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At least 1,261 records · Page 70

A Parallel Genetic Algorithm for Automated Electronic Circuit Design

Parallelized versions of genetic algorithms (GAs) are popular primarily for three reasons: the GA is an inherently parallel algorithm, typical GA applications are very compute intensive, and powerful computing platforms, especially Beowulf-style computing clusters, are becoming more affordable and easier to implement. In addition, the low communication bandwidth required allows the use of inexpensive networking hardware such as standard office ethernet. In this paper we describe a parallel GA and its use in automated high-level circuit design. Genetic algorithms are a type of trial-and-error search technique that are guided by principles of Darwinian evolution. Just as the genetic material of two living organisms can intermix to produce offspring that are better adapted to their environment, GAs expose genetic material, frequently strings of 1s and Os, to the forces of artificial evolution: selection, mutation, recombination, etc. GAs start with a pool of randomly-generated candidate solutions which are then tested and scored with respect to their utility. Solutions are then bred by probabilistically selecting high quality parents and recombining their genetic representations to produce offspring solutions. Offspring are typically subjected to a small amount of random mutation. After a pool of offspring is produced, this process iterates until a satisfactory solution is found or an iteration limit is reached. Genetic algorithms have been applied to a wide variety of problems in many fields, including chemistry, biology, and many engineering disciplines. There are many styles of parallelism used in implementing parallel GAs. One such method is called the master-slave or processor farm approach. In this technique, slave nodes are used solely to compute fitness evaluations (the most time consuming part). The master processor collects fitness scores from the nodes and performs the genetic operators (selection, reproduction, variation, etc.). Because of dependency issues in the GA, it is possible to have idle processors. However, as long as the load at each processing node is similar, the processors are kept busy nearly all of the time. In applying GAs to circuit design, a suitable genetic representation 'is that of a circuit-construction program. We discuss one such circuit-construction programming language and show how evolution can generate useful analog circuit designs. This language has the desirable property that virtually all sets of combinations of primitives result in valid circuit graphs. Our system allows circuit size (number of devices), circuit topology, and device values to be evolved. Using a parallel genetic algorithm and circuit simulation software, we present experimental results as applied to three analog filter and two amplifier design tasks. For example, a figure shows an 85 dB amplifier design evolved by our system, and another figure shows the performance of that circuit (gain and frequency response). In all tasks, our system is able to generate circuits that achieve the target specifications.

Long, Jason D.↗

Automated label flows for excited states of correlation functions in lattice gauge theory

Extracting excited states from lattice gauge theory correlation functions can be achieved through $χ^2$ minimization fits or algebraic approaches such as the variational method and Prony's method. Performing any kind of error analysis often leads to overlapping confidence regions of model parameters, even when the spectrum is not particularly dense. To correctly estimate errors, one must beware of mislabeling the states. In this work, we provide an algorithm that we call automated label flows which consistently and systematically identifies a deterministic labeling of states. This is a black-box approach in the sense that it gives a sensible set of labels without user guidance. Further, as an example, we pair one black box method with another, analyzing a lattice correlation function from real data using automated label flows in the context of Prony's method.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

EMOS (Energy Management Optimization System) [SWR-21-46]

EMOS software performs a real-time hierarchal optimal control for energy systems like multi-port electric vehicles charging site with distributed energy resources (DERs) and energy storage systems (ESSs). It gathers information in real-time from electric vehicles, power grid, and DERs, solves a multi-objective energy management optimization problem, and output setpoint for chargers, ESS converters, DERs converters, and grid converters. The software incorporates a novel integration of two control tasks: a) An Energy Management Optimization (EMO), which is the brain of EMOS controller that gathers information in real-time from EVs [e.g., battery size, state-of-charge (SOC), desired SOC, and charge acceptance curve], grid (e.g., electricity price, allowed feeder capacity, ramp rate limit, and reactive power), and DERs (e.g., prediction for solar generation for PV systems). It solves a control optimization problem in real-time to find optimal setpoint for ESSs power dispatch, EVs charging rate, and grid inverters. The objectives are to (1) minimize the charging cost considering grid energy, demand charges, and battery energy, (2) minimize charging time to meet fast charging criterion, (3) keep high energy level on ESSs at the end of an operating period, while satisfying constraints related to grid, EVs, and power converters. b) Real-Time Energy Management System (RT-EMS) is a rule-based algorithm that has faster response than EMO. It receives optimal setpoint from EMO and actual measurements from the system and modify the setpoint to compensate for any fast disturbance in the system, until a new optimum solution is received. Fast disturbances may include vehicle connect/disconnect, unpredicted variation in DERs profiles, variation in grid voltage, errors in PV generation prediction, and others. In addition, RT-EMS regulates voltage at point of common coupling (PCC) by managing reactive power of grid converters.

