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NASA NTRS1992

Recursive time-varying filter banks for subband image coding

Filter banks and wavelet decompositions that employ recursive filters have been considered previously and are recognized for their efficiency in partitioning the frequency spectrum. This paper presents an analysis of a new infinite impulse response (IIR) filter bank in which these computationally efficient filters may be changed adaptively in response to the input. The filter bank is presented and discussed in the context of finite-support signals with the intended application in subband image coding. In the absence of quantization errors, exact reconstruction can be achieved and by the proper choice of an adaptation scheme, it is shown that IIR time-varying filter banks can yield improvement over conventional ones.

Smith, Mark J. T.↗

NASA NTRS1992

Optical computing and neural networks; Proceedings of the Meeting, National Chiao Tung Univ., Hsinchu, Taiwan, Dec. 16, 17, 1992

The present conference discusses optical neural networks, photorefractive nonlinear optics, optical pattern recognition, digital and analog processors, and holography and its applications. Attention is given to bifurcating optical information processing, neural structures in digital halftoning, an exemplar-based optical neural net classifier for color pattern recognition, volume storage in photorefractive disks, and microlaser-based compact optical neuroprocessors. Also treated are the optical implementation of a feature-enhanced optical interpattern-associative neural network model and its optical implementation, an optical pattern binary dual-rail logic gate module, a theoretical analysis for holographic associative memories, joint transform correlators, image addition and subtraction via the Talbot effect, and optical wavelet-matched filters. (No individual items are abstracted in this volume)

Hsu, Ken-Yuh↗

NASA NTRS2005

Model-Based, Multiscale Self-Tuning Controller Developed for Active Combustion Control

New challenges concerning system health-monitoring and life-extending robust controls for the Ultra-Efficient Engine Technology Project, as well as other advanced engine and power system concepts at NASA and elsewhere, have renewed the control community s interest in smart, model-based methods. In particular, these challenges have further motivated efforts at the NASA Glenn Research Center to exploit the versatility and superiority of the dynamic features extraction of multiscale analysis for controls--such as with "wavelets" and "wavelet filter-banks.' The accomplishments reported herein pertain to the active suppression of combustion instabilities in liquid-fuel combustors via fuel modulation. The fundamentals and initial success of this innovation were reported for a unique demonstration of active combustion control (a research collaboration of NASA Glenn with Pratt & Whitney and the United Technologies Research Center, UTRC). This demonstration, conducted in 2002 at UTRC on the NASA single nozzle rig (SNR) combustor, was the first known suppression of high-frequency instability with a liquid-fueled combustor. The SNR is based on a high-powered military engine combustor that exhibited well-known instabilities.

Le, Dzu K.↗

NASA NTRS2014

AE Geomagnetic Index Predictability for High Speed Solar Wind Streams: A Wavelet Decomposition Technique

High speed solar wind streams cause geomagnetic activity at Earth. In this study we have applied a wavelet interactive filtering and reconstruction technique on the solar wind magnetic field components and AE index series to allowed us to investigate the relationship between the two. The IMF Bz component was found as the most significant solar wind parameter responsible by the control of the AE activity. Assuming magnetic reconnection associated to southward directed Bz is the main mechanism transferring energy into the magnetosphere, we adjust parameters to forecast the AE index. The adjusted routine is able to forecast AE, based only on the Bz measured at the L1 Lagrangian point. This gives a prediction approximately 30-70 minutes in advance of the actual geomagnetic activity. The correlation coefficient between the observed AE data and the forecasted series reached values higher than 0.90. In some cases the forecast reproduced particularities observed in the signal very well.The high correlation values observed and the high efficacy of the forecasting can be taken as a confirmation that reconnection is the main physical mechanism responsible for the energy transfer during HILDCAAs. The study also shows that the IMF Bz component low frequencies are most important for AE prediction.

Space weather↗

NASA NTRS1997

Correlation Filtering of Modal Dynamics using the Laplace Wavelet

Wavelet analysis allows processing of transient response data commonly encountered in vibration health monitoring tasks such as aircraft flutter testing. The Laplace wavelet is formulated as an impulse response of a single mode system to be similar to data features commonly encountered in these health monitoring tasks. A correlation filtering approach is introduced using the Laplace wavelet to decompose a signal into impulse responses of single mode subsystems. Applications using responses from flutter testing of aeroelastic systems demonstrate modal parameters and stability estimates can be estimated by correlation filtering free decay data with a set of Laplace wavelets.

