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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

On the Effective Construction of Compactly Supported Wavelets Satisfying Homogenous Boundary Conditions on the Interval

We construct compactly supported wavelet bases satisfying homogeneous boundary conditions on the interval (0,1). The maximum features of multiresolution analysis on the line are retained, including polynomial approximation and tree algorithms. The case of H(sub 0)(sup 1)(0, 1)is detailed, and numerical values, required for the implementation, are provided for the Neumann and Dirichlet boundary conditions.

Chiavassa, G.↗
NASA NTRS1996

Multilevel Algorithm for Atmospheric Data Assimilation

A multiscale algorithm for the problem of optimal statistical interpolation of observed data has been developed. This problem includes the calculation of the vector of the 'analyzed' (best estimated) atmosphere flow field w(sup a) by the formula: w(sup a) = w(sup f) + P(sup f) H(sup T) y, where the quantity y is defined by the equation (H P(sup f) H(sup T) + R)y = w(sup o) - H w(sup f), using the given model forecast first guess w(sup f) and the vector of observations w(sup o); H is an interpolation operator from the regular grid to the observation network, P(sup f) is the forecast error covariance matrix, and R is the observation error covariance matrix. At this initial stage the case of univariate analysis of single level radiosonde height data is considered. The matrix R is assumed to be diagonal, and the matrix P(sup f) is assumed to be given by the formula P(sub ij)(sup f) = sigma(sub i)(sup f) mu(sub ij) sigma(sub j)(sub f), where mu(sub ij) is a smooth, decreasing function of the distance between the i-th and the j-th points. In this paper we describe a multiscale iterative process based on a multiresolution, simultaneous displacement technique and a localized variational calculation of iteration parameters.

Brandt, Achi↗
NASA NTRS1995

A Subband Coding Method for HDTV

This paper introduces a new HDTV coder based on motion compensation, subband coding, and high order conditional entropy coding. The proposed coder exploits the temporal and spatial statistical dependencies inherent in the HDTV signal by using intra- and inter-subband conditioning for coding both the motion coordinates and the residual signal. The new framework provides an easy way to control the system complexity and performance, and inherently supports multiresolution transmission. Experimental results show that the coder outperforms MPEG-2, while still maintaining relatively low complexity.

Chung, Wilson↗
NASA NTRS1997

Advanced Signal Processing Methods Applied to Digital Mammography

The work reported here is on the extension of the earlier proposal of the same title, August 1994-June 1996. The report for that work is also being submitted. The work reported there forms the foundation for this work from January 1997 to September 1997. After the earlier work was completed there were a few items that needed to be completed prior to submission of a new and more comprehensive proposal for further research. Those tasks have been completed and two new proposals have been submitted, one to NASA, and one to Health & Human Services WS). The main purpose of this extension was to refine some of the techniques that lead to automatic large scale evaluation of full mammograms. Progress on each of the proposed tasks follows. Task 1: A multiresolution segmentation of background from breast has been developed and tested. The method is based on the different noise characteristics of the two different fields. The breast field has more power in the lower octaves and the off-breast field behaves similar to a wideband process, where more power is in the high frequency octaves. After the two fields are separated by lowpass filtering, a region labeling routine is used to find the largest contiguous region, the breast. Task 2: A wavelet expansion that can decompose the image without zero padding has been developed. The method preserves all properties of the power-of-two wavelet transform and does not add appreciably to computation time or storage. This work is essential for analysis of the full mammogram, as opposed to selecting sections from the full mammogram. Task 3: A clustering method has been developed based on a simple counting mechanism. No ROC analysis has been performed (and was not proposed), so we cannot finally evaluate this work without further support. Task 4: Further testing of the filter reveals that different wavelet bases do yield slightly different qualitative results. We cannot provide quantitative conclusions about this for all possible bases without further support. Task 5: Better modeling does indeed make an improvement in the detection output. After the proposal ended, we came up with some new theoretical explanations that helps in understanding when the D4 filter should be better. This work is currently in the review process. Task 6: N/A. This no longer applies in view of Tasks 4-5. Task 7: Comprehensive plans for further work have been completed. These plans are the subject of two proposals, one to NASA and one to HHS. These proposals represent plans for a complete evaluation of the methods for identifying normal mammograms, augmented with significant further theoretical work.