Mohamed, Ahmed↗

Evaluation of gravimetric ground truth soil moisture data collected for the agricultural soil moisture experiment, 1978 Colby, Kansas, aircraft mission

Soil moisture data acquired to support the development of algorithms for estimating surface soil moisture from remotely sensed backscattering of microwaves from ground surfaces are presented. Aspects of field uniformity and variability of gravimetric soil moisture measurements are discussed. Moisture distribution patterns are illustrated by frequency distributions and contour plots. Standard deviations and coefficients of variation relative to degree of wetness and agronomic features of the fields are examined. Influence of sampling depth on observed moisture content an variability are indicated. For the various sets of measurements, soil moisture values that appear as outliers are flagged. The distribution and legal descriptions of the test fields are included along with examinations of soil types, agronomic features, and sampling plan. Bulk density data for experimental fields are appended, should analyses involving volumetric moisture content be of interest to the users of data in this report.

Arya, L. M.↗

A semianalytic radiance model of ocean color

A semianalytical radiance model is developed which predicts the upwelled spectral radiance at the sea surface as a function of the phytoplankton pigment concentration for Morel Case 1 waters. The model is in good agreement with experimental measurements carried out in waters which were not included in the data base used to derive it. It suggests that the observed variability in the radiance is due to variations in the backscattering of plankton and the associated detrital material. The model is extended to include other material in the water, such as dissolved organic material, referred to as yellow substances, and detached coccoliths from coccolithophorids, e.g., Emiliana huxleyi. Potential applications include an improved biooptical algorithm for the retrieval of pigment concentrations from satellite imagery in the presence of interference from detached coccoliths and an improved atmospheric correction for satellite imagery. The model also serves to identify and to interpret deviations from Case 1 waters.

Gordon, Howard R.↗

Analysis of hypercube cache performance using address traces generated by TRAPEDS

The authors utilize a recently developed software method of capturing and analyzing address traces, known as TRAPEDS (TRAce Producing Execution Driven Simulation), to provide address traces for cache performance evaluation on a hypercube multicomputer. Utilizing TRAPEDS user code traces obtained from the implementations of several parallel algorithms on the Intel iPSC/2 hypercube, the authors simulate the cache performance effects of changing cache size, line size, and set associativity. Particular attention is devoted to the effect on cache performance of changing the dimension of the hypercube for a particular program and to the variation in cache statistics among the nodes of the hypercube.

Stunkel, Craig B.↗

Adaptive Gas Turbine Engine Control for Deterioration Compensation Due to Aging

This paper presents an ad hoc adaptive, multivariable controller tuning rule that compensates for a thrust response variation in an engine whose performance has been degraded though use and wear. The upset appears when a large throttle transient is performed such that the engine controller switches from low-speed to high-speed mode. A relationship was observed between the level of engine degradation and the overshoot in engine temperature ratio, which was determined to cause the thrust response variation. This relationship was used to adapt the controller. The method is shown to work very well up to the operability limits of the engine. Additionally, since the level of degradation can be estimated from sensor data, it would be feasible to implement the adaptive control algorithm on-line.

