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All sources NASA NTRS DOE OSTI

DOE OSTI2016

WE-FG-207B-03: Multi-Energy CT Reconstruction with Spatial Spectral Nonlocal Means Regularization

Purpose: Multi-energy computed tomography (MECT) is an emerging application in medical imaging due to its ability of material differentiation and potential for molecular imaging. In MECT, image correlations at different spatial and channels exist. It is desirable to incorporate these correlations in reconstruction to improve image quality. For this purpose, this study proposes a MECT reconstruction technique that employes spatial spectral non-local means (ssNLM) regularization. Methods: We consider a kVp-switching scanning method in which source energy is rapidly switched during data acquisition. For each energy channel, this yields projection data acquired at a number of angles, whereas projection angles among channels are different. We formulate the reconstruction task as an optimziation problem. A least square term enfores data fidelity. A ssNLM term is used as regularization to encourage similarities among image patches at different spatial locations and channels. When comparing image patches at different channels, intensity difference were corrected by a transformation estimated via histogram equalization during the reconstruction process. Results: We tested our method in a simulation study with a NCAT phantom and an experimental study with a Gammex phantom. For comparison purpose, we also performed reconstructions using conjugate-gradient least square (CGLS) method and conventional NLM method that only considers spatial correlation in an image. ssNLM is able to better suppress streak artifacts. The streaks are along different projection directions in images at different channels. ssNLM discourages this dissimilarity and hence removes them. True image structures are preserved in this process. Measurements in regions of interests yield 1.1 to 3.2 and 1.5 to 1.8 times higher contrast to noise ratio than the NLM approach. Improvements over CGLS is even more profound due to lack of regularization in the CGLS method and hence amplified noise. Conclusion: The proposed ssNLM method for kVp-switching MECT reconstruction can achieve high quality MECT images.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Pauli–Villars regularization elucidated in Bopp–Podolsky’s generalized electrodynamics

We discuss an inherent Pauli–Villars regularization in Bopp–Podolsky’s generalized electrodynamics. Introducing gauge-fixing terms for Bopp–Podolsky’s generalized electrodynamic action, we realize a unique feature for the corresponding photon propagator with a built-in Pauli–Villars regularization independent of the gauge choice made in Maxwell’s usual electromagnetism. According to our realization, the length dimensional parameter a associated with Bopp–Podolsky’s higher order derivatives corresponds to the inverse of the Pauli–Villars regularization mass scale Λ, i.e. a=1/Λ. Solving explicitly the classical static Bopp–Podolsky’s equations of motion for a specific charge distribution, we explore the physical meaning of the parameter a in terms of the size of the charge distribution. As an offspring of the generalized photon propagator analysis, we also discuss our findings regarding on the issue of the two-term vs. three-term photon propagator in light-front dynamics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Two-level structural sparsity regularization for identifying lattices and defects in noisy images

Here, this paper presents a regularized regression model with a two-level structural sparsity penalty applied to locate individual atoms in a noisy scanning transmission electron microscopy image (STEM). In crystals, the locations of atoms is symmetric, condensed into a few lattice groups. Therefore, by identifying the underlying lattice in a given image, individual atoms can be accurately located. We propose to formulate the identification of the lattice groups as a sparse group selection problem. Furthermore, real atomic scale images contain defects and vacancies, so atomic identification based solely on a lattice group may result in false positives and false negatives. To minimize error, model includes an individual sparsity regularization in addition to the group sparsity for a within-group selection, which results in a regression model with a two-level sparsity regularization. We propose a modification of the group orthogonal matching pursuit (gOMP) algorithm with a thresholding step to solve the atom finding problem. The convergence and statistical analyses of the proposed algorithm are presented. The proposed algorithm is also evaluated through numerical experiments with simulated images. The applicability of the algorithm on determination of atom structures and identification of imaging distortions and atomic defects was demonstrated using three real STEM images. In conclusion, we believe this is an important step toward automatic phase identification and assignment with the advent of genomic databases for materials.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Epi-Regularization of Risk Measures