Stauduhar, Richard P.↗
NASA NTRS1998

The Wavelet Element Method: Realization and Additional Features in 2D and 3D - Part 2

The Wavelet Element Method (WEM) provides a construction of multiresolution systems and biorthogonal wavelets on fairly general domains. These are split into subdomains that are mapped to a single reference hypercube. Tensor products of scaling functions and wavelets defined on the unit interval are used on the reference domain. By introducing appropriate matching conditions across the interelement boundaries, a globally continuous biorthogonal wavelet basis on the general domain is obtained. This construction does not uniquely define the basis functions but rather leaves some freedom for fulfilling additional features. In this paper we detail the general construction principle of the WEM to the 1D, 2D and 3D cases. We address additional features such as symmetry, vanishing moments and minimal support of the wavelet functions in each particular dimension. The construction is illustrated by using biorthogonal spline wavelets on the interval.

Canuto, Claudio↗
NASA NTRS1997

Automatic registration of satellite imagery

Image registration is one of the basic image processing operations in remote sensing. With the increase in the number of images collected every day from different sensors, automated registration of multi-sensor/multi-spectral images has become an important issue. A wide range of registration techniques has been developed for many different types of applications and data. The objective of this paper is to present an automatic registration algorithm which uses a multiresolution analysis procedure based upon the wavelet transform. The procedure is completely automatic and relies on the grey level information content of the images and their local wavelet transform modulus maxima. The registration algorithm is very simple and easy to apply because it needs basically one parameter. We have obtained very encouraging results on test data sets from the TM and SPOT sensor images of forest, urban and agricultural areas.

Fonseca, Leila M. G.↗
NASA NTRS2000

On the Spatial Distribution of High Velocity Al-26 Near the Galactic Center

We present results of simulations of the distribution of 1809 keV radiation from the decay of Al-26 in the Galaxy. Recent observations of this emission line using the Gamma Ray Imaging Spectrometer (GRIS) have indicated that the bulk of the AL-26 must have a velocity of approx. 500 km/ s. We have previously shown that a velocity this large could be maintained over the 10(exp 6) year lifetime of the Al-26 if it is trapped in dust grains that are reaccelerated periodically in the ISM. Here we investigate whether a dust grain velocity of approx. 500 km/ s will produce a distribution of 1809 keV emission in latitude that is consistent with the narrow distribution seen by COMPTEL. We find that dust grain velocities in the range 275 - 1000 km/ s are able to reproduce the COMPTEL 1809 keV emission maps reconstructed using the Richardson-Lucy and Maximum Entropy image reconstruction methods while the emission map reconstructed using the Multiresolution Regularized Expectation Maximization algorithm is not well fit by any of our models. The Al-26 production rate that is needed to reproduce the observed 1809 keV intensity yields in a Galactic mass of Al-26 of approx. 1.5 - 2 solar mass which is in good agreement with both other observations and theoretical production rates.

Sturner, Steven J.↗
NASA NTRS2000

BOREAS AFM-12 1-km AVHRR Seasonal Land Cover Classification

The Boreal Ecosystem-Atmosphere Study (BOREAS) Airborne Fluxes and Meteorology (AFM)-12 team's efforts focused on regional scale Surface Vegetation and Atmosphere (SVAT) modeling to improve parameterization of the heterogeneous BOREAS landscape for use in larger scale Global Circulation Models (GCMs). This regional land cover data set was developed as part of a multitemporal one-kilometer Advanced Very High Resolution Radiometer (AVHRR) land cover analysis approach that was used as the basis for regional land cover mapping, fire disturbance-regeneration, and multiresolution land cover scaling studies in the boreal forest ecosystem of central Canada. This land cover classification was derived by using regional field observations from ground and low-level aircraft transits to analyze spectral-temporal clusters that were derived from an unsupervised cluster analysis of monthly Normalized Difference Vegetation Index (NDVI) image composites (April-September 1992). This regional data set was developed for use by BOREAS investigators, especially those involved in simulation modeling, remote sensing algorithm development, and aircraft flux studies. Based on regional field data verification, this multitemporal one-kilometer AVHRR land cover mapping approach was effective in characterizing the biome-level land cover structure, embedded spatially heterogeneous landscape patterns, and other types of key land cover information of interest to BOREAS modelers.The land cover mosaics in this classification include: (1) wet conifer mosaic (low, medium, and high tree stand density), (2) mixed coniferous-deciduous forest (80% coniferous, codominant, and 80% deciduous), (3) recent visible bum, vegetation regeneration, or rock outcrops-bare ground-sparsely vegetated slow regeneration bum (four classes), (4) open water and grassland marshes, and (5) general agricultural land use/ grasslands (three classes). This land cover mapping approach did not detect small subpixel-scale landscape features such as fens, bogs, and small water bodies. Field observations and comparisons with Landsat Thematic Mapper (TM) suggest a minimum effective resolution of these land cover classes in the range of three to four kilometers, in part, because of the daily to monthly compositing process. In general, potential accuracy limitations are mitigated by the use of conservative parameterization rules such as aggregation of predominant land cover classes within minimum horizontal grid cell sizes of ten kilometers. The AFM-12 one-kilometer AVHRR seasonal land cover classification data are available from the Earth Observing System Data and Information System (EOSDIS) Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC). The data files are available on a CD-ROM (see document number 20010000884).

