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Results for “Alternating minimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

A Note on Alternating Minimization Algorithm for the Matrix Completion Problem

Here, we consider the problem of reconstructing a low-rank matrix from a subset of its entries and analyze two variants of the so-called alternating minimization algorithm, which has been proposed in the past.We establish that when the underlying matrix has rank one, has positive bounded entries, and the graph underlying the revealed entries has diameter which is logarithmic in the size of the matrix, both algorithms succeed in reconstructing the matrix approximately in polynomial time starting from an arbitrary initialization.We further provide simulation results which suggest that the second variant which is based on the message passing type updates performs significantly better.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Matrix Completion Using Alternating Minimization for Distribution System State Estimation

This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power flow constraints has been shown to be effective in estimating voltage phasors under low-observability conditions using single-snapshot information. However, the method requires solving a semidefinite programming (SDP) problem, which becomes computationally infeasible for large systems and if multiple-snapshot (time-series) information is used. This paper proposes an efficient algorithm to solve the constrained matrix completion problem with time-series data. This algorithm is based on reformulating the matrix completion problem as a bilinear (non-convex) optimization problem, and applying the alternating minimization algorithm to solve this problem. This paper proves the summable convergence of the proposed algorithm, and demonstrates its efficacy and scalability via IEEE 123-bus system and a real utility feeder system. This paper also explores the value of adding more data from the history in terms of computation time and estimation accuracy.

41 EE - Solar Energy Technologies Office (EE-4S)↗
DOE OSTI2020

Matrix Completion Using Alternating Minimization for Distribution System State Estimation: Preprint

This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power flow constraints has been shown to be effective in estimating voltage phasors under low-observability conditions using single-snapshot information. However, the method requires solving a semidefinite programming (SDP) problem, which becomes computationally infeasible for large systems and if multiple-snapshot (time-series) information is used. This paper proposes an efficient algorithm to solve the constrained matrix completion problem with time-series data. This algorithm is based on reformulating the matrix completion problem as a bilinear (non-convex) optimization problem, and applying the alternating minimization algorithm to solve this problem. This paper proves the summable convergence of the proposed algorithm, and demonstrates its efficacy and scalability via IEEE 123-bus system and a real utility feeder system. This paper also explores the value of adding more data from the history in terms of computation time and estimation accuracy.

41 EE - Solar Energy Technologies Office (EE-4S)↗
DOE OSTI2018

Denoising Poisson phaseless measurements via orthogonal dictionary learning

Phaseless diffraction measurements recorded by CCD detectors are often affected by Poisson noise. In this paper, we propose a dictionary learning model by employing patches based sparsity in order to denoise such Poisson phaseless measurements. The model consists of three terms: (i) A representation term by an orthogonal dictionary, (ii) an L 0 pseudo norm of the coefficient matrix, and (iii) a Kullback-Leibler divergence term to fit phaseless Poisson data. Fast alternating minimization method (AMM) and proximal alternating linearized minimization (PALM) are adopted to solve the proposed model, and especially the theoretical guarantee of the convergence of PALM is provided. The subproblems for these two algorithms both have fast solvers, and indeed, the solutions for the sparse coding and dictionary updating both have closed forms due to the orthogonality of learned dictionaries. Numerical experiments for phase retrieval using coded diffraction and ptychographic patterns are conducted to show the efficiency and robustness of proposed methods, which, by preserving texture features, produce visually and quantitatively improved restored images compared with other phase retrieval algorithms without regularization and local sparsity promoting algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Partitioning sources of CO 2 emission after soil wetting using high-resolution observations and minimal models

Wetting dry soil triggers a pulse of microbial respiration. Respiration pulses after wetting can be complex, evolving through several stages before subsiding—possibly reflecting contributions from multiple carbon (C) sources. In this work we hypothesized that respiration after wetting combines C from cellular sources (notably trehalose, a cellular osmo-protectant) and soluble extracellular C made available by the physical effects of wetting, with cellular sources contributing early during the pulse and extracellular C dominating later. We tested this hypothesis by making measurements of soil respiration, microbial biomass, trehalose, and water extractable organic C after wetting dry soil in the laboratory. We then devised several alternative minimal models to evaluate the potential contributions of trehalose and extracellular C to the respiration pulse. We found that the chloroform-labile fraction of the microbial biomass was comprised of 50% trehalose in dry soil. Both trehalose and water extractable organic C pools declined rapidly after wetting; trehalose disappeared within 3 h of water addition. Chloroform-labile glucose increased 3 h after water addition and then declined, suggesting rapid hydrolysis of trehalose and consumption of the resulting glucose. Respiration dynamics after wetting could be best explained by models that included two C sources, combining rapid metabolism of trehalose with slower consumption of extracellular soluble C. These results suggest that pulses of respiration after wetting reflect both osmolyte consumption within the microbial biomass and enhanced extracellular C availability; hence, models of microbial drought response must account for both processes to fully resolve soil C dynamics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Reverse-mode differentiation in arbitrary tensor network format: with application to supervised learning.