Uncertainty pervades virtually every branch of science and engineering, and in many disciplines, the underlying phenomena can be modeled by partial differential equations (PDEs) with uncertain or random inputs. This work is motivated by risk-averse stochastic programming problems constrained by PDEs. These problems are posed in infinite dimensions, which leads to a significant increase in the scale of the (discretized) problem. In order to handle the inherent nonsmoothness of, for example, coherent risk measures and to exploit existing solution techniques for smooth, PDE-constrained optimization problems, we propose a variational smoothing technique called epigraphical (epi-)regularization. Here, we investigate the effects of epi-regularization on the axioms of coherency and prove differentiability of the smoothed risk measures. In addition, we demonstrate variational convergence of the epi-regularized risk measures and prove the consistency of minimizers and first-order stationary points for the approximate risk-averse optimization problem. We conclude with numerical experiments confirming our theoretical results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

RegularizedOptimization.jl: A Julia framework for regularized and nonsmooth optimization

RegularizedOptimization.jl is a Julia package that implements families of quadratic regularization and trust-region methods for solving the nonsmooth optimization problem $^{\textrm{minimize}}_{𝑥∈ℝ^𝑛}$ 𝑓(𝑥) + ℎ(𝑥) subject to 𝑐(𝑥) = 0, (1) where 𝑓 ∶ ℝ 𝑛 → ℝ and 𝑐 ∶ ℝ 𝑛 → ℝ 𝑚 are continuously differentiable, and ℎ ∶ ℝ 𝑛 → ℝ∪{+∞} is lower semi-continuous. The nonsmooth objective ℎ can be a regularizer, such as a sparsity inducing penalty, model simple constraints, such as 𝑥 belonging to a simple convex set, or can be a combination of both. All 𝑓, ℎ, and 𝑐 can be nonconvex. RegularizedOptimization.jl provides a modular and extensible framework for solving (1), and developing novel solvers. Currently, the following solvers are implemented: • Trust-region solvers TR and TRDH (Aravkin et al., 2022; Leconte & Orban, 2025) • Quadratic regularization solvers R2, R2DH and R2N (Aravkin et al., 2022; Diouane, Habiboullah, et al., 2024) • Levenberg-Marquardt solvers LM and LMTR (Aravkin et al., 2024) used when 𝑓 is a least-squares residual. • Augmented Lagrangian solver AL (De Marchi et al., 2023). All solvers rely on first derivatives of 𝑓 and 𝑐, and optionally on their second derivatives in the form of Hessian-vector products. If second derivatives are not available, quasi-Newton approximations can be used. In addition, the proximal mapping of the nonsmooth part ℎ, or adequate models thereof, must be evaluated. At each iteration, a step is computed by solving a subproblem of the form (1) inexactly, in which 𝑓, ℎ, and 𝑐 are replaced with appropriate models around the current iterate. The solvers R2, R2DH, and TRDH are particularly well suited to solve the subproblems, though they are general enough to solve (1). All solvers are allocation-free, so re-solves incur no additional allocations. To illustrate our claim of extensibility, a first version of the AL solver was implemented by an external contributor. Furthermore, a nonsmooth penalty approach, described in Diouane, Gollier, et al. (2024), is currently being developed, that relies on the library to efficiently solve the subproblems.