Freudinger, Lawrence C.↗

NASA NTRS2000

CVS Decomposition of 3D Homogeneous Turbulence Using Orthogonal Wavelets

This paper compares the filtering used in Coherent Vortex Simulation (CVS) decomposition with an orthogonal wavelet basis, with the Proper Orthogonal Decomposition (POD) or Fourier filtering. Both methods are applied to a field of Direct Numerical Simulation (DNS) data of 3D forced homogeneous isotropic turbulence at microscale Reynolds number R(sub lambda) = 168. We show that, with only 3%N retained modes, CVS filtering separates the coherent vortex tubes from the incoherent background flow. The latter is structureless, has an equipartition energy spectrum, and has a Gaussian velocity probability distribution function (PDF) and an exponential vorticity PDF. On the other hand, the Fourier basis does not extract the coherent vortex tubes cleanly and leaves organized structures in the residual high wavenumber modes whose PDFs are stretched exponentials for both the velocity and the vorticity.

Farge, Marie↗

NASA NTRS1997

Wavelet Analyses of F/A-18 Aeroelastic and Aeroservoelastic Flight Test Data

Time-frequency signal representations combined with subspace identification methods were used to analyze aeroelastic flight data from the F/A-18 Systems Research Aircraft (SRA) and aeroservoelastic data from the F/A-18 High Alpha Research Vehicle (HARV). The F/A-18 SRA data were produced from a wingtip excitation system that generated linear frequency chirps and logarithmic sweeps. HARV data were acquired from digital Schroeder-phased and sinc pulse excitation signals to actuator commands. Nondilated continuous Morlet wavelets implemented as a filter bank were chosen for the time-frequency analysis to eliminate phase distortion as it occurs with sliding window discrete Fourier transform techniques. Wavelet coefficients were filtered to reduce effects of noise and nonlinear distortions identically in all inputs and outputs. Cleaned reconstructed time domain signals were used to compute improved transfer functions. Time and frequency domain subspace identification methods were applied to enhanced reconstructed time domain data and improved transfer functions, respectively. Time domain subspace performed poorly, even with the enhanced data, compared with frequency domain techniques. A frequency domain subspace method is shown to produce better results with the data processed using the Morlet time-frequency technique.

Martin J Brenner↗

NASA NTRS2004

Adaptive Numerical Dissipative Control in High Order Schemes for Multi-D Non-Ideal MHD

The goal is to extend our adaptive numerical dissipation control in high order filter schemes and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free of numerical dissipation contamination. These scheme-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multi-resolution wavelets (WAV) (for the above types of flow feature). These filter approaches also provide a natural and efficient way for the minimization of Div(B) numerical error. The filter scheme consists of spatially sixth order or higher non-dissipative spatial difference operators as the base scheme for the inviscid flux derivatives. If necessary, a small amount of high order linear dissipation is used to remove spurious high frequency oscillations. For example, an eighth-order centered linear dissipation (AD8) might be included in conjunction with a spatially sixth-order base scheme. The inviscid difference operator is applied twice for the viscous flux derivatives. After the completion of a full time step of the base scheme step, the solution is adaptively filtered by the product of a 'flow detector' and the 'nonlinear dissipative portion' of a high-resolution shock-capturing scheme. In addition, the scheme independent wavelet flow detector can be used in conjunction with spatially compact, spectral or spectral element type of base schemes. The ACM and wavelet filter schemes using the dissipative portion of a second-order shock-capturing scheme with sixth-order spatial central base scheme for both the inviscid and viscous MHD flux derivatives and a fourth-order Runge-Kutta method are denoted.

Yee, H. C.↗

NASA NTRS1998

On-Line Robust Modal Stability Prediction using Wavelet Processing

Wavelet analysis for filtering and system identification has been used to improve the estimation of aeroservoelastic stability margins. The conservatism of the robust stability margins is reduced with parametric and nonparametric time- frequency analysis of flight data in the model validation process. Nonparametric wavelet processing of data is used to reduce the effects of external disturbances and unmodeled dynamics. Parametric estimates of modal stability are also extracted using the wavelet transform. Computation of robust stability margins for stability boundary prediction depends on uncertainty descriptions derived from the data for model validation. The F-18 High Alpha Research Vehicle aeroservoelastic flight test data demonstrates improved robust stability prediction by extension of the stability boundary beyond the flight regime. Guidelines and computation times are presented to show the efficiency and practical aspects of these procedures for on-line implementation. Feasibility of the method is shown for processing flight data from time- varying nonstationary test points.

