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At least 433 records · Page 24

Image Reconstruction from Under sampled Fourier Data Using the Polynomial Annihilation Transform

Fourier samples are collected in a variety of applications including magnetic resonance imaging and synthetic aperture radar. The data are typically under-sampled and noisy. In recent years, l 1 regularization has received considerable attention in designing image reconstruction algorithms from under-sampled and noisy Fourier data. The underlying image is assumed to have some sparsity features, that is, some measurable features of the image have sparse representation. The reconstruction algorithm is typically designed to solve a convex optimization problem, which consists of a fidelity term penalized by one or more l 1 regularization terms. The Split Bregman Algorithm provides a fast explicit solution for the case when TV is used for the l1l1 regularization terms. Due to its numerical efficiency, it has been widely adopted for a variety of applications. A well known drawback in using TV as an l 1 regularization term is that the reconstructed image will tend to default to a piecewise constant image. This issue has been addressed in several ways. Recently, the polynomial annihilation edge detection method was used to generate a higher order sparsifying transform, and was coined the “polynomial annihilation (PA) transform.” This paper adapts the Split Bregman Algorithm for the case when the PA transform is used as the l 1 regularization term. In so doing, we achieve a more accurate image reconstruction method from under-sampled and noisy Fourier data. Our new method compares favorably to the TV Split Bregman Algorithm, as well as to the popular TGV combined with shearlet approach.

97 MATHEMATICS AND COMPUTING↗

Cross-Modal Guidance for Fast Diffusion-Based Computed Tomography

Diffusion models have emerged as powerful priors for solving inverse problems in computed tomography (CT). In certain applications, such as neutron CT, it can be expensive to collect large amounts of measurements even for a single scan leading to sparse data sets from which it is challenging to obtain high quality reconstructions even with diffusion models. One strategy to mitigate this challenge is to leverage a complementary, easily available imaging modality; however, such approaches typically require retraining the diffusion model with large datasets. In this work, we propose incorporating an additional modality without retraining the diffusion prior, enabling accelerated imaging of costly modalities. We further examine the impact of imperfect side modalities on cross-modal guidance. Our method is evaluated on sparse-view neutron computed tomography, where reconstruction quality is substantially improved by incorporating X-ray computed tomography of the same samples.

Efimov, Timofey [ORNL] (ORCID:000900090098471X)↗

Estimation of multidimensional precipitation parameters by areal estimates of oceanic rainfall

The parameters of the multidimensional precipitation model proposed by Waymire et al. (1984) are estimated using the areal-averaged radar measurements of precipitation of the Global Atlantic Tropical Experiment (GATE) data set. The procedure followed was the fitting of the first- and second-order moments at different aggregation scales by nonlinear regression techniques. The numerical estimates of the parameters using different subsets of GATE information were reasonably stable, i.e., they were not affected by changes of the area-averaging size, temporal length of the records, and percentage of areal coverage of rainfall. This suggests that the estimation procedure is relatively robust and suitable to estimate the parameters of the multidimensional model in areas of sparse density of rain gages. The use of the space-time spectrum of rainfall to help in the determination of sampling errors due to intermittent visits of future space-borne low-altitude sensors of precipitation is also discussed.

Valdes, J. B.↗

New prospects for analyzing lunar pyroclastic glass

Pyroclastic glass particles of diverse compositions are sparsely distributed in the lunar soil. Numerous suspected pyroclastic deposits have been pinpointed on the nearside. However, a dearth of pure samples large enough for spectral study, coupled with the kilometer spatial resolution of earth-based telescope spectrometry, makes it difficult to remotely analyze these deposits or tie most glasses to specific sources. Two developments should soon improve this situation. First, the technique of microscope photometry combined with microprobe analysis allows the correlation of the reflectance spectra and chemical compositions of individual glass particles. Second, the Clementine spacecraft will provide multispectral images of pyroclastic deposits at much higher spatial resolution than is currently achievable. These developments, combined with traditional laboratory and telescope studies, should allow compositions of many pyroclastic deposits and sources of many soil particles to be determined.