Gollier, Maxence [Polytechnique Montréal, QC (Cana↗

DOE OSTI2024

On the connection between least squares, regularization, and classical shadows

Classical shadows (CS) offer a resource-efficient means to estimate quantum observables, circumventing the need for exhaustive state tomography. Here, we clarify and explore the connection between CS techniques and least squares (LS) and regularized least squares (RLS) methods commonly used in machine learning and data analysis. By formal identification of LS and RLS ``shadows'' completely analogous to those in CS---namely, point estimators calculated from the empirical frequencies of single measurements---we show that both RLS and CS can be viewed as regularizers for the underdetermined regime, replacing the pseudoinverse with invertible alternatives. Through numerical simulations, we evaluate RLS and CS from three distinct angles: the tradeoff in bias and variance, mismatch between the expected and actual measurement distributions, and the interplay between the number of measurements and number of shots per measurement. Compared to CS, RLS attains lower variance at the expense of bias, is robust to distribution mismatch, and is more sensitive to the number of shots for a fixed number of state copies---differences that can be understood from the distinct approaches taken to regularization. Conceptually, our integration of LS, RLS, and CS under a unifying ``shadow'' umbrella aids in advancing the overall picture of CS techniques, while practically our results highlight the tradeoffs intrinsic to these measurement approaches, illuminating the circumstances under which either RLS or CS would be preferred, such as unverified randomness for the former or unbiased estimation for the latter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1971

The topology of the regularized integral surfaces of the 3-body problem

Momentum, angular momentum, and energy of integral surfaces in the planar three-body problem are considered. The end points of orbits which cross an isolating block are identified. It is shown that this identification has a unique extension to an identification which pairs the end points of orbits entering the block and which end in a binary collision with the end points of orbits leaving the block and which come from a binary collision. The problem of regularization is that of showing that the identification of the end points of crossing orbits has a continuous, unique extension. The regularized phase space for the three-body problem was obtained, as were regularized integral surfaces for the problem on which the three-body equations of motion induce flows. Finally the topology of these surfaces is described.

Easton, R.↗

NASA NTRS1988

Partitioning of regular computation on multiprocessor systems

Problem partitioning of regular computation over two dimensional meshes on multiprocessor systems is examined. The regular computation model considered involves repetitive evaluation of values at each mesh point with local communication. The computational workload and the communication pattern are the same at each mesh point. The regular computation model arises in numerical solutions of partial differential equations and simulations of cellular automata. Given a communication pattern, a systematic way to generate a family of partitions is presented. The influence of various partitioning schemes on performance is compared on the basis of computation to communication ratio.

Lee, Fung Fung↗

NASA NTRS1990

Partitioning of regular computation on multiprocessor systems

Lee, Fung F.↗

NASA NTRS1991

Analysis of regularized Navier-Stokes equations. I, II

A regularized form of the conventional Navier-Stokes equations is analyzed. The global existence and uniqueness are established for two classes of generalized solutions. It is shown that the solution of this regularized system converges to the solution of the conventional Navier-Stokes equations for low Reynolds numbers. Particular attention is given to the structure of attractors characterizing the solutions. Both local and global invariant manifolds are found, and the regularity properties of these manifolds are analyzed.

Ou, Yuh-Roung↗

NASA NTRS1992

Clustering, randomness and regularity in cloud fields. I - Theoretical considerations. II - Cumulus cloud fields

The current controversy existing in reference to the regularity vs. clustering in cloud fields is examined by means of analysis and simulation studies based upon nearest-neighbor cumulative distribution statistics. It is shown that the Poisson representation of random point processes is superior to pseudorandom-number-generated models and that pseudorandom-number-generated models bias the observed nearest-neighbor statistics towards regularity. Interpretation of this nearest-neighbor statistics is discussed for many cases of superpositions of clustering, randomness, and regularity. A detailed analysis is carried out of cumulus cloud field spatial distributions based upon Landsat, AVHRR, and Skylab data, showing that, when both large and small clouds are included in the cloud field distributions, the cloud field always has a strong clustering signal.

Weger, R. C.↗

NASA NTRS2006

Manufacture of Regularly Shaped Sol-Gel Pellets

An extrusion batch process for manufacturing regularly shaped sol-gel pellets has been devised as an improved alternative to a spray process that yields irregularly shaped pellets. The aspect ratio of regularly shaped pellets can be controlled more easily, while regularly shaped pellets pack more efficiently. In the extrusion process, a wet gel is pushed out of a mold and chopped repetitively into short, cylindrical pieces as it emerges from the mold. The pieces are collected and can be either (1) dried at ambient pressure to xerogel, (2) solvent exchanged and dried under ambient pressure to ambigels, or (3) supercritically dried to aerogel. Advantageously, the extruded pellets can be dropped directly in a cross-linking bath, where they develop a conformal polymer coating around the skeletal framework of the wet gel via reaction with the cross linker. These pellets can be dried to mechanically robust X-Aerogel.