Steyaert, Lou↗
NASA NTRS1996

Statistical Challenges in Modern Astronomy II

Wavelets are the central idea of a broad framework for thinking about displaying, and analyzing data - not just a new specialized technique. They are localized basis functions that provide an extremely flexible and efficient representation of time series. Current developments in the theory and application of wavelets are yielding powerful multiresolution techniques for the analysis of time series and image data. Wavelet methods can effect noise removal. characterization of stochastic behavior, depiction of power spectrum time-variations, and data compression - for time series data, image data, and data of higher dimensions. I review published applications of wavelets in astronomy.

Scargle, Jeffrey D.↗
NASA NTRS2002

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These schemes are suitable for the problems in question. Basically, the scheme consists of sixth-order or higher non-dissipative spatial difference operators as the base scheme. To control the amount of numerical dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of numerical dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing schemes for the MHD in the literature, these schemes are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution schemes to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate numerical schemes for multiscale MHD equations pose a great challenge to algorithm development. In addition, controlling the numerical error of the divergence free condition of the magnetic fields for high order methods has been a stumbling block. Lower order methods are not practical for the astrophysical problems in question. We propose to extend our hydrodynamics schemes to the MHD equations with several desired properties over commonly used MHD schemes.

Sjoegreen, Bjoern↗
NASA NTRS2002

Dynamical Approach Study of Spurious Numerics in Nonlinear Computations

The last two decades have been an era when computation is ahead of analysis and when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems and non-traditional fields. Ensuring a higher level of confidence in the predictability and reliability (PAR) of these numerical simulations could play a major role in furthering the design, understanding, affordability and safety of our next generation air and space transportation systems, and systems for planetary and atmospheric sciences, and in understanding the evolution and origin of life. The need to guarantee PAR becomes acute when computations offer the ONLY way of solving these types of data limited problems. Employing theory from nonlinear dynamical systems, some building blocks to ensure a higher level of confidence in PAR of numerical simulations have been revealed by the author and world expert collaborators in relevant fields. Five building blocks with supporting numerical examples were discussed. The next step is to utilize knowledge gained by including nonlinear dynamics, bifurcation and chaos theories as an integral part of the numerical process. The third step is to design integrated criteria for reliable and accurate algorithms that cater to the different multiscale nonlinear physics. This includes but is not limited to the construction of appropriate adaptive spatial and temporal discretizations that are suitable for the underlying governing equations. In addition, a multiresolution wavelets approach for adaptive numerical dissipation/filter controls for high speed turbulence, acoustics and combustion simulations will be sought. These steps are corner stones for guarding against spurious numerical solutions that are solutions of the discretized counterparts but are not solutions of the underlying governing equations.

Yee, H. C.↗
NASA NTRS2002

Extension of Low Dissipative High Order Hydrodynamics Schemes for MHD Equations

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD (magnetohydrodynamic) equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls to limit the amount and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvi-linear grids. The three features of the present MHD scheme over existing schemes in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion magnetized flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike existing schemes for the conservative MHD equations which suffer from ill-conditioned eigen-decompositions, the present scheme makes use of a well-conditioned eigen-decomposition to solve the conservative form of the MHD equations. This is due to, partly. the fact that the divergence of the magnetic field condition is a different type of constraint from its incompressible Navier-Stokes cousin. Third, a new approach to minimize the numerical error of the divergence free magnetic condition for high order scheme is introduced.