Litt, Jonathan S.↗

High-Performance Scanning Acousto-Ultrasonic System

A high-performance scanning acousto-ultrasonic system, now undergoing development, is designed to afford enhanced capabilities for imaging microstructural features, including flaws, inside plate specimens of materials. The system is expected to be especially helpful in analyzing defects that contribute to failures in polymer- and ceramic-matrix composite materials, which are difficult to characterize by conventional scanning ultrasonic techniques and other conventional nondestructive testing techniques. Selected aspects of the acousto-ultrasonic method have been described in several NASA Tech Briefs articles in recent years. Summarizing briefly: The acousto-ultrasonic method involves the use of an apparatus like the one depicted in the figure (or an apparatus of similar functionality). Pulses are excited at one location on a surface of a plate specimen by use of a broadband transmitting ultrasonic transducer. The stress waves associated with these pulses propagate along the specimen to a receiving transducer at a different location on the same surface. Along the way, the stress waves interact with the microstructure and flaws present between the transducers. The received signal is analyzed to evaluate the microstructure and flaws. The specific variant of the acousto-ultrasonic method implemented in the present developmental system goes beyond the basic principle described above to include the following major additional features: Computer-controlled motorized translation stages are used to automatically position the transducers at specified locations. Scanning is performed in the sense that the measurement, data-acquisition, and data-analysis processes are repeated at different specified transducer locations in an array that spans the specimen surface (or a specified portion of the surface). A pneumatic actuator with a load cell is used to apply a controlled contact force. In analyzing the measurement data for each pair of transducer locations in the scan, the total (multimode) acousto-ultrasonic response of the specimen is utilized. The analysis is performed by custom software that extracts parameters of signals in the time and frequency domains. The computer hardware and software provide both real-time and postscan processing and display options. For example, oscilloscope displays of waveforms and power spectral densities are available in real time. Images can be computed while scanning continues. Signals can be digitally preprocessed and/or post-processed by filtering, windowing, time-segmenting, and running-waveform-averaging algorithms. In addition, the software affords options for off-line simulation of the waveform-data-acquisition and scanning processes. In tests, the system has been shown to be capable of characterizing microstructural changes and defects in SiC/SiC and C/SiC ceramic-matrix composites. Delaminations, variations in density, microstructural changes attributable to infiltration by silicon, and crack-space indications (defined in the next sentence) have been revealed in images formed from several time- and frequency-domain parameters of scanning acousto-ultrasonic signals. The crack-space indications were image features that were not revealed by other nondestructive testing methods and are so named because they turned out to mark locations where cracking eventually occurred.

Roth, Don↗

Symmetric Phase Only Filtering for Improved DPIV Data Processing

The standard approach in Digital Particle Image Velocimetry (DPIV) data processing is to use Fast Fourier Transforms to obtain the cross-correlation of two single exposure subregions, where the location of the cross-correlation peak is representative of the most probable particle displacement across the subregion. This standard DPIV processing technique is analogous to Matched Spatial Filtering, a technique commonly used in optical correlators to perform the crosscorrelation operation. Phase only filtering is a well known variation of Matched Spatial Filtering, which when used to process DPIV image data yields correlation peaks which are narrower and up to an order of magnitude larger than those obtained using traditional DPIV processing. In addition to possessing desirable correlation plane features, phase only filters also provide superior performance in the presence of DC noise in the correlation subregion. When DPIV image subregions contaminated with surface flare light or high background noise levels are processed using phase only filters, the correlation peak pertaining only to the particle displacement is readily detected above any signal stemming from the DC objects. Tedious image masking or background image subtraction are not required. Both theoretical and experimental analyses of the signal-to-noise ratio performance of the filter functions are presented. In addition, a new Symmetric Phase Only Filtering (SPOF) technique, which is a variation on the traditional phase only filtering technique, is described and demonstrated. The SPOF technique exceeds the performance of the traditionally accepted phase only filtering techniques and is easily implemented in standard DPIV FFT based correlation processing with no significant computational performance penalty. An "Automatic" SPOF algorithm is presented which determines when the SPOF is able to provide better signal to noise results than traditional PIV processing. The SPOF based optical correlation processing approach is presented as a new paradigm for more robust cross-correlation processing of low signal-to-noise ratio DPIV image data."

Wernet, Mark P.↗

TensorFlow Quantum: A Software Framework for Quantum Machine Learning

We introduce TensorFlow Quantum (TFQ), an open source library for the rapid prototyping of hybrid quantum-classical models for classical or quantum data. This framework offers high-level abstractions for the design and training of both discriminative and generative quantum models under TensorFlow and supports high-performance quantum circuit simulators. We provide an overview of the software architecture and building blocks through several examples and review the theory of hybrid quantum-classical neural networks. We illustrate TFQ functionalities via several basic applications including supervised learning for quantum classification, quantum control, simulating noisy quantum circuits, and quantum approximate optimization. Moreover, we demonstrate how one can apply TFQ to tackle advanced quantum learning tasks including meta-learning, layerwise learning, Hamiltonian learning, sampling thermal states, variational quantum eigensolvers, classification of quantum phase transitions, generative adversarial networks, and reinforcement learning. We hope this framework provides the necessary tools for the quantum computing and machine learning research communities to explore models of both natural and artificial quantum systems, and ultimately discover new quantum algorithms which could potentially yield a quantum advantage.