Allen, C. C.↗

Linear and Geometrically Nonlinear Structural Shape Sensing from Strain Data

An aircraft’s shape must be measured during flight to implement active shape controls such as active trim shape, divergence, and sonic boom controls. A basis function method for linear as well as geometrically nonlinear structural shape sensing is proposed in this study. Basis functions can be mode shapes, linear static deformation shapes, and/or geometrically nonlinear static deformation shapes. The proposed basis function method is validated using a high-aspect-ratio wing, a swept test plate, and the National Aeronautics and Space Administration X-59 aircraft. A large structural deformation of a high-aspect-ratio wing is successfully captured using the proposed basis function method with less than 0.3%prediction error at the wing-tip section. The basis function method gives excellent deformation prediction, even with stress concentration. Performance of the basis functions is compared using the X-59 stabilator sample case. In most of the sample load cases, static deformations give a better correlation with the target deformation than do mode shapes. Wing shape sensing with sparse strain data are also demonstrated in this study using the X-59 aircraft. Predicted structural deformations match reasonably with the target deformations, even without strain gauges on some structural components. The predicted deformations have a good match with the target deformations.

Static Deformation↗

Structural Shape Sensing from Strain Data Using the Basis Function Method

An aircraft shape must be measured during flight to implement an active trim shape control, such as an active dihedral control for a highly flexible aircraft with a high-aspect-ratio wing, and an active sonic boom control for a supersonic transport aircraft. A basis function method for linear as well as geometrically nonlinear structural shape sensing is proposed in this study. Basis functions can be mode shapes, linear static deformation shapes, or geometrically nonlinear static deformation shapes. The proposed basis function method is validated using a high-aspect-ratio wing, a swept test plate, and the National Aeronautics and Space Administration Low Boom Flight Demonstration mission X-59 Quiet Supersonic Technology (QueSST) aircraft (Lockheed Martin, Bethesda, Maryland). A large structural deformation of a high-aspect-ratio wing is successfully captured using the proposed basis function method with less than 0.3-percentprediction error at the wing-tip section. The basis function method gives excellent deformation prediction, even with stress concentration. Performance of the basis functions is compared using the X-59 stabilator sample case. In most of the sample load cases, static deformations give a better correlation with the target deformation than do mode shapes. Wing shape sensing with sparse strain data is also demonstrated in this study using the X-59 QueSST aircraft. Predicted structural deformations match reasonably with the target deformations even without strain gauges on some structural components. The predicted deformations have a good match with the target deformations.

Chan-gi Pak↗

SubTSBR to tackle high noise and outliers for data-driven discovery of differential equations

Data-driven discovery of differential equations has been an emerging research topic. We propose a novel algorithm subsampling-based threshold sparse Bayesian regression (SubTSBR) to tackle high noise and outliers. The subsampling technique is used for improving the accuracy of the Bayesian learning algorithm. It has two parameters: subsampling size and the number of subsamples. When the subsampling size increases with fixed total sample size, the accuracy of our algorithm goes up and then down. When the number of subsamples increases, the accuracy of our algorithm keeps going up. We demonstrate how to use our algorithm step by step and compare our algorithm with threshold sparse Bayesian regression (TSBR) for the discovery of differential equations. We show that our algorithm produces better results. We also discuss the merits of discovering differential equations from data and demonstrate how to discover models with random initial and boundary condition as well as models with bifurcations. The numerical examples are: (1) predator-prey model with noise, (2) shallow water equations with outliers, (3) heat diffusion with random initial and boundary condition, and (4) fish-harvesting problem with bifurcations.

97 MATHEMATICS AND COMPUTING↗

A phase transition for finding needles in nonlinear haystacks with LASSO artificial neural networks

To fit sparse linear associations, a LASSO sparsity inducing penalty with a single hyperparameter provably allows to recover the important features (needles) with high probability in certain regimes even if the sample size is smaller than the dimension of the input vector (haystack). More recently learners known as artificial neural networks (ANN) have shown great successes in many machine learning tasks, in particular fitting nonlinear associations. Small learning rate, stochastic gradient descent algorithm and large training set help to cope with the explosion in the number of parameters present in deep neural networks. Yet few ANN learners have been developed and studied to find needles in nonlinear haystacks. Driven by a single hyperparameter, our ANN learner, like for sparse linear associations, exhibits a phase transition in the probability of retrieving the needles, which we do not observe with other ANN learners. To select our penalty parameter, we generalize the universal threshold of Donoho and Johnstone (Biometrika 81(3):425–455, 1994) which is a better rule than the conservative (too many false detections) and expensive cross-validation. In the spirit of simulated annealing, we propose a warm-start sparsity inducing algorithm to solve the high-dimensional, non-convex and non-differentiable optimization problem. We perform simulated and real data Monte Carlo experiments to quantify the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗

