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NASA NTRS2009

Highly Scalable Matching Pursuit Signal Decomposition Algorithm

Matching Pursuit Decomposition (MPD) is a powerful iterative algorithm for signal decomposition and feature extraction. MPD decomposes any signal into linear combinations of its dictionary elements or atoms . A best fit atom from an arbitrarily defined dictionary is determined through cross-correlation. The selected atom is subtracted from the signal and this procedure is repeated on the residual in the subsequent iterations until a stopping criterion is met. The reconstructed signal reveals the waveform structure of the original signal. However, a sufficiently large dictionary is required for an accurate reconstruction; this in return increases the computational burden of the algorithm, thus limiting its applicability and level of adoption. The purpose of this research is to improve the scalability and performance of the classical MPD algorithm. Correlation thresholds were defined to prune insignificant atoms from the dictionary. The Coarse-Fine Grids and Multiple Atom Extraction techniques were proposed to decrease the computational burden of the algorithm. The Coarse-Fine Grids method enabled the approximation and refinement of the parameters for the best fit atom. The ability to extract multiple atoms within a single iteration enhanced the effectiveness and efficiency of each iteration. These improvements were implemented to produce an improved Matching Pursuit Decomposition algorithm entitled MPD++. Disparate signal decomposition applications may require a particular emphasis of accuracy or computational efficiency. The prominence of the key signal features required for the proper signal classification dictates the level of accuracy necessary in the decomposition. The MPD++ algorithm may be easily adapted to accommodate the imposed requirements. Certain feature extraction applications may require rapid signal decomposition. The full potential of MPD++ may be utilized to produce incredible performance gains while extracting only slightly less energy than the standard algorithm. When the utmost accuracy must be achieved, the modified algorithm extracts atoms more conservatively but still exhibits computational gains over classical MPD. The MPD++ algorithm was demonstrated using an over-complete dictionary on real life data. Computational times were reduced by factors of 1.9 and 44 for the emphases of accuracy and performance, respectively. The modified algorithm extracted similar amounts of energy compared to classical MPD. The degree of the improvement in computational time depends on the complexity of the data, the initialization parameters, and the breadth of the dictionary. The results of the research confirm that the three modifications successfully improved the scalability and computational efficiency of the MPD algorithm. Correlation Thresholding decreased the time complexity by reducing the dictionary size. Multiple Atom Extraction also reduced the time complexity by decreasing the number of iterations required for a stopping criterion to be reached. The Course-Fine Grids technique enabled complicated atoms with numerous variable parameters to be effectively represented in the dictionary. Due to the nature of the three proposed modifications, they are capable of being stacked and have cumulative effects on the reduction of the time complexity.

Christensen, Daniel↗

NASA NTRS2003

Aeroservoelastic Model Validation and Test Data Analysis of the F/A-18 Active Aeroelastic Wing

Model validation and flight test data analysis require careful consideration of the effects of uncertainty, noise, and nonlinearity. Uncertainty prevails in the data analysis techniques and results in a composite model uncertainty from unmodeled dynamics, assumptions and mechanics of the estimation procedures, noise, and nonlinearity. A fundamental requirement for reliable and robust model development is an attempt to account for each of these sources of error, in particular, for model validation, robust stability prediction, and flight control system development. This paper is concerned with data processing procedures for uncertainty reduction in model validation for stability estimation and nonlinear identification. F/A-18 Active Aeroelastic Wing (AAW) aircraft data is used to demonstrate signal representation effects on uncertain model development, stability estimation, and nonlinear identification. Data is decomposed using adaptive orthonormal best-basis and wavelet-basis signal decompositions for signal denoising into linear and nonlinear identification algorithms. Nonlinear identification from a wavelet-based Volterra kernel procedure is used to extract nonlinear dynamics from aeroelastic responses, and to assist model development and uncertainty reduction for model validation and stability prediction by removing a class of nonlinearity from the uncertainty.

Brenner, Martin J.↗

NASA NTRS1992

Multiresolution image gathering and restoration

In this paper we integrate multiresolution decomposition with image gathering and restoration. This integration leads to a Wiener-matrix filter that accounts for the aliasing, blurring, and noise in image gathering, together with the digital filtering and decimation in signal decomposition. Moreover, as implemented here, the Wiener-matrix filter completely suppresses the blurring and raster effects of the image-display device. We demonstrate that this filter can significantly improve the fidelity and visual quality produced by conventional image reconstruction. The extent of this improvement, in turn, depends on the design of the image-gathering device.