Broughton, Michael↗

Sea Surface Salinity and Wind Retrieval Algorithm Using Combined Passive-Active L-Band Microwave Data

Aquarius is a combined passive/active L-band microwave instrument developed to map the salinity field at the surface of the ocean from space. The data will support studies of the coupling between ocean circulation, the global water cycle, and climate. The primary science objective of this mission is to monitor the seasonal and interannual variation of the large scale features of the surface salinity field in the open ocean with a spatial resolution of 150 kilometers and a retrieval accuracy of 0.2 practical salinity units globally on a monthly basis. The measurement principle is based on the response of the L-band (1.413 gigahertz) sea surface brightness temperatures (T (sub B)) to sea surface salinity. To achieve the required 0.2 practical salinity units accuracy, the impact of sea surface roughness (e.g. wind-generated ripples and waves) along with several factors on the observed brightness temperature has to be corrected to better than a few tenths of a degree Kelvin. To the end, Aquarius includes a scatterometer to help correct for this surface roughness effect.

ocean salinity↗

Exploring the Capabilities of a Machine Learning Algorithm to Detect Space Weather-Significant Emerging Active Regions

Active regions are a source of various phenomena responsible for Space Weather disturbances; therefore, developing a technology for early warning about upcoming magnetic activity is crucial to mitigate its impact. However, observational limitations and the high nonlinearity of processes associated with the accumulation of magnetic flux and its interaction with the surrounding plasma during the emergence through the convection zone make early activity detection a challenging problem. To address these challenges, we developed a physics-driven machine learning model that allows us to detect active regions (ARs) before they become visible on the solar surface by analyzing the power spectra of acoustic oscillations observed by the SDO/HMI instrument. This study is based on a time series of Doppler shift maps of 31x31-degree areas tracked with the Carrington rotation rate for four days before and after the emergence. The Doppler shift time series are processed into the oscillation power maps for four frequency ranges and accompanied by line-of-sight magnetograms and the continuum intensity maps from SDO/HMI. The resulting data are converted into a 1D time series representing the mean temporal variations of these quantities. The redacted time series are used as input to predict AR emergence using the Long Short Term Memory (LSTM) method. The training of the LSTM model is based on 40 ARs, which includes an independent analysis for each sub region that exhibits AR emergence or remains quiet. The emergence of magnetic flux (defined as a decrease of the continuum intensity) was detected with the developed LSTM algorithm from 5 to 48 hours before the reported time by NOAA. The developed model is capable of pointing to the time and location of active region formation. In this presentation, we discuss reasons that impact how early in advance the model can identify the upcoming activity and the possibility of improving the current predictive skills and steps to transition to the operational forecast.

Heliophysics↗

Wildfire Segmentation From Remotely Sensed Data Using Quantum-Compatible Conditional Vector Quantized-Variational Autoencoders