Leventis, Nicholas↗

NASA NTRS2003

Preparation of Regular Specimens for Atom Probes

A method of preparation of specimens of non-electropolishable materials for analysis by atom probes is being developed as a superior alternative to a prior method. In comparison with the prior method, the present method involves less processing time. Also, whereas the prior method yields irregularly shaped and sized specimens, the present developmental method offers the potential to prepare specimens of regular shape and size. The prior method is called the method of sharp shards because it involves crushing the material of interest and selecting microscopic sharp shards of the material for use as specimens. Each selected shard is oriented with its sharp tip facing away from the tip of a stainless-steel pin and is glued to the tip of the pin by use of silver epoxy. Then the shard is milled by use of a focused ion beam (FIB) to make the shard very thin (relative to its length) and to make its tip sharp enough for atom-probe analysis. The method of sharp shards is extremely time-consuming because the selection of shards must be performed with the help of a microscope, the shards must be positioned on the pins by use of micromanipulators, and the irregularity of size and shape necessitates many hours of FIB milling to sharpen each shard. In the present method, a flat slab of the material of interest (e.g., a polished sample of rock or a coated semiconductor wafer) is mounted in the sample holder of a dicing saw of the type conventionally used to cut individual integrated circuits out of the wafers on which they are fabricated in batches. A saw blade appropriate to the material of interest is selected. The depth of cut and the distance between successive parallel cuts is made such that what is left after the cuts is a series of thin, parallel ridges on a solid base. Then the workpiece is rotated 90 and the pattern of cuts is repeated, leaving behind a square array of square posts on the solid base. The posts can be made regular, long, and thin, as required for samples for atom-probe analysis. Because of their small volume and regularity, the amount of FIB-milling time can be much less than that of the method of sharp shards. Individual posts can be broken off for mounting in a manner similar to that of the method of sharp shards. Alternatively, the posts can be left intact on the base and the base can be cut to a small square (e.g., 3 by 3 mm) suitable for mounting in an atom probe of a type capable of accepting multiple-tip specimens. The advantage of multiple-tip specimens is the possibility of analyzing many tips without the time-consuming interchange of specimens.

Kuhlman, Kim↗

NASA NTRS2013

Downscaling Satellite Precipitation with Emphasis on Extremes: A Variational 1-Norm Regularization in the Derivative Domain

The increasing availability of precipitation observations from space, e.g., from the Tropical Rainfall Measuring Mission (TRMM) and the forthcoming Global Precipitation Measuring (GPM) Mission, has fueled renewed interest in developing frameworks for downscaling and multi-sensor data fusion that can handle large data sets in computationally efficient ways while optimally reproducing desired properties of the underlying rainfall fields. Of special interest is the reproduction of extreme precipitation intensities and gradients, as these are directly relevant to hazard prediction. In this paper, we present a new formalism for downscaling satellite precipitation observations, which explicitly allows for the preservation of some key geometrical and statistical properties of spatial precipitation. These include sharp intensity gradients (due to high-intensity regions embedded within lower-intensity areas), coherent spatial structures (due to regions of slowly varying rainfall),and thicker-than-Gaussian tails of precipitation gradients and intensities. Specifically, we pose the downscaling problem as a discrete inverse problem and solve it via a regularized variational approach (variational downscaling) where the regularization term is selected to impose the desired smoothness in the solution while allowing for some steep gradients(called 1-norm or total variation regularization). We demonstrate the duality between this geometrically inspired solution and its Bayesian statistical interpretation, which is equivalent to assuming a Laplace prior distribution for the precipitation intensities in the derivative (wavelet) space. When the observation operator is not known, we discuss the effect of its misspecification and explore a previously proposed dictionary-based sparse inverse downscaling methodology to indirectly learn the observation operator from a database of coincidental high- and low-resolution observations. The proposed method and ideas are illustrated in case studies featuring the downscaling of a hurricane precipitation field.