Fales, Carl L.↗

NASA NTRS2002

Spectral Data Reduction via Wavelet Decomposition

The greatest advantage gained from hyperspectral imagery is that narrow spectral features can be used to give more information about materials than was previously possible with broad-band multispectral imagery. For many applications, the new larger data volumes from such hyperspectral sensors, however, present a challenge for traditional processing techniques. For example, the actual identification of each ground surface pixel by its corresponding reflecting spectral signature is still one of the most difficult challenges in the exploitation of this advanced technology, because of the immense volume of data collected. Therefore, conventional classification methods require a preprocessing step of dimension reduction to conquer the so-called "curse of dimensionality." Spectral data reduction using wavelet decomposition could be useful, as it does not only reduce the data volume, but also preserves the distinctions between spectral signatures. This characteristic is related to the intrinsic property of wavelet transforms that preserves high- and low-frequency features during the signal decomposition, therefore preserving peaks and valleys found in typical spectra. When comparing to the most widespread dimension reduction technique, the Principal Component Analysis (PCA), and looking at the same level of compression rate, we show that Wavelet Reduction yields better classification accuracy, for hyperspectral data processed with a conventional supervised classification such as a maximum likelihood method.

Kaewpijit, S.↗

NASA NTRS1992

Sub-band/transform compression of video sequences

The progress on compression of video sequences is discussed. The overall goal of the research was the development of data compression algorithms for high-definition television (HDTV) sequences, but most of our research is general enough to be applicable to much more general problems. We have concentrated on coding algorithms based on both sub-band and transform approaches. Two very fundamental issues arise in designing a sub-band coder. First, the form of the signal decomposition must be chosen to yield band-pass images with characteristics favorable to efficient coding. A second basic consideration, whether coding is to be done in two or three dimensions, is the form of the coders to be applied to each sub-band. Computational simplicity is of essence. We review the first portion of the year, during which we improved and extended some of the previous grant period's results. The pyramid nonrectangular sub-band coder limited to intra-frame application is discussed. Perhaps the most critical component of the sub-band structure is the design of bandsplitting filters. We apply very simple recursive filters, which operate at alternating levels on rectangularly sampled, and quincunx sampled images. We will also cover the techniques we have studied for the coding of the resulting bandpass signals. We discuss adaptive three-dimensional coding which takes advantage of the detection algorithm developed last year. To this point, all the work on this project has been done without the benefit of motion compensation (MC). Motion compensation is included in many proposed codecs, but adds significant computational burden and hardware expense. We have sought to find a lower-cost alternative featuring a simple adaptation to motion in the form of the codec. In sequences of high spatial detail and zooming or panning, it appears that MC will likely be necessary for the proposed quality and bit rates.

Sauer, Ken↗

NASA NTRS1991

Full complex modulation with two one-parameter SLMs

Although the action of a spatial light modulator (SLM) is usually restricted to certain locations on the operating curve of the complex plane, NASA is planning to use architectures that allow two continuously variable SLMs to function jointly so as to access the full interior of a closed curve in the complex plane. This paper describes three fundamental methods for attaining full complex modulation. The mathematics for two of these methods is presented, and signal decomposition in their terms is outlined.

Juday, Richard D.↗

NASA NTRS2004

Measurements With a Split-Fiber Probe in Complex Unsteady Flows

A split-fiber probe was used to acquire unsteady data in a research compressor. A calibration method was devised for a split-fiber probe, and a new algorithm was developed to decompose split-fiber probe signals into velocity magnitude and direction. The algorithm is based on the minimum value of a merit function that is built over the entire range of flow velocities for which the probe was calibrated. The split-fiber probe performance and signal decomposition was first verified in a free-jet facility by comparing the data from three thermo-anemometric probes, namely a single-wire, a single-fiber, and the split-fiber probe. All three probes performed extremely well as far as the velocity magnitude was concerned. However, there are differences in the peak values of measured velocity unsteadiness in the jet shear layer. The single-wire probe indicates the highest unsteadiness level, followed closely by the split-fiber probe. The single-fiber probe indicates a noticeably lower level of velocity unsteadiness. Experiments in the NASA Low Speed Axial Compressor facility revealed similar results. The mean velocities agreed well, and differences in the velocity unsteadiness are similar to the case of a free jet. A reason for these discrepancies is in the different frequency response characteristics of probes used. It follows that the single-fiber probe has the slowest frequency response. In summary, the split-fiber probe worked reliably during the entire program. The acquired data averaged in time followed closely data acquired by conventional pneumatic probes.