Wildfires represent a critical environmental hazard with multifaceted implications for ecosystems, communities, and public health [1]. The escalating frequency and intensity of wildfires globally have intensified the urgency for robust segmentation methodologies to facilitate effective mitigation, response, and recovery strategies [2]. Accurate wildfire segmentation is pivotal for delineating fire boundaries, assessing progression patterns, and prioritizing resource allocation during emergency scenarios. Furthermore, precise segmentation enables stakeholders, including policymakers, environmental scientists, and emergency responders, to formulate evidence-based strategies, thereby minimizing socio-economic disruptions and ecological degradation. Consequently, advancing wildfire segmentation techniques through innovative technological interventions remains a paramount research imperative. Although foundational in wildfire segmentation, traditional deterministic models exhibit inherent limitations that compromise their efficacy in dynamic and uncertain environments. These models often operate on rigid algorithms prioritizing deterministic classifications, thereby overlooking the inherent complexities and uncertainties associated with wildfire behavior and satellite data variability. Such deterministic frameworks tend to produce oversimplified representations that fail to capture the intricate nuances of evolving fire dynamics, spatial heterogeneity, and environmental interactions [1]. Consequently, the deterministic approach’s propensity for uncertainty collapsing [1, 3] hampers the accuracy, reliability, and applicability of segmentation outcomes in real-world scenarios. Contrastingly, stochastic models offer a more nuanced and adaptable framework for wildfire segmentation. By integrating probabilistic elements into the modeling paradigm, stochastic approaches, particularly probabilistic approaches such as variational auto encoders (VAEs) [4], facilitate comprehensive uncertainty assessment, enabling researchers to quantify and incorporate uncertainties into segmentation outcomes effectively. This probabilistic nature empowers stochastic models to encapsulate variability, account for data inconsistencies, and adapt to evolving environmental conditions, enhancing segmentation accuracy, reliability, and robustness. Embracing stochastic methodologies thus catalyzes advancements in wildfire science by fostering a more holistic, adaptive, and resilient segmentation framework. Despite VAEs demonstrating significant promise in various applications, they come with inherent limitations that have garnered attention within the machine learning community. One of the primary drawbacks lies in their reliance on static priors, which essentially assume a fixed distribution for latent variables, thereby limiting the model’s flexibility to capture complex data structures effectively [5]. This static nature leads to suboptimal representations, especially when dealing with complex and high-dimensional data. Additionally, VAEs often struggle with generating sharp and realistic samples, a phenomenon commonly referred to as mode collapse [5, 7, 6]. Furthermore, the optimization process in VAEs, which involves balancing the reconstruction loss and the regularization term, can sometimes be challenging to fine-tune [7]. In recent efforts to address these shortcomings, alternative approaches like Vector Quantized Variational Auto encoders(VQ-VAEs) [7], address the challenges by incorporating discrete latent variables and leveraging techniques that enhance the quality and diversity of generated samples while maintaining efficient training dynamics. VQ-VAEs propose a dynamic prior distribution generation mechanism that diverges from the static priors commonly associated with traditional VAEs. This dynamic approach allows for more adaptive and context-aware latent variable representations, thereby potentially capturing complex data structures more effectively. Unlike autoregressive prior models such as PixelCNN, which, despite their ability to model dependencies across data dimensions, suffer from significant computational inefficiencies and lack flexibility in handling diverse datasets. In our work, we propose to use a generative quantum-compatible approach to help alleviate the shortcomings of autoregressive prior model in VQ-VAEs. Restricted Boltzmann Machines (RBMs) are a viable alternative prior model that can learn prior distributions in a faster and more flexible manner. In this research endeavor, we meticulously curate a state-of-the-art dataset leveraging satellite MODIS data in conjunction with VIIRS fire masks, derived from Fire Radiative Power (FRP), thereby encapsulating diverse wildfire scenarios and environmental contexts. We developed a conditional VQ-VAE architecture with the RBM prior model that is trained in a supervised manner for segmenting wildfire masks. This innovative approach synergistically harnesses deep learning capabilities, enabling the generation of segmentation maps characterized by heightened precision, granularity, and contextual relevance. Furthermore, replacing the autoregressive prior learning method proposed by the original VQ-VAE with a prior density approximation via quantum-compatible RBM facilitates expedited inference processes, augments flexibility in prior sampling, optimizes computational efficiency and establishes a groundbreaking benchmark in wildfire segmentation methodologies.

quantum machine learning↗

Sensitivity of Passive Microwave Snow Depth Retrievals to Weather Effects and Snow Evolution

Snow fall and snow accumulation are key climate parameters due to the snow's high albedo, its thermal insulation, and its importance to the global water cycle. Satellite passive microwave radiometers currently provide the only means for the retrieval of snow depth and/or snow water equivalent (SWE) over land as well as over sea ice from space. All algorithms make use of the frequency-dependent amount of scattering of snow over a high-emissivity surface. Specifically, the difference between 37- and 19-GHz brightness temperatures is used to determine the depth of the snow or the SWE. With the availability of the Advanced Microwave Scanning Radiometer (AMSR-E) on the National Aeronautics and Space Administration's Earth Observing System Aqua satellite (launched in May 2002), a wider range of frequencies can be utilized. In this study we investigate, using model simulations, how snow depth retrievals are affected by the evolution of the physical properties of the snow (mainly grain size growth and densification), how they are affected by variations in atmospheric conditions and, finally, how the additional channels may help to reduce errors in passive microwave snow retrievals. The sensitivity of snow depth retrievals to atmospheric water vapor is confirmed through the comparison with precipitable water retrievals from the National Oceanic and Atmospheric Administration's Advanced Microwave Sounding Unit (AMSU-B). The results suggest that a combination of the 10-, 19-, 37-, and 89-GHz channels may significantly improve retrieval accuracy. Additionally, the development of a multisensor algorithm utilizing AMSR-E and AMSU-B data may help to obtain weather-corrected snow retrievals.