This paper describes an efficient reverse-mode differentiation algorithm for contraction operations of tensor networks that may have arbitrary and unconventional network topologies. The approach leverages the tensor contraction tree of Evenbly and Pfeifer (2014), which provides an instruction set for the contraction sequence of a network. We show that this tree can be efficiently leveraged for differentiation of a full tensor network contraction using a recursive scheme that exploits (1) the bilinear property of contraction and (2) the property that trees have single path from root to leaves. While differentiation of tensor-tensor contraction is already possible in most automatic differentiation packages, we show that exploiting these two additional properties in the specific context of contraction sequences can improve efficiency. Following a description of the algorithm and computational complexity analysis, we investigate its utility for gradient-based supervised learning for low-rank function recovery and for fitting real-world unstructured datasets. We demonstrate improved performance over alternating least-squares optimization approaches and the capability to handle heterogeneous and arbitrary tensor network formats. When compared to alternating minimization algorithms, we find that the gradient-based approach requires a smaller oversampling ratio (number of samples compared to number model parameters) for recovery. This increased efficiency extends to fitting unstructured data of varying dimensionality and when employing a variety of tensor network formats. Here, we show improved learning using the hierarchical Tucker method over the tensor-train in high-dimensional settings on a number of benchmark problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A realistic theory of E6 unification through novel intermediate symmetries

Abstract We propose a non-supersymmetric E 6 GUT with the scalar sector consisting of650⨁351′ ⨁27. Making use of the first representation for the initial symmetry breaking to an intermediate stage, and the latter two representations for second-stage breaking to the Standard Model and a realistic Yukawa sector, this theory represents the minimal E 6 GUT that proceeds through one of the intermediate stages that are novel compared to SU(5) or SO(10) GUT: trinification SU(3) C × SU(3) L × SU(3) R , SU(6) × SU(2) and flipped SO(10) × U(1). We analyze these possibilities under the choice of vacuum that preserves a ℤ 2 “spinorial parity”, which disentangles the chiral and vector-like fermions of E 6 and provides a dark matter candidate in the form of a (scalar) inert doublet. Three cases are shown to consistently unify under the extended survival hypothesis (with minimal fine-tuning): trinification symmetry SU(3) C × SU(3) L × SU(3) R with eitherLRorCRparity, and SU(6) CR × SU(2) L . Although the successful cases give a large range for proton lifetime estimates, all of them include regions consistent with current experimental bounds and within reach of forthcoming experiments. The scenario investigated in this paper essentially represents the unique (potentially) viable choice in the class of E 6 GUTs proceeding through a novel-symmetry intermediate stage, since non-minimal alternatives seem to be intrinsically non-perturbative.

Physics↗
DOE OSTI2017

Scientific data interpolation with low dimensional manifold model

Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Ptychographic phase retrieval by proximal algorithms

We derive a set of ptychography phase-retrieval iterative engines based on proximal algorithms originally developed in convex optimization theory, and discuss their connections with existing ones. The use of proximal operator creates a simple frame work that allows us to incorporate the effect of noise from a maximum-likelihood (ML) principle. We focus on three particular algorithms, namely proximal minimization, alternating direction method of multiplier and accelerated proximal gradient (APG). We benchmark their performance with numerical simulations, and discuss their optimal conditions for convergence and accuracy. An experimental dataset is used to demonstrate their effectiveness as well, in which case an array of cubic Au nanoparticles with a size of 50 nm is imaged. We show that with the presence of Poisson noise, a dataset with photon counts up to 10 4 at one detector pixel already requires ML-based methods to achieve a stable convergence. Among the three algorithms derived in this work, APG method is reported first time for its application in ptychographic reconstruction and shows superior performance in terms of both accuracy and convergence rate with a noisy dataset.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Subspace-Aware Index Codes

