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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Domain Decomposition for Integer Optimal Control with Total Variation Regularization

Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer from high numerical cost associated with the combinatorial nature of integer programming. Hence, such methods are often limited to small and medium-sized problems. We propose a globally convergent, coordinate descent–inspired algorithm that allows tractable subproblem solutions restricted to a partition of the domain. Our decomposition method solves relatively small trust-region subproblems that modify the control variable on a subdomain only. Given nontrivial subdomain overlap, we prove that a global first-order necessary optimality condition is equivalent to a first-order necessary optimality condition per subdomain. We additionally show that a sufficient decrease is achieved on a single subdomain by way of a trust-region subproblem solver using geometric measure–theoretic arguments, which we integrate with a greedy patch selection to prove convergence of our algorithm. In conclusion, we demonstrate the practicality of our algorithm on a benchmark large-scale, PDE-constrained integer optimal control problem and find that our method is faster than the state of the art.

domain decomposition↗
DOE OSTI2022

Sequential linear integer programming for integer optimal control with total variation regularization

We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty implies that the considered integer control problems admit minimizers. We introduce a local optimality concept for the problem, which arises from the infinite-dimensional perspective. In the case of a one-dimensional domain of the control function, we prove convergence of the iterates produced by our algorithm to points that satisfy first-order stationarity conditions for local optimality. We demonstrate the theoretical findings on a computational example.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

A Lagged Diffusivity Method for Computing Total Variation Regularized Fluid Flow

There is a great deal of recent work using optical flow methods for analyzing the dynamics of fluids, and much attention has been paid to developing regularization schemes for variational approaches that are consistent with the physics of fluid flow. In this work we show that using total variation to regularize two different kinds of optical flow functionals leads to very good flow field reconstructions for the kinds of dynamical structures that appear in fluid flow. The first optical flow functional is the classical component-based conservation of intensity, and the second approach is to reconstruct the potential of the flow, rather than the flow components. In the two cases, total variation regularization corresponds to imposing different scientific priors on the solution, which we compute using a variation of the Lagged Diffusivity Fixed Point Iteration. Numerical details are presented, and the results are demonstrated on synthetic data and on a data-driven oceanic flow model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Iterative Joint Ptychography-Tomography with Total Variation Regularization

In order to determine the 3D structure of a thick sample, researchers have recently combined ptychography (for high resolution) and tomography (for 3D imaging) in a single experiment. 2-step methods are usually adopted for reconstruction, where the ptychography and tomography problems are often solved independently. In this paper, we provide a novel model and ADMM-based algorithm to jointly solve the ptychography-tomography problem iteratively, also employing total variation regularization. The proposed method permits large scan stepsizes for the ptychography experiment, requiring less measurements and being more robust to noise with respect to other strategies, while achieving higher reconstruction quality results.

2-step methods↗
DOE OSTI2019

An iterative reconstruction algorithm for pole figure inversion using total variation regularization

This paper describes a new discrete method for inverting X-ray pole figures to estimate the orientation distribution function (ODF). The method employs the equal-volume `cubochoric' representation for uniform discretization of orientation space, SO(3). The forward-projection model is combined with an anisotropic total variation term to iteratively determine the ODF. Here, the efficacy of the new method is evaluated with both model and experimental data and compared with existing discrete and series expansion methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Cerebral perfusion computed tomography deconvolution via structure tensor total variation regularization

Purpose: Cerebral perfusion computed tomography (PCT) imaging as an accurate and fast acute ischemic stroke examination has been widely used in clinic. Meanwhile, a major drawback of PCT imaging is the high radiation dose due to its dynamic scan protocol. The purpose of this work is to develop a robust perfusion deconvolution approach via structure tensor total variation (STV) regularization (PD-STV) for estimating an accurate residue function in PCT imaging with the low-milliampere-seconds (low-mAs) data acquisition. Methods: Besides modeling the spatio-temporal structure information of PCT data, the STV regularization of the present PD-STV approach can utilize the higher order derivatives of the residue function to enhance denoising performance. To minimize the objective function, the authors propose an effective iterative algorithm with a shrinkage/thresholding scheme. A simulation study on a digital brain perfusion phantom and a clinical study on an old infarction patient were conducted to validate and evaluate the performance of the present PD-STV approach. Results: In the digital phantom study, visual inspection and quantitative metrics (i.e., the normalized mean square error, the peak signal-to-noise ratio, and the universal quality index) assessments demonstrated that the PD-STV approach outperformed other existing approaches in terms of the performance of noise-induced artifacts reduction and accurate perfusion hemodynamic maps (PHM) estimation. In the patient data study, the present PD-STV approach could yield accurate PHM estimation with several noticeable gains over other existing approaches in terms of visual inspection and correlation analysis. Conclusions: This study demonstrated the feasibility and efficacy of the present PD-STV approach in utilizing STV regularization to improve the accuracy of residue function estimation of cerebral PCT imaging in the case of low-mAs.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Combined iterative reconstruction and image-domain decomposition for dual energy CT using total-variation regularization

