setting the threshold for the metric.

Pryor, Anna H.↗

NASA NTRS2003

Detailed Vibration Analysis of Pinion Gear with Time-Frequency Methods

In this paper, the authors show a detailed analysis of the vibration signal from the destructive testing of a spiral bevel gear and pinion pair containing seeded faults. The vibration signal is analyzed in the time domain, frequency domain and with four time-frequency transforms: the Short Time Frequency Transform (STFT), the Wigner-Ville Distribution with the Choi-Williams kernel (WV-CW), the Continuous Wavelet' Transform (CWT) and the Discrete Wavelet Transform (DWT). Vibration data of bevel gear tooth fatigue cracks, under a variety of operating load levels and damage conditions, are analyzed using these methods. A new metric for automatic anomaly detection is developed and can be produced from any systematic numerical representation of the vibration signals. This new metric reveals indications of gear damage with all of the time-frequency transforms, as well as time and frequency representations, on this data set. Analysis with the CWT detects changes in the signal at low torque levels not found with the other transforms. The WV-CW and CWT use considerably more resources than the STFT and the DWT. More testing of the new metric is needed to determine its value for automatic anomaly detection and to develop fault detection methods for the metric.

Mosher, Marianne↗

NASA NTRS1999

How far can sodium substitute for potassium in red beet?

Sodium (Na) movement between plants and humans is one of the more critical aspects of bioregenerative systems of life support, which NASA is studying for the establishment of long-term bases on the Lunar or Martian surface. This study was conducted to determine the extent to which Na can replace potassium (K) in red beet (Beta vulgaris L. ssp vulgaris) without adversely affecting metabolic functions such as water relations, photosynthetic rates, and thus growth. Two cultivars, Ruby Queen and Klein Bol, were grown for 42 days at 1200 micromoles mol-1 CO2 in a growth chamber using a re-circulating nutrient film technique with 0%, 75%, 95%, and 98% Na substitution for K in a modified half-strength Hoagland solution. Total biomass of Ruby Queen was greatest at 95% Na substitution and equal at 0% and 98% Na substitution. For Klein Bol, there was a 75% reduction in total biomass at 98% Na substitution. Nearly 95% of the total plant K was replaced with Na at 98% Na substitution in both cultivars. Potassium concentrations in leaves decreased from 120 g kg-1 dwt in 0% Na substitution to 3.5 g kg-1 dwt at 98% Na substitution. Leaf chlorophyll concentration, photosynthetic rate, and osmotic potential were not affected in either cultivar by Na substitution for K. Leaf glycinebetaine levels were doubled at 75% Na substitution in Klein Bol, but decreased at higher levels of Na substitution. For Ruby Queen, glycinebetaine levels in leaf increased with the first increase of Na levels and were maintained at the higher Na levels. These results indicate that in some cultivars of red beet, 95% of the normal tissue K can be replaced by Na without a reduction in growth.

NASA Discipline Life Support Systems↗

NASA NTRS2010

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↗

NASA NTRS1996

Stratospheric Horizontal Wavenumber Spectra of Winds, Potential Temperature, and Atmospheric Tracers Observed by High-Altitude Aircraft

Horizontal wavenumber power spectra of vertical and horizontal wind velocities, potential temperatures, and ozone and N(2)O mixing ratios, as measured in the mid-stratosphere during 73 ER-2 flights (altitude approx. 20km) are presented. The velocity and potential temperature spectra in the 100 to 1-km wavelength range deviate significantly from the uniform -5/3 power law expected for the inverse energy-cascade regime of two-dimensional turbulence and also for inertial-range, three-dimensional turbulence. Instead, steeper spectra approximately consistent with a -3 power law are observed at horizontal scales smaller than 3 km for all velocity components as well as potential temperature. Shallower spectra are observed at scales longer than 6 km. For horizontal velocity and potential temperature the spectral indices at longer scales are between -1.5 and -2.0. For vertical velocity the spectrum at longer scales become flat. It is argued that the observed velocity and potential temperature spectra are consistent with gravity waves. At smaller scales, the shapes are also superficially consistent with a Lumley-Shur-Weinstock buoyant subrange of turbulence and/or nonlinear gravity waves. Contemporaneous spectra of ozone and N(sub 2)O mixing ratio in the 100 to 1-km wavelength range do conform to an approximately uniform -5/3 power law. It is argued that this may reflect interactions between gravity wave air-parcel displacements and laminar or filamentary structures in the trace gas mixing ratio field produced by enstropy-cascading two-dimensional turbulence.

TRACE GAS MIXING RATIO FIELDS↗