In this paper, we generalize the well-known index coding problem to exploit the structure in the source-data to improve system throughput. In many applications (e.g., multimedia), the data to be transmitted may lie (or can be well approximated) in a low-dimensional subspace. We exploit this low-dimensional structure of the data using an algebraic framework to solve the index coding problem (referred to as subspace-aware index coding) as opposed to the traditional index coding problem which is subspace-unaware. Also, we propose an efficient algorithm based on the alternating minimization approach to obtain near optimal index codes for both subspace-aware and -unaware cases. In conclusion, our simulations indicate that under certain conditions, a significant throughput gain (about 90%) can be achieved by subspace-aware index codes over conventional subspace-unaware index codes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

TU-FG-BRB-03: Basis Vector Model Based Method for Proton Stopping Power Estimation From Experimental Dual Energy CT Data

Purpose: This work aims at reducing the uncertainty in proton stopping power (SP) estimation by a novel combination of a linear, separable basis vector model (BVM) for stopping power calculation (Med Phys 43:600) and a statistical, model-based dual-energy CT (DECT) image reconstruction algorithm (TMI 35:685). The method was applied to experimental data. Methods: BVM assumes the photon attenuation coefficients, electron densities, and mean excitation energies (I-values) of unknown materials can be approximated by a combination of the corresponding quantities of two reference materials. The DECT projection data for a phantom with 5 different known materials was collected on a Philips Brilliance scanner using two scans at 90 kVp and 140 kVp. The line integral alternating minimization (LIAM) algorithm was used to recover the two BVM coefficient images using the measured source spectra. The proton stopping powers are then estimated from the Bethe-Bloch equation using electron densities and I-values derived from the BVM coefficients. The proton stopping powers and proton ranges for the phantom materials estimated via our BVM based DECT method are compared to ICRU reference values and a post-processing DECT analysis (Yang PMB 55:1343) applied to vendorreconstructed images using the Torikoshi parametric fit model (tPFM). Results: For the phantom materials, the average stopping power estimations for 175 MeV protons derived from our method are within 1% of the ICRU reference values (except for Teflon with a 1.48% error), with an average standard deviation of 0.46% over pixels. The resultant proton ranges agree with the reference values within 2 mm. Conclusion: Our principled DECT iterative reconstruction algorithm, incorporating optimal beam hardening and scatter corrections, in conjunction with a simple linear BVM model, achieves more accurate and robust proton stopping power maps than the post-processing, nonlinear tPFM based DECT analysis applied to conventional reconstructions of low and high energy scans. Funding Support: NIH R01CA 75371; NCI grant R01 CA 149305.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

TU-H-CAMPUS-IeP3-01: Simultaneous PET Restoration and PET/CT Co-Segmentation Using a Variational Method

Purpose: PET images are usually blurred due to the finite spatial resolution, while CT images suffer from low contrast. Segment a tumor from either a single PET or CT image is thus challenging. To make full use of the complementary information between PET and CT, we propose a novel variational method for simultaneous PET image restoration and PET/CT images co-segmentation. Methods: The proposed model was constructed based on the Γ-convergence approximation of Mumford-Shah (MS) segmentation model for PET/CT co-segmentation. Moreover, a PET de-blur process was integrated into the MS model to improve the segmentation accuracy. An interaction edge constraint term over the two modalities were specially designed to share the complementary information. The energy functional was iteratively optimized using an alternate minimization (AM) algorithm. The performance of the proposed method was validated on ten lung cancer cases and five esophageal cancer cases. The ground truth were manually delineated by an experienced radiation oncologist using the complementary visual features of PET and CT. The segmentation accuracy was evaluated by Dice similarity index (DSI) and volume error (VE). Results: The proposed method achieved an expected restoration result for PET image and satisfactory segmentation results for both PET and CT images. For lung cancer dataset, the average DSI (0.72) increased by 0.17 and 0.40 than single PET and CT segmentation. For esophageal cancer dataset, the average DSI (0.85) increased by 0.07 and 0.43 than single PET and CT segmentation. Conclusion: The proposed method took full advantage of the complementary information from PET and CT images. This work was supported in part by the National Cancer Institute Grants R01CA172638. Shan Tan and Laquan Li were supported in part by the National Natural Science Foundation of China, under Grant Nos. 60971112 and 61375018.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Acoustic- and elastic-waveform inversion with total generalized p-variation regularization