Deformable segmentation of 3D MR prostate images via distributed discriminative dictionary and ensemble learning

Purpose: Automatic prostate segmentation from MR images is an important task in various clinical applications such as prostate cancer staging and MR-guided radiotherapy planning. However, the large appearance and shape variations of the prostate in MR images make the segmentation problem difficult to solve. Traditional Active Shape/Appearance Model (ASM/AAM) has limited accuracy on this problem, since its basic assumption, i.e., both shape and appearance of the targeted organ follow Gaussian distributions, is invalid in prostate MR images. To this end, the authors propose a sparse dictionary learning method to model the image appearance in a nonparametric fashion and further integrate the appearance model into a deformable segmentation framework for prostate MR segmentation. Methods: To drive the deformable model for prostate segmentation, the authors propose nonparametric appearance and shape models. The nonparametric appearance model is based on a novel dictionary learning method, namely distributed discriminative dictionary (DDD) learning, which is able to capture fine distinctions in image appearance. To increase the differential power of traditional dictionary-based classification methods, the authors' DDD learning approach takes three strategies. First, two dictionaries for prostate and nonprostate tissues are built, respectively, using the discriminative features obtained from minimum redundancy maximum relevance feature selection. Second, linear discriminant analysis is employed as a linear classifier to boost the optimal separation between prostate and nonprostate tissues, based on the representation residuals from sparse representation. Third, to enhance the robustness of the authors' classification method, multiple local dictionaries are learned for local regions along the prostate boundary (each with small appearance variations), instead of learning one global classifier for the entire prostate. These discriminative dictionaries are located on different patches of the prostate surface and trained to adaptively capture the appearance in different prostate zones, thus achieving better local tissue differentiation. For each local region, multiple classifiers are trained based on the randomly selected samples and finally assembled by a specific fusion method. In addition to this nonparametric appearance model, a prostate shape model is learned from the shape statistics using a novel approach, sparse shape composition, which can model nonGaussian distributions of shape variation and regularize the 3D mesh deformation by constraining it within the observed shape subspace. Results: The proposed method has been evaluated on two datasets consisting of T2-weighted MR prostate images. For the first (internal) dataset, the classification effectiveness of the authors' improved dictionary learning has been validated by comparing it with three other variants of traditional dictionary learning methods. The experimental results show that the authors' method yields a Dice Ratio of 89.1% compared to the manual segmentation, which is more accurate than the three state-of-the-art MR prostate segmentation methods under comparison. For the second dataset, the MICCAI 2012 challenge dataset, the authors' proposed method yields a Dice Ratio of 87.4%, which also achieves better segmentation accuracy than other methods under comparison. Conclusions: A new magnetic resonance image prostate segmentation method is proposed based on the combination of deformable model and dictionary learning methods, which achieves more accurate segmentation performance on prostate T2 MR images.

60 APPLIED LIFE SCIENCES↗

Stochastic modeling and statistical calibration with model error and scarce data

This paper introduces a procedure to assess the predictive accuracy of stochastic models subject to model error and sparse data. Model error is introduced as uncertainty on the coefficients of appropriate polynomial chaos expansions (PCE). The error associated with finite sample size allows us to conceive of these coefficients as statistics of the data that we describe as random variables whose influence on output quantities of interest is evaluated through the extended polynomial chaos expansion (EPCE). A Bayesian data assimilation scheme is introduced to update these expansions by considering the resulting nested chaos expansion as a hierarchical probabilistic model. Stochastic models of quantities of interest (QoI) are thus constructed and efficiently evaluated. Here, the Metropolis–Hastings Markov chain Monte Carlo procedure is used to sample the posterior. Two illustrative analytical and numerical problems are used to demonstrate the proposed approach.

