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Results for “total variation (TV)”

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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9 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Protection Against Graph-Based False Data Injection Attacks on Power Systems

Graph signal processing (GSP) has emerged as a powerful tool for practical network applications, including power system monitoring. By representing power system voltages as smooth graph signals, recent research has focused on developing GSP-based methods for state estimation, attack detection, and topology identification. Included, efficient methods have been developed for detecting false data injection (FDI) attacks, which until now were perceived as non-smooth with respect to the graph Laplacian matrix. Consequently, these methods may not be effective against smooth FDI attacks. In this paper, we propose a graph FDI (GFDI) attack that minimizes the Laplacian-based graph total variation (TV) under practical constraints. In addition, we develop a low-complexity algorithm that solves the non-convex GDFI attack optimization problem using ell_1-norm relaxation, the projected gradient descent (PGD) algorithm, and the alternating direction method of multipliers (ADMM). We then propose a protection scheme that identifies the minimal set of measurements necessary to constrain the GFDI output to high graph TV, thereby enabling its detection by existing GSP-based detectors. Our numerical simulations on the IEEE-57 bus test case reveal the potential threat posed by well-designed GSP-based FDI attacks. Moreover, we demonstrate that integrating the proposed protection design with GSP-based detection can lead to significant hardware cost savings compared to previous designs of protection methods against FDI attacks.

Morgenstern, Gal↗
DOE OSTI2025

Iterative Reconstruction for Multimodal Neutron Tomography

Here, we describe a unified framework for model-based iterative 3-D reconstruction of multimodal neutron transmission, hydrogen-scatter, and induced-fission images from low resolution data recorded using 14.1-MeV neutrons and the associated-particle imaging (API) technique. The framework, which was developed to facilitate use in challenging field-deployment scenarios, is centered around physics-based system models and a total variation (TV) constrained implementation of the simultaneous iterative reconstruction technique (SIRT). Modified to solve a statistically weighted least squares (WLS) problem, the SIRT algorithm is accelerated using ordered subsets and Nesterov’s momentum for which we derive a near-optimal value of the governing Lipschitz constant. The approach enables the reconstruction of images that are high resolution compared to the acquired data and is robust to both limited statistics and a limited number of projection angles. Moreover, the framework is fast enough to be practical. Example images are provided that demonstrate both the ability to perform fast-neutron imaging of high-atomic-number materials with low radiation dose and the benefit of multimodal neutron imaging to identify key materials.

Hydrogen scatter↗
DOE OSTI2025

Closed-Form Approximation of the Total Variation Proximal Operator

Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved using proximal methods, but the way in which they are applied is constrained by the absence of a closed-form expression for the proximal operator of the TV function. A closed-form approximation of the TV proximal operator has previously been proposed, but its accuracy was not theoretically explored in detail. Here, we address this gap by making several new theoretical contributions, proving that the approximation leads to a proximal operator of some convex function, it is equivalent to a gradient descent step on a smoothed version of TV, and that its error can be fully characterized and controlled with its scaling parameter. We experimentally validate our theoretical results on image denoising and sparse-view computed tomography (CT) image reconstruction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Source function from two-particle correlation function through entropy-regularized Richardson-Lucy deblurring

Source functions are obtained from p – p and d – α correlation functions by applying the Richardson-Lucy (RL) deblurring to the Koonin-Pratt (KP) equation. To prevent fitting of noise in the correlation function, total-variation (TV) regularization is employed that has been effective in ordinary image restoration. TV alone cannot ensure normalization of the source functions. To ensure the latter, we propose a maximum-entropy regularized RL algorithm (MEM-RL). We outline the MEM-RL formalism and optimization strategy for the KP equation, demonstrating its effectiveness on both simulated and experimental data, including the p – p and d – α correlation functions.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2025

Image Reconstruction from Sparse-view Data Acquired with Portable X-ray Devices

• Portable X-ray systems enable on-site 3D imaging for non-invasive inspection of suspicious packages and explosives. • Existing reconstruction algorithms (e.g., FDK or Feldkamp, Davis and Kress) require hundreds of projections over 360 degrees. • Sparse-view scan reduces scanning time and setup effort, making it ideal for field use in timecritical scenarios. • Existing reconstruction algorithms introduce severe artifacts when applied to sparse-view data. • We developed a total variation (TV)-based optimization algorithm for yielding 3D images from sparse-view data collected with our portable X-ray imaging system.