Yee, H. C.↗
NASA NTRS2002

A New Low Dissipative High Order Schemes for MHD Equations

The goal of this talk is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls to limit the amount and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids.

Yee, H. C.↗
NASA NTRS2003

Scalability of a Low-Cost Multi-Teraflop Linux Cluster for High-End Classical Atomistic and Quantum Mechanical Simulations

Scalability of a low-cost, Intel Xeon-based, multi-Teraflop Linux cluster is tested for two high-end scientific applications: Classical atomistic simulation based on the molecular dynamics method and quantum mechanical calculation based on the density functional theory. These scalable parallel applications use space-time multiresolution algorithms and feature computational-space decomposition, wavelet-based adaptive load balancing, and spacefilling-curve-based data compression for scalable I/O. Comparative performance tests are performed on a 1,024-processor Linux cluster and a conventional higher-end parallel supercomputer, 1,184-processor IBM SP4. The results show that the performance of the Linux cluster is comparable to that of the SP4. We also study various effects, such as the sharing of memory and L2 cache among processors, on the performance.

Kikuchi, Hideaki↗
NASA NTRS2003

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

Sjoegreen, Bjoern↗
NASA NTRS1999

New approaches to virtual environment surgery

This research focused on two main problems: 1) low cost, high fidelity stereoscopic imaging of complex tissues and organs; and 2) virtual cutting of tissue. A further objective was to develop these images and virtual tissue cutting methods for use in a telemedicine project that would connect remote sites using the Next Generation Internet. For goal one we used a CT scan of a human heart, a desktop PC with an OpenGL graphics accelerator card, and LCD stereoscopic glasses. Use of multiresolution meshes ranging from approximately 1,000,000 to 20,000 polygons speeded interactive rendering rates enormously while retaining general topography of the dataset. For goal two, we used a CT scan of an infant skull with premature closure of the right coronal suture, a Silicon Graphics Onyx workstation, a Fakespace Immersive WorkBench and CrystalEyes LCD glasses. The high fidelity mesh of the skull was reduced from one million to 50,000 polygons. The cut path was automatically calculated as the shortest distance along the mesh between a small number of hand selected vertices. The region outlined by the cut path was then separated from the skull and translated/rotated to assume a new position. The results indicate that widespread high fidelity imaging in virtual environment is possible using ordinary PC capabilities if appropriate mesh reduction methods are employed. The software cutting tool is applicable to heart and other organs for surgery planning, for training surgeons in a virtual environment, and for telemedicine purposes.

NASA Discipline Neuroscience↗
NASA NTRS2005

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

The required type and amount of numerical dissipation/filter to accurately resolve all relevant multiscales of complex MHD unsteady high-speed shock/shear/turbulence/combustion problems are not only physical problem dependent, but also vary from one flow region to another. In addition, proper and efficient control of the divergence of the magnetic field (Div(B)) numerical error for high order shock-capturing methods poses extra requirements for the considered type of CPU intensive computations. 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 from 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 multiresolution wavelets (WAV) (for the above types of flow feature). These filters also provide a natural and efficient way for the minimization of Div(B) numerical error.

Yee, H. C.↗
NASA NTRS2004

Use of EO-1 Hyperion Data for Inter-Sensor Calibration of Vegetation Indices

Numerous satellite sensor systems useful in terrestrial Earth observation and monitoring have recently been launched and their derived products are increasingly being used in regional and global vegetation studies. The increasing availability of multiple sensors offer much opportunity for vegetation studies aimed at understanding the terrestrial carbon cycle, climate change, and land cover conversions. Potential applications include improved multiresolution characterization of the surface (scaling); improved optical-geometric characterization of vegetation canopies; improved assessments of surface phenology and ecosystem seasonal dynamics; and improved maintenance of long-term, inter-annual, time series data records. The Landsat series of sensors represent one group of sensors that have produced a long-term, archived data set of the Earth s surface, at fine resolution and since 1972, capable of being processed into useful information for global change studies (Hall et al., 1991).

Huete, Alfredo↗