Bayesian inference↗

A multilevel Cartesian non-uniform grid time domain algorithm

A multilevel Cartesian non-uniform grid time domain algorithm (CNGTDA) is introduced to rapidly compute transient wave fields radiated by time dependent three-dimensional source constellations. CNGTDA leverages the observation that transient wave fields generated by temporally bandlimited and spatially confined source constellations can be recovered via interpolation from appropriately delay- and amplitude-compensated field samples. This property is used in conjunction with a multilevel scheme, in which the computational domain is hierarchically decomposed into subdomains with sparse non-uniform grids used to obtain the fields. For both surface and volumetric source distributions, the computational cost of CNGTDA to compute the transient field at N{sub s} observation locations from N{sub s} collocated sources for N{sub t} discrete time instances scales as O(N{sub t}N{sub s}logN{sub s}) and O(N{sub t}N{sub s}log{sup 2}N{sub s}) in the low- and high-frequency regimes, respectively. Coupled with marching-on-in-time (MOT) time domain integral equations, CNGTDA can facilitate efficient analysis of large scale time domain electromagnetic and acoustic problems.

97 MATHEMATICS AND COMPUTING↗

Bridging multimodal microscopy for advanced characterization on nuclear fuel using machine learning

Uranium dioxide (UO 2 ), widely used as driver fuel in light water reactors, experiences microstructure and property change by nuclear fission reactions. This paper bridges the characterization of fresh UO 2 fuel at different length scales, serving as a baseline for future post irradiation examination of irradiated UO 2 fuel. To characterize the microstructural change of nuclear fuel, modern approaches cover a wide range of length scales through different characterization techniques, such as mm scale for Synchrotron-based X-ray computed tomography (SXCT) and microscale for focused ion beam (FIB) and scanning electron microscopy (SEM). It is challenging to bridge the data and knowledge of the same sample in different length scales. This paper proposed a deep learning framework leveraging transfer learning to detect microstructural defects, trained from a sparse FIB, SEM, and SXCT images. The proposed model achieved superior performance in defect segmentation on multiscale microscopic data compared to four of the latest deep learning models.

36 MATERIALS SCIENCE↗

Plasma acceleration, injection, and loss - Observational aspects

A history of the understanding of the sudden accelerations of charged particles noted in plasmas, and the accompanying intrusions of energized plasma into adjacent regions of space, is presented. It is pointed out that studies of the earth's magnetosphere are hampered by the lack of adequate sampling in space and time. Although the feature matching technique of building magnetic and electric field models can help compensate for the sparseness of experimental data, future studies will nonetheless require large numbers of spacecraft placed in carefully coordinated orbits. The notion that the ignition of portions of the auroral shell in association with earth flares results in the heating of ionospheric particles that are then convected inward to form the ring current is considered.

Mcilwain, C. E.↗

NREPS Applications for Water Supply and Management in California and Tennessee

Management of water resources is a balancing act between temporally and spatially limited sources and competitive needs which can often exceed the supply. In order to manage water resources over a region such as the San Joaquin Valley or the Tennessee River Valley, it is pertinent to know the amount of water that has fallen in the watershed and where the water is going within it. Since rain gauge networks are typically sparsely spaced, it is typical that the majority of rainfall on the region may not be measured. To mitigate this under-sampling of rainfall, weather radar has long been employed to provide areal rainfall estimates. The Next-Generation Weather Radars (NEXRAD) make it possible to estimate rainfall over the majority of the conterminous United States. The NEXRAD Rainfall Estimation Processing System (NREPS) was developed specifically for the purpose of using weather radar to estimate rainfall for water resources management. The NREPS is tailored to meet customer needs on spatial and temporal scales relevant to the hydrologic or land-surface models of the end-user. It utilizes several techniques to mitigate artifacts in the NEXRAD data from contaminating the rainfall field. These techniques include clutter filtering, correction for occultation by topography as well as accounting for the vertical profile of reflectivity. This presentation will focus on improvements made to the NREPS system to map rainfall in the San Joaquin Valley for NASA s Water Supply and Management Project in California, but also ongoing rainfall mapping work in the Tennessee River watershed for the Tennessee Valley Authority and possible future applications in other areas of the continent.