Markus, Thorsten↗

Analysis of core asymmetries in inertial confinement fusion implosions using three-dimensional hot-spot reconstruction

Three-dimensional effects play a crucial role during the hot-spot formation in inertial confinement fusion (ICF) implosions. A data analysis technique for 3D hot-spot reconstruction from experimental observables has been developed to characterize the effects of low modes on 3D hot-spot formations. In nuclear measurements, the effective flow direction, governed by the maximum eigenvalue in the velocity variance of apparent ion temperatures, has been found to agree with the measured hot-spot flows for implosions dominated by mode ℓ = 1. Asymmetries in areal-density (ρR) measurements were found to be characterized by a unique cosine variation along the hot-spot flow axis. In x-ray images, a 3D hot-spot x-ray emission tomography method was developed to reconstruct the 3D hot-spot plasma emissivity using a generalized spherical-harmonic Gaussian function. The gradient-descent algorithm was used to optimize the mapping between the projections from the 3D hot-spot emission model and the measured x-ray images along multiple views. Furthermore, this work establishes a platform to analyze 3D low-mode core asymmetries in ICF.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The characteristics of atmospheric boundary layer height over the Arctic Ocean during MOSAiC

The important roles that the atmospheric boundary layer (ABL) plays in the central Arctic climate system have been recognized, but the atmospheric boundary layer height (ABLH), defined as the layer of continuous turbulence adjacent to the surface, has rarely been investigated. Using a year-round radiosonde dataset during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition, we improve a Richardson-number-based algorithm that takes cloud effects into consideration and subsequently analyze the characteristics and variability of the ABLH over the Arctic Ocean. The results reveal that the annual cycle is clearly characterized by a distinct peak in May and two respective minima in January and July. This annual variation in the ABLH is primarily controlled by the evolution of the ABL thermal structure. Temperature inversions in the winter and summer are intensified by seasonal radiative cooling and warm-air advection with the surface temperature constrained by melting, respectively, leading to the low ABLH at these times. Meteorological and turbulence variables also play a significant role in ABLH variation, including the near-surface potential temperature gradient, friction velocity, and turbulent kinetic energy (TKE) dissipation rate. In addition, the MOSAiC ABLH is more suppressed than the ABLH during the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment in the summer, which indicates that there is large variability in the Arctic ABL structure during the summer melting season.

54 ENVIRONMENTAL SCIENCES↗

Computational strategies and improvements in the linear algebraic variational approach to rearrangement scattering

The computational steps in calculating quantum mechanical reactive scattering amplitudes by the L2 generalized Newton variational principle are discussed with emphasis on computational strategies and recent improvements that make the calculations more efficient. Special emphasis is placed on quadrature techniques, storage management strategies, use of symmetry, and boundary conditions. It is concluded that an efficient implementation of these procedures provides a powerful algorithm for the accurate solution of the Schroedinger equation for rearrangements.

Schwenke, David W.↗

Topography estimation with interferometric synthetic aperture radar using fringe detection

Methods are presented for using Synthetic Aperture Radar (SAR) interferometry data to estimate surface topography. An expression is given to relate the elevation of a ground point to the phase difference of SAR images received from two spatially separated antennas. An iterative algorithm which solves for the position and elevation of each point in the image simultaneously is developed. One of the critical issues that determines the accuracy of the terrain mapping is the phase unwrapping. An approach to the problem by fringe line detection is proposed. The algorithms are tested with two Seasat SAR images of terrain near Yellowstone National Park. The resultant elevation map is compared with a USGS terrain elevation model. The error of the SAR elevation with respect to the digital terrain map is about 8.2 percent of the total terrain variation.

Lin, Qian↗