Geophysical models usually contain both sharp interfaces and smooth variations, and it is difficult to accurately account for both of these two types of medium parameter variations using conventional full-waveform inversion methods. We develop a novel full-waveform inversion method for acoustic and elastic waves using a total generalized p-variation regularization scheme to address these challenging problems. We decompose the full-waveform inversion into two subproblems and solve these two minimization subproblems using an alternating-direction minimization strategy. One significant advantage of the total generalized p-variation regularization scheme is that it can simultaneously reconstruct sharp interfaces and smooth background variations of geophysical parameters. Such capability can also effectively suppress the noises in source-encoded inversion and sparse-data inversion, or inversion of noisy data. We demonstrate the advantages of our full-waveform inversion method using a checkerboard model, a modified elastic SEG/EAGE overthrust model, and a land field seismic data set. Our conclusions of synthetic and field seismic data demonstrate that our method reconstructs both smooth background variations and sharp interfaces of subsurface geophysical properties accurately, and provides a useful tool for accurate and reliable inversion of field seismic data.

58 GEOSCIENCES↗
DOE OSTI2016

Iterative metal artifact reduction for x-ray computed tomography using unmatched projector/backprojector pairs

Purpose: Metal artifact reduction (MAR) is a major problem and a challenging issue in x-ray computed tomography (CT) examinations. Iterative reconstruction from sinograms unaffected by metals shows promising potential in detail recovery. This reconstruction has been the subject of much research in recent years. However, conventional iterative reconstruction methods easily introduce new artifacts around metal implants because of incomplete data reconstruction and inconsistencies in practical data acquisition. Hence, this work aims at developing a method to suppress newly introduced artifacts and improve the image quality around metal implants for the iterative MAR scheme. Methods: The proposed method consists of two steps based on the general iterative MAR framework. An uncorrected image is initially reconstructed, and the corresponding metal trace is obtained. The iterative reconstruction method is then used to reconstruct images from the unaffected sinogram. In the reconstruction step of this work, an iterative strategy utilizing unmatched projector/backprojector pairs is used. A ramp filter is introduced into the back-projection procedure to restrain the inconsistency components in low frequencies and generate more reliable images of the regions around metals. Furthermore, a constrained total variation (TV) minimization model is also incorporated to enhance efficiency. The proposed strategy is implemented based on an iterative FBP and an alternating direction minimization (ADM) scheme, respectively. The developed algorithms are referred to as “iFBP-TV” and “TV-FADM,” respectively. Two projection-completion-based MAR methods and three iterative MAR methods are performed simultaneously for comparison. Results: The proposed method performs reasonably on both simulation and real CT-scanned datasets. This approach could reduce streak metal artifacts effectively and avoid the mentioned effects in the vicinity of the metals. The improvements are evaluated by inspecting regions of interest and by comparing the root-mean-square errors, normalized mean absolute distance, and universal quality index metrics of the images. Both iFBP-TV and TV-FADM methods outperform other counterparts in all cases. Unlike the conventional iterative methods, the proposed strategy utilizing unmatched projector/backprojector pairs shows excellent performance in detail preservation and prevention of the introduction of new artifacts. Conclusions: Qualitative and quantitative evaluations of experimental results indicate that the developed method outperforms classical MAR algorithms in suppressing streak artifacts and preserving the edge structural information of the object. In particular, structures lying close to metals can be gradually recovered because of the reduction of artifacts caused by inconsistency effects.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Energy of injection-induced seismicity predicted from in-situ experiments

The ability to predict the magnitude of an earthquake caused by deep fluid injections is an important factor for assessing the safety of the reservoir storage and the seismic hazard. Here, we propose a new approach to evaluate the seismic energy released during fluid injection by integrating injection parameters, induced aseismic deformation, and the distance of earthquake sources from injection. We use data from ten injection experiments performed at a decameter scale into fault zones in limestone and shale formations. We observe that the seismic energy and the hydraulic energy similarly depend on the injected fluid volume (V), as they both scale as V 3/2 . They show, however, a large discrepancy, partly related to a large aseismic deformation. Therefore, to accurately predict the released seismic energy, aseismic deformation should be considered in the budget through the residual deformation measured at the injection. Alternatively, the minimal hypocentral distance from injection points and the critical fluid pressure for fault reactivation can be used for a better prediction of the seismic moment in the total compilation of earthquakes observed during these experiments. Complementary to the prediction based only on the injected fluid volume, our approach opens the possibility of using alternative monitoring parameters to improve traffic-light protocols for induced earthquakes and the regulation of operational injection activities.

58 GEOSCIENCES↗