Brenner, Martin J.↗

NASA NTRS2010

Searching for Turbulent Spectra in Mutliple Spacecraft Observations

The subject of magnetohydrodynamic simulations in the 1980's, magnetic turbulence has reemerged as a favored explanation for the production of fast magnetic reconnection. Recent three-dimensional simulations reveal the formation of secondary islands that serve to shorten the current sheet and increase the accelerating electric field, while both simulations and observations witness electron holes whose collapse energizes electrons. However, little work has been done to investigate the presence of turbulent magnetic and electric field spectra in association with in situ reconnection observations in space. In this study we address this deficiency by analyzing the wavelength spectra of two reconnection events established by multiple spacecraft observations in previous publications. We apply a k-filtering analysis to determine the wave vectors. To optimize the quality of the k-filtering analysis and minimize aliasing, we select multi-spacecraft observations having optimal spacecraft tetrahedral geometry and dimensions that resolve wavelengths within the ion diffusion region. We have chosen one dayside and one nightside reconnection event each observed by the Cluster spacecraft. Spatial correlation between the reconnecting current sheet and a turbulent magnetic spectrum supports an association between turbulence and reconnection in space. The k-filtering method, a wavelet time-frequency spectrum, and a polarization analysis serve to identify wave modes associated with the turbulence. A calculation of the reconnection electric field based on the normal component of the reconnecting magnetic field provides an estimate of the reconnection rate.

Wendel, Deirdre E.↗

NASA NTRS2010

Transiting Planet Search in the Kepler Pipeline

The Kepler Mission simultaneously measures the brightness of more than 160,000 stars every 29.4 minutes over a 3.5-year mission to search for transiting planets. Detecting transits is a signal-detection problem where the signal of interest is a periodic pulse train and the predominant noise source is non-white, non-stationary (1/f) type process of stellar variability. Many stars also exhibit coherent or quasi-coherent oscillations. The detection algorithm first identifies and removes strong oscillations followed by an adaptive, wavelet-based matched filter. We discuss how we obtain super-resolution detection statistics and the effectiveness of the algorithm for Kepler flight data.

Jenkins, Jon M.↗

NASA NTRS2010

An Algorithm for the Fitting of Planet Models to Kepler Light Curves

We describe an algorithm which fits model planetary system parameters to light curves from Kepler Mission target stars. The algorithm begins by producing an initial model of the system which is used to seed the fit,with particular emphasis on obtaining good transit timing parameters. An attempt is then made to determine whether the observed transits are more likely due to a planet or an eclipsing binary. In the event that the transits are consistent with a transiting planet, an iterative fitting process is initiated: a wavelet-based whitening filter is used to eliminate stellar variations on timescales long compared to a transit; a robust nonlinear fitter operating on the whitened light curve produces a new model of the system; and the procedure iterates until convergence upon a self-consistent whitening filter and planet model. The fitted transits are removed from the light curve anda search for additional planet candidates is performed upon the residual light curve. The fitted models are used in additional tests which identify false positive planet detections: multiple planet candidates with near-identical fitted periods are far more likely to be an eclipsing binary, for example, while target stars in which the model lightcurve is correlated with the star centroid position may indicate a background eclipsing binary, and subtraction of all model planet candidates yields a light curve of pure noise and stellar variability, which can be used to study the probability that the planet candidates result from statistical fluctuations in the data.

Exoplanet↗

NASA NTRS2018

The Impact of Stellar Variability on the Detection of Transiting Earth-like Planets