Hurricanes↗

NASA NTRS2016

Product of the SNPP VIIRS SD Screen Transmittance and the SD BRDF (RSB) From Both Yaw Maneuver and Regular On-Orbit Data

To assure data quality, the Earth-observing Visible Infrared Imaging Radiometer Suite (VIIRS) regularly performs on-orbit radiometric calibrations of its 22 spectral bands. The primary calibration radiance source for the reflective solar bands (RSBs) is a sunlit solar diffuser (SD). During the calibration process, sunlight goes through a perforated plate (the SD screen) and then strikes the SD. The SD scattered sunlight is used for the calibration, with the spectral radiance proportional to the product of the SD screen transmittance and the SD bidirectional reflectance distribution function (BRDF). The BRDF is decomposed to the product of its value at launch and a numerical factor quantifying its change since launch. Therefore, the RSB calibration requires accurate knowledge of the product of the SD screen transmittance and the BRDF (RSB; launch time). Previously, we calculated the product with yaw maneuver data and found that the product had improved accuracy over the prelaunch one. With both yaw maneuver and regular on orbit data, we were able to improve the accuracy of the SDSM screen transmittance and the product for the solar diffuser stability monitor SD view. In this study, we use both yaw maneuver and a small portion of regular on-orbit data to determine the product for the RSB SD view.

Lei, Ning↗

NASA NTRS2019

Regularization and Error Characterization of GRACE Mascons

We present a new global time-variable gravity mascon solution derived from Gravity Recovery and Climate Experiment (GRACE) Level 1B data. The new product from the NASA Goddard Space Flight Center (GSFC) results from a novel approach that combines an iterative solution strategy with geographical binning of inter-satellite range-acceleration residuals in the construction of time-dependent regularization matrices applied in the inversion of mascon parameters. This estimation strategy is intentionally conservative as it seeks to maximize the role of the GRACE measurements on the final solution while minimizing the influence of the regularization design process. We fully reprocess the Level 1B data in the presence of the final mascon solution to generate true post-fit inter-satellite residuals, which are utilized to confirm solution convergence and to validate the mascon noise uncertainties. We also present the mathematical case that regularized mascon solutions are biased, and that this bias, or leakage, must be combined with the estimated noise variance to accurately assess total mascon uncertainties. The estimated leakage errors are determined from the monthly resolution operators. We present a simple approach to compute the total uncertainty for both individual mascon and regional analysis of the GSFC mascon product, and validate the results in comparison with independent mascon solutions and calibrated Stokes uncertainties. Lastly, we present the new solution and uncertainties with global analyses of the mass trends and annual amplitudes, and compute updated trends for the global ocean, and the respective contributions of the Greenland Ice Sheet, Antarctic Ice Sheet, Gulf of Alaska, and terrestrial water storage. This analysis highlights the successful closure of the global mean sea level budget, that is, the sum of global ocean mass from the GSFC mascons and the steric component from Argo floats agrees well with the total determined from sea surface altimetry.

B. D. Loomis↗

NASA NTRS2019

Regularization and Error Characterization of GRACE Mascons

Loomis, B. D.↗

DOE OSTI2018

Ultrasound waveform tomography with spatial and edge regularization

Synthetic-aperture ultrasound tomography systems and methods using scanning arrays and algorithms configured to simultaneously acquire ultrasound transmission and reflection data, and process the data for improved ultrasound tomography imaging, wherein the tomography imaging comprises total-variation regularization, or a modified total variation regularization, particularly with edge-guided or spatially variant regularization.

47 OTHER INSTRUMENTATION↗