Xia, Dan [University of Chicago, Chicago, IL]↗
DOE OSTI2023

Binary Control Pulse Optimization for Quantum Systems

Quantum control aims to manipulate quantum systems toward specific quantum states or desired operations. Designing highly accurate and effective control steps is vitally important to various quantum applications, including energy minimization and circuit compilation. In this paper we focus on discrete binary quantum control problems and apply different optimization algorithms and techniques to improve computational efficiency and solution quality. Specifically, we develop a generic model and extend it in several ways. We introduce a squared L 2 -penalty function to handle additional side constraints, to model requirements such as allowing at most one control to be active. We introduce a total variation (TV) regularizer to reduce the number of switches in the control. We modify the popular gradient ascent pulse engineering (GRAPE) algorithm, develop a new alternating direction method of multipliers (ADMM) algorithm to solve the continuous relaxation of the penalized model, and then apply rounding techniques to obtain binary control solutions. We propose a modified trust-region method to further improve the solutions. Our algorithms can obtain high-quality control results, as demonstrated by numerical studies on diverse quantum control examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Ginzburg--Landau functionals in the large-graph limit

Ginzburg–Landau (GL) functionals on graphs, which are relaxations of graph-cut functionals on graphs, have yielded a variety of insights in image segmentation and graph clustering. In this paper, we study large-graph limits of GL functionals by taking a functional-analytic view of graphs as nonlocal kernels. For a graph Wn with n nodes, the corresponding graph GL functional GL W n ϵ is an energy for functions on Wn. We minimize GL functionals on sequences of growing graphs that converge to functions called graphons. For such sequences of graphs, we show that the graph GL functional Γ-converges to a continuous and nonlocal functional that we call the graphon GL functional. We investigate the sharp-interface limits of the graph GL and graphon GL functionals, and we relate these limits to a nonlocal total-variation (TV) functional. We express the limiting GL functional in terms of Young measures and thereby obtain a probabilistic interpretation of the minimization problem in the large-graph limit. Finally, to develop intuition about graphon GL functionals, we determine the GL minimizer for several example families of graphons.

Zhang, Edith↗
DOE OSTI2025

Nondestructive Evaluation of Concrete: Elastic Property Imaging Through Full-Waveform Inversion

Concrete is a vital material in construction—especially in the nuclear industry, where it is used in critical structures such as containment vessels. Over time, concrete can degrade due to harsh operational and environmental conditions, necessitating that its elastic properties be accurately evaluated to ensure structural integrity and safety. Traditional nondestructive evaluation methods such as ultrasound-based techniques often rely on simplifying assumptions that may not hold true for concrete. This paper presents an advanced ultrasound-based method that uses elastic full-waveform inversion (EFWI) to create detailed images of concrete’s mechanical properties. By accurately modeling wave behaviors such as scattering and reflection, we aim to overcome the limitations of conventional ultrasonic-based methods. In this work, the imaging problem involved reconstructing the various elastic properties of a heterogenous concrete block with three steel rebars embedded in it. The ultrasonic measurements were synthetically generated from multiple sources and receivers, and the reconstruction process was performed using a gradient-based optimization algorithm. Our approach leveraged EFWI to reconstruct high-resolution images of the pressure wave speed, shear wave speed, and density. Multiple misfit functions—including L2-norm, cross-correlation (CC), and L1-norm—combined with total variation (TV) regularization and parameter constraints using a Sigmoid function—were explored for the reconstruction. The results demonstrated that using the L1-norm misfit function in conjunction with TV regularization and Sigmoid constraints significantly improved the reconstruction quality in comparison to traditional methods. This approach provided clearer images with fewer artifacts and better captured background heterogeneity. Our findings highlight that, when properly designed, EFWI carries great potential for providing comprehensive, more accurate, and more reliable assessments of concrete conditions, as is crucial for the maintenance and safety of nuclear power plant structures.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Rapid Optimization of Total Variation with Applications in Imaging, Additive Manufacturing, and Qualification

Total Variation optimization penalizes the gradient of a control variable or state. While this work focuses on image processing in particular, it has also found applications in inverse problems and topology optimization. In image processing, the goal is to maintain faithfulness to the original image while denoising and/or deblurring. Additionally, bilevel optimization over the spatially varying regularization weights can illuminate interfaces such as damage regions and other anomalies. We will address two fundamental challenges with TV-optimization: (i) the typical slow convergence of existing TV-optimization methods, and (ii) the selection of spatially varying TV parameters to promote interface detection. Additionally, we will apply such techniques to image data collected in additive manufacturing. In said context, stochasticity in build events induces flaws in the manufactured piece, compromising the integrity of said part. There is a critical need for in-situ monitoring to spot anomalies once they form, and in this setting we apply our total variation and hyperparameter solvers. We will develop a customized algorithm based on for extreme-scale TV-optimization that achieves super-linear or quadratic-convergence, a critical property for real-time, image-by-image analysis. A worst-case outcome is a preprocessing step that enhances image quality in-situ, specifically for out-of-focus and noisy images.

36 MATERIALS SCIENCE↗