Gatlin, P.↗

Characterization and Measurement of Spacecraft Airborne Particulate Matter

The International Space Station (ISS) gives a 6-member astronaut crew the ability to live and work in low Earth orbit. It is a unique indoor environment, which has served as both home and workplace to over 230 people since the year 2000. In this low gravity environment, smoke does not rise and cookie crumbs do not settle the way they do on Earth, causing airborne particulate matter, or aerosols, to behave differently and pose unique hazards for crew members. In its existence, virtually the same volume of ISS air has been continuously conditioned and ‘revitalized,’ including the removal of particles by filtration. While gaseous constituents of ISS air are monitored meticulously, sparse data exists on the indoor aerosols. The quantity and types of ISS airborne debris have been investigated in NASA’s Aerosol Sampling Experiment. Both active and passive samplers successfully collected airborne particulate matter in U.S. segments of the ISS, which were returned to Earth for characterization by microscopy and other techniques. The resulting data has informed the design of candidate particle instruments for spacecraft. In 2020, a reference-quality aerosol instrument will be flown to ISS, and will provide real-time data of particle concentrations in various modules. Smaller, more compact instruments will be necessary in future space missions, for example, in smaller vehicles, in habitats on lunar and planetary surfaces with ubiquitous dust, and also for use as wearable technology throughout missions. Miniaturized aerosol sensors, though lower fidelity than reference-quality instruments, can monitor the environment well when calibrated appropriately. Indoor air quality in spacecraft is fundamentally important to human health and comfort, and several particulate monitoring technologies will be at sufficient technology readiness levels for operational use within the next two years. Results of the Aerosol Sampling Experiment will be presented, along with the status of NASA’s aerosol instrument technology demonstrations on ISS.

Meyer, Marit E.↗

Quantum Search Approaches to Sampling-Based Motion Planning

In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse environments, we formulate the Quantum Full Path Search Algorithm (q-FPS), which creates a superposition of full random path solutions, manipulates probability amplitudes with Quantum Amplitude Amplification (QAA), and quantum measures a single obstacle free full path solution. For dense unstructured environments, we formulate the Quantum Rapidly Exploring Random Tree algorithm, q-RRT, that creates quantum superpositions of possible parent-child connections, manipulates probability amplitudes with QAA, and quantum measures a single reachable state, which is added to a tree. As performance depends on the number of oracle calls and the probability of measuring good quantum states, we quantify how these errors factor into the probabilistic completeness properties of the algorithm. We then numerically estimate the expected number of database solutions to provide an approximation of the optimal number of oracle calls in the algorithm. We compare the q-RRT algorithm with a classical implementation and verify quadratic run-time speedup in the largest connected component of a 2D dense random lattice. We conclude by evaluating a proposed approach to limit the expected number of database solutions and thus limit the optimal number of oracle calls to a given number.

97 MATHEMATICS AND COMPUTING↗

Application of adaptive hierarchical sparse grid collocation to the uncertainty quantification of nuclear reactor simulators

Recent efforts in the application of uncertainty quantification to nuclear systems have utilized methods based on generalized perturbation theory and stochastic sampling. While these methods have proven to be effective they both have major drawbacks that may impede further progress. A relatively new approach based on spectral elements for uncertainty quantification is applied in this paper to several problems in reactor simulation. Spectral methods based on collocation attempt to couple the approximation free nature of stochastic sampling methods with the determinism of generalized perturbation theory. The specific spectral method used in this paper employs both the Smolyak algorithm and adaptivity by using Newton-Cotes collocation points along with linear hat basis functions. Using this approach, a surrogate model for the outputs of a computer code is constructed hierarchically by adaptively refining the collocation grid until the interpolant is converged to a user-defined threshold. The method inherently fits into the framework of parallel computing and allows for the extraction of meaningful statistics and data that are not within reach of stochastic sampling and generalized perturbation theory. This paper aims to demonstrate the advantages of spectral methods-especially when compared to current methods used in reactor physics for uncertainty quantification-and to illustrate their full potential. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Interactive volumetric segmentation for textile micro-tomography data using wavelets and nonlocal means

This work addresses segmentation of volumetric images of woven carbon fiber textiles from micro-tomography data. We propose a semi-supervised algorithm to classify carbon fibers that requires sparse input as opposed to completely labeled images. The main contributions are: (a) design of effective discriminative classifiers, for three-dimensional textile samples, trained on wavelet features for segmentation; (b) coupling of previous step with nonlocal means as simple, efficient alternative to the Potts model; and (c) demonstration of reuse of classifier to diverse samples containing similar content. We evaluate our work by curating test sets of voxels in the absence of a complete ground truth mask. The algorithm obtains an average 0.95 F1 score on test sets and average F1 score of 0.93 on new samples. Finally, we conclude with discussion of failure cases and propose future directions toward analysis of spatiotemporal high-resolution micro-tomography images.

3D image processing↗