Stellar variability represents a key limitation on the detectability of weak transit signatures of small, Earth-size planets with space-based missions such as NASA's Kepler Mission or ESA's PLATO Mission. The expectations for the performance of the Kepler Mission in the face of solar-like variability were predicated on observations of the Sun with the Variability of Solar Irradiance and Gravity Oscillations (VIRGO) instrument aboard NASA and ESA's joint Solar and Heliospheric Observatory (SOHO) mission, which was launched in December 1995. Analyses of SOHO data indicated that solar-like variability would contribute approx.10 ppm to Kepler's noise budget at 6.5 ours, a typical grazing transit timescale. This proved to be optimistic as the typical 12th mag G2V star in the Kepler field of view exhibited 20 ppm of stellar variability-related noise at 6.5 hours, making the detection of true Earth-Sun analogs more difficult. While the consequent increase in the total noise at 6.5 hours from 20 ppm to 30 ppm could have been overcome by extending the mission to a total duration of 7 to 8 years. Unfortunately, a second reaction wheel failed in May 2013, ending the Kepler primary mission. Nevertheless, Kepler proved to be a veritable cornucopia of science results, both for exoplanets and for astrophysics. The phenomenal photometric precision and continuous observations required in order to identify small, rocky transiting planets enables the study of a large range of phenomena contributing to stellar variability for many thousands of solar-like stars in Kepler's field of view in exquisite detail. These effects range from less than 1 ppm acoustic oscillations on timescales from a few minutes and longward, to flares on timescales of hours, to spot-induced modulation on timescales of days to weeks to activity cycles on timescales of months to years. Kepler discovered over 2600 validated and confirmed exoplanets, and measured the pressure-mode oscillations of over 15000 stars over the course of its mission and the reconstituted K2 mission. We present the adaptive, wavelet-based matched filter used for both the Kepler and the TESS missions, and discuss the connections between this detection algorithm and fundamental detection theory, which allows the detector to function as a noise characterization engine. This provides a dynamical measurement of the photometric noise at transit timescales and thus, a key performance metric for missions like PLATO and Kepler. We give an overview of the stellar variability we see across the full range of spectral types observed by Kepler, from the cool, small red M stars to the hot, large late A stars, both in terms of amplitude as well as timescale.

transit surveys↗

NASA NTRS2019

Time Series Analysis in the Search for Other Worlds Through Transit Photometry

The Kepler Mission launched in June 2009 to commence NASA's first mission to search for potentially habitable, Earth-size planets orbiting Sun-like stars. Kepler discovered explanets via the transit method: searching for minute (100 ppm) drops in brightness lasting 1 - 13 hours corresponding to occasions where the planet crosses the face of its host star from Kepler's point of view. The exquisite precision required to carry out the Kepler mission (20 ppm in 6.5 hours) pushed astronomical time series analysis to the limits, and motivated the development of novel algorithmic approaches. Transit signatures of rocky planets are often dwarfed by the intrinsic stellar variability, which is not white noise, and often is non-stationary, and by instrumental systematic effects, which can include transients and electronic artifacts. Surmounting this challenging regime of weak, temporally compact, periodic signals in observation noise with strong systematics and other sources of variability motivated the development of 1) an overcomplete, non-decimated, wavelet-based matched filter to jointly estimate the properties of the non-stationary, non-white observation noise process, and 2) a multi-scale, maximum a posteriori (msMAP) approach to identifying and removing instrumental systematic effects. After over nine years of observations, the Kepler spacecraft finally ran out of fuel in November 2018, ending its data collection activities. Over 2300 planets were discovered by Kepler in its primary mission, and over 355 have been discovered by K2, the repurposed mission that followed Kepler's primary mission after the loss of a second reaction wheel in May 2013. We have ported the Kepler science pipeline for the Transiting Exoplanet Survey Satellite (TESS) Mission, which began science observations in July 2019, and report initial results and performance of the modified science pipeline.The Kepler and TESS Missions are supported by NASA's Science Mission Directorate.

transit surveys↗

NASA NTRS2018

The Impact of Stellar Variability on the Detection of Transiting Earth-Like Planets