Lepicovsky, Jan↗

NASA NTRS2003

Non-Linear Structural Dynamics Characterization using a Scanning Laser Vibrometer

This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal \ielocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second. third, and fourth natural frequencies are examined in detail. Influences of the fixture mass. gravity. mass centers of mode shapes. and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances. energy transfer from high-frequency modes to the first mode. and amplitude- and phase- modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.

Pai, P. F.↗

NASA NTRS2005

Empirical mode decomposition for analyzing acoustical signals

The present invention discloses a computer implemented signal analysis method through the Hilbert-Huang Transformation (HHT) for analyzing acoustical signals, which are assumed to be nonlinear and nonstationary. The Empirical Decomposition Method (EMD) and the Hilbert Spectral Analysis (HSA) are used to obtain the HHT. Essentially, the acoustical signal will be decomposed into the Intrinsic Mode Function Components (IMFs). Once the invention decomposes the acoustic signal into its constituting components, all operations such as analyzing, identifying, and removing unwanted signals can be performed on these components. Upon transforming the IMFs into Hilbert spectrum, the acoustical signal may be compared with other acoustical signals.

Huang, Norden E.↗

NASA NTRS1984

An experimental study of the properties of surface pressure fluctuations in strong adverse pressure gradient turbulent boundary layers

Experimental data were obtained on blade self-noise generation by strong adverse-pressure-gradient attached boundary layers and by separated turbulent boundary layers that accompany stall. Two microphones were calibrated, placed in plastic housing, and installed in a wind tunnel where observations of acoustic and turbulent signals permitted decomposition of the surface pressure fluctuation signals into the propagated acoustic part and the turbulent-flow generated portion. To determine the convective wave speed of the turbulent contributions, the microphones were spaced a small distance apart in the streamwise direction and correlations were obtained. The turbulent surface pressure spectra upstream of detachment and downstream of the beginning of separation are discussed as well as measurements of turbulent velocity spectra and wavespeeds.

Simpson, R. L.↗

NASA NTRS1991

Superfine resolution acoustooptic spectrum analysis

High resolution spectrum analysis of RF signals is required in applications such as the search for extraterrestrial intelligence, RF interference monitoring, or general purpose decomposition of signals. Sub-Hertz resolution in three-dimensional acoustooptic spectrum analysis is theoretically and experimentally demonstrated. The operation of a two-dimensional acoustooptic spectrum analyzer is extended to include time integration over a sequence of CCD frames.

Ansari, Homayoon↗

NASA NTRS1992

Thermal degradation study of silicon carbide threads developed for advanced flexible thermal protection systems

Silicon carbide (SiC) fiber is a material that may be used in advanced thermal protection systems (TPS) for future aerospace vehicles. SiC fiber's mechanical properties depend greatly on the presence or absence of sizing and its microstructure. In this research, silicon dioxide is found to be present on the surface of the fiber. Electron Spectroscopy for Chemical Analysis (ESCA) and Scanning Electron Microscopy (SEM) show that a thin oxide layer (SiO2) exists on the as-received fibers, and the oxide thickness increases when the fibers are exposed to high temperature. ESCA also reveals no evidence of Si-C bonding on the fiber surface on both as-received and heat treated fibers. The silicon oxide layer is thought to signal the decomposition of SiC bonds and may be partially responsible for the degradation in the breaking strength observed at temperatures above 400 C. The variation in electrical resistivity of the fibers with increasing temperature indicates a transition to a higher band gap material at 350 to 600 C. This is consistent with a decomposition of SiC involving silicon oxide formation.

Tran, Huy Kim↗

NASA NTRS2002

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal.

Huang, Norden E.↗

NASA NTRS2004

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

Huang, Norden E.↗

NASA NTRS2007

Construction and Use of Resting 12-Lead High Fidelity ECG "SuperScores" in Screening for Heart Disease

We investigated the accuracy of several conventional and advanced resting ECG parameters for identifying obstructive coronary artery disease (CAD) and cardiomyopathy (CM). Advanced high-fidelity 12-lead ECG tests (approx. 5-min supine) were first performed on a "training set" of 99 individuals: 33 with ischemic or dilated CM and low ejection fraction (EF less than 40%); 33 with catheterization-proven obstructive CAD but normal EF; and 33 age-/gender-matched healthy controls. Multiple conventional and advanced ECG parameters were studied for their individual and combined retrospective accuracies in detecting underlying disease, the advanced parameters falling within the following categories: 1) Signal averaged ECG, including 12-lead high frequency QRS (150-250 Hz) plus multiple filtered and unfiltered parameters from the derived Frank leads; 2) 12-lead P, QRS and T-wave morphology via singular value decomposition (SVD) plus signal averaging; 3) Multichannel (12-lead, derived Frank lead, SVD lead) beat-to-beat QT interval variability; 4) Spatial ventricular gradient (and gradient component) variability; and 5) Heart rate variability. Several multiparameter ECG SuperScores were derivable, using stepwise and then generalized additive logistic modeling, that each had 100% retrospective accuracy in detecting underlying CM or CAD. The performance of these same SuperScores was then prospectively evaluated using a test set of another 120 individuals (40 new individuals in each of the CM, CAD and control groups, respectively). All 12-lead ECG SuperScores retrospectively generated for CM continued to perform well in prospectively identifying CM (i.e., areas under the ROC curve greater than 0.95), with one such score (containing just 4 components) maintaining 100% prospective accuracy. SuperScores retrospectively generated for CAD performed somewhat less accurately, with prospective areas under the ROC curve typically in the 0.90-0.95 range. We conclude that resting 12-lead high-fidelity ECG employing and combining the results of several advanced ECG software techniques shows great promise as a rapid and inexpensive tool for screening of heart disease.

Schlegel, T. T.↗

NASA NTRS2006

Computing frequency by using generalized zero-crossing applied to intrinsic mode functions

This invention presents a method for computing Instantaneous Frequency by applying Empirical Mode Decomposition to a signal and using Generalized Zero-Crossing (GZC) and Extrema Sifting. The GZC approach is the most direct, local, and also the most accurate in the mean. Furthermore, this approach will also give a statistical measure of the scattering of the frequency value. For most practical applications, this mean frequency localized down to quarter of a wave period is already a well-accepted result. As this method physically measures the period, or part of it, the values obtained can serve as the best local mean over the period to which it applies. Through Extrema Sifting, instead of the cubic spline fitting, this invention constructs the upper envelope and the lower envelope by connecting local maxima points and local minima points of the signal with straight lines, respectively, when extracting a collection of Intrinsic Mode Functions (IMFs) from a signal under consideration.

Huang, Norden E.↗

NASA NTRS1990

Reliable and Efficient Parallel Processing Algorithms and Architectures for Modern Signal Processing

Least-squares (LS) estimations and spectral decomposition algorithms constitute the heart of modern signal processing and communication problems. Implementations of recursive LS and spectral decomposition algorithms onto parallel processing architectures such as systolic arrays with efficient fault-tolerant schemes are the major concerns of this dissertation. There are four major results in this dissertation. First, we propose the systolic block Householder transformation with application to the recursive least-squares minimization. It is successfully implemented on a systolic array with a two-level pipelined implementation at the vector level as well as at the word level. Second, a real-time algorithm-based concurrent error detection scheme based on the residual method is proposed for the QRD RLS systolic array. The fault diagnosis, order degraded reconfiguration, and performance analysis are also considered. Third, the dynamic range, stability, error detection capability under finite-precision implementation, order degraded performance, and residual estimation under faulty situations for the QRD RLS systolic array are studied in details. Finally, we propose the use of multi-phase systolic algorithms for spectral decomposition based on the QR algorithm. Two systolic architectures, one based on triangular array and another based on rectangular array, are presented for the multiphase operations with fault-tolerant considerations. Eigenvectors and singular vectors can be easily obtained by using the multi-pase operations. Performance issues are also considered.

Liu, Kuojuey Ray↗

NASA NTRS1999

Computer implemented empirical mode decomposition method, apparatus and article of manufacture

A computer implemented physical signal analysis method is invented. This method includes two essential steps and the associated presentation techniques of the results. All the steps exist only in a computer: there are no analytic expressions resulting from the method. The first step is a computer implemented Empirical Mode Decomposition to extract a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform. The final result is the Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum.

Huang, Norden E.↗