Stellar variability represents a key limitation on the detectability of weak transit signatures of small, Earth-size planets with space-based missions such as NASA's Kepler Mission or ESA's PLATO Mission. The expectations for the performance of the Kepler Mission in the face of solar-like variability were predicated on observations of the Sun with the Variability of Solar Irradiance and Gravity Oscillations (VIRGO) instrument aboard NASA and ESA's joint Solar and Heliospheric Observatory (SOHO) mission, which was launched in December 1995. Analyses of SOHO data indicated that solar-like variability would contribute ~10 ppm to Kepler's noise budget at 6.5 ours, a typical grazing transit timescale. This proved to be optimistic as the typical 12th mag G2V star in the Kepler field of view exhibited 20 ppm of stellar variability-related noise at 6.5 hours, making the detection of true Earth-Sun analogs more difficult. While the consequent increase in the total noise at 6.5 hours from 20 ppm to 30 ppm could have been overcome by extending the mission to a total duration of 7 to 8 years. Unfortunately, a second reaction wheel failed in May 2013, ending the Kepler primary mission. Nevertheless, Kepler proved to be a veritable cornucopia of science results, both for exoplanets and for astrophysics. The phenomenal photometric precision and continuous observations required in order to identify small, rocky transiting planets enables the study of a large range of phenomena contributing to stellar variability for many thousands of solar-like stars in Kepler's field of view in exquisite detail. These effects range from <1 ppm acoustic oscillations on timescales from a few minutes and longward, to flares on timescales of hours, to spot-induced modulation on timescales of days to weeks to activity cycles on timescales of months to years. Kepler discovered over 2600 validated and confirmed exoplanets, and measured the pressure-mode oscillations of over 15000 stars over the course of its mission and the reconstituted K2 mission. We present the adaptive, wavelet-based matched filter used for both the Kepler and the TESS missions, and discuss the connections between this detection algorithm and fundamental detection theory, which allows the detector to function as a noise characterization engine. This provides a dynamical measurement of the photometric noise at transit timescales and thus, a key performance metric for missions like PLATO and Kepler. We give an overview of the stellar variability we see across the full range of spectral types observed by Kepler, from the cool, small red M stars to the hot, large late A stars, both in terms of amplitude as well as timescale.

exoplanets↗

NASA NTRS1999

An Application of Rotation- and Translation-Invariant Overcomplete Wavelets to the Registration of Remotely Sensed Imagery

A wavelet-based image registration approach has previously been proposed by the authors. In this work, wavelet coefficient maxima obtained from an orthogonal wavelet decomposition using Daubechies filters were utilized to register images in a multi-resolution fashion. Tested on several remote sensing datasets, this method gave very encouraging results. Despite the lack of translation-invariance of these filters, we showed that when using cross-correlation as a feature matching technique, features of size larger than twice the size of the filters are correctly registered by using the low-frequency subbands of the Daubechies wavelet decomposition. Nevertheless, high-frequency subbands are still sensitive to translation effects. In this work, we are considering a rotation- and translation-invariant representation developed by E. Simoncelli and integrate it in our image registration scheme. The two types of filters, Daubechies and Simoncelli filters, are then being compared from a registration point of view, utilizing synthetic data as well as data from the Landsat/ Thematic Mapper (TM) and from the NOAA Advanced Very High Resolution Radiometer (AVHRR).

LeMoigne, Jacqueline↗

NASA NTRS1999

An Application of Rotation- and Translation-Invariant Overcomplete Wavelets to the registration of Remotely Sensed Imagery

LeMoigne, Jacqueline↗

NASA NTRS2010

Multi-Stage System for Automatic Target Recognition

A multi-stage automated target recognition (ATR) system has been designed to perform computer vision tasks with adequate proficiency in mimicking human vision. The system is able to detect, identify, and track targets of interest. Potential regions of interest (ROIs) are first identified by the detection stage using an Optimum Trade-off Maximum Average Correlation Height (OT-MACH) filter combined with a wavelet transform. False positives are then eliminated by the verification stage using feature extraction methods in conjunction with neural networks. Feature extraction transforms the ROIs using filtering and binning algorithms to create feature vectors. A feedforward back-propagation neural network (NN) is then trained to classify each feature vector and to remove false positives. The system parameter optimizations process has been developed to adapt to various targets and datasets. The objective was to design an efficient computer vision system that can learn to detect multiple targets in large images with unknown backgrounds. Because the target size is small relative to the image size in this problem, there are many regions of the image that could potentially contain the target. A cursory analysis of every region can be computationally efficient, but may yield too many false positives. On the other hand, a detailed analysis of every region can yield better results, but may be computationally inefficient. The multi-stage ATR system was designed to achieve an optimal balance between accuracy and computational efficiency by incorporating both models. The detection stage first identifies potential ROIs where the target may be present by performing a fast Fourier domain OT-MACH filter-based correlation. Because threshold for this stage is chosen with the goal of detecting all true positives, a number of false positives are also detected as ROIs. The verification stage then transforms the regions of interest into feature space, and eliminates false positives using an artificial neural network classifier. The multi-stage system allows tuning the detection sensitivity and the identification specificity individually in each stage. It is easier to achieve optimized ATR operation based on its specific goal. The test results show that the system was successful in substantially reducing the false positive rate when tested on a sonar and video image datasets.

Chao, Tien-Hsin↗