Purpose: Dual-energy CT (DECT) is being increasingly used for its capability of material decomposition and energy-selective imaging. A generic problem of DECT, however, is that the decomposition process is unstable in the sense that the relative magnitude of decomposed signals is reduced due to signal cancellation while the image noise is accumulating from the two CT images of independent scans. Direct image decomposition, therefore, leads to severe degradation of signal-to-noise ratio on the resultant images. Existing noise suppression techniques are typically implemented in DECT with the procedures of reconstruction and decomposition performed independently, which do not explore the statistical properties of decomposed images during the reconstruction for noise reduction. In this work, the authors propose an iterative approach that combines the reconstruction and the signal decomposition procedures to minimize the DECT image noise without noticeable loss of resolution. Methods: The proposed algorithm is formulated as an optimization problem, which balances the data fidelity and total variation of decomposed images in one framework, and the decomposition step is carried out iteratively together with reconstruction. The noise in the CT images from the proposed algorithm becomes well correlated even though the noise of the raw projections is independent on the two CT scans. Due to this feature, the proposed algorithm avoids noise accumulation during the decomposition process. The authors evaluate the method performance on noise suppression and spatial resolution using phantom studies and compare the algorithm with conventional denoising approaches as well as combined iterative reconstruction methods with different forms of regularization. Results: On the Catphan©600 phantom, the proposed method outperforms the existing denoising methods on preserving spatial resolution at the same level of noise suppression, i.e., a reduction of noise standard deviation by one order of magnitude. This improvement is mainly attributed to the high noise correlation in the CT images reconstructed by the proposed algorithm. Iterative reconstruction using different regularization, including quadratic orq-generalized Gaussian Markov random field regularization, achieves similar noise suppression from high noise correlation. However, the proposed TV regularization obtains a better edge preserving performance. Studies of electron density measurement also show that our method reduces the average estimation error from 9.5% to 7.1%. On the anthropomorphic head phantom, the proposed method suppresses the noise standard deviation of the decomposed images by a factor of ∼14 without blurring the fine structures in the sinus area. Conclusions: The authors propose a practical method for DECT imaging reconstruction, which combines the image reconstruction and material decomposition into one optimization framework. Compared to the existing approaches, our method achieves a superior performance on DECT imaging with respect to decomposition accuracy, noise reduction, and spatial resolution.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
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↗
DOE OSTI2022

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.

Huang, Lianjie↗
DOE OSTI2020

Bilevel optimization, deep learning and fractional Laplacian regularization with applications in tomography

Here we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction quality, and compare it with the total variation regularization. We emphasize that the key advantage of using fractional Laplacian as a regularizer is that it leads to a linear operator, as opposed to the total variation regularization which results in a nonlinear degenerate operator. Inspired by residual neural networks, to learn the optimal strength of regularization and the exponent of fractional Laplacian, we develop a dedicated bilevel optimization neural network with a variable depth for a general regularized inverse problem. We illustrate how to incorporate various regularizer choices into our proposed network. As an example, we consider tomographic reconstruction as a model problem and show an improvement in reconstruction quality, especially for limited data, via fractional Laplacian regularization. We successfully learn the regularization strength and the fractional exponent via our proposed bilevel optimization neural network. We observe that the fractional Laplacian regularization outperforms total variation regularization. This is specially encouraging, and important, in the case of limited and noisy data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Sparse Recovery for Scientific Data

We have built build and analyzed fundamental mathematical tools that enable sparse recovery of scientific data for high performance computing, experimental facilities and sensor measurement. The proposed work will impact many areas of research across the DOE. We have designed, developed and analyzed fast scalable algorithms for the sparse recovery of scientific data sets that may be extremely large, generated very quickly and distributed across multiple storage devices. The algorithms we developed will be used to process the copious amounts of scientific data generated by the DOE supercomputer simulations and by DOE experimental and observational facilities. They leverage the fact that while the amount of data produced can be extremely large, the actual quantities of interest (QoI's) are often sparse, either in space time, or in some feature space. Mathematically, notions of compressive sensing, including l1 regularized and total variation regularized optimization have played an important part in this effort.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ 1 regularization

Over the last decade or so, reconstruction methods using ℓ 1 regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The most popular ℓ 1 regularization approach within electron tomography has been total variation (TV) regularization. In addition to reducing unwanted noise, TV regularization encourages a piecewise constant solution with sparse boundary regions. In this paper we propose an alternative ℓ 1 regularization approach for electron tomography based on higher order total variation (HOTV). Like TV, the HOTV approach promotes solutions with sparse boundary regions. In smooth regions however, the solution is not limited to piecewise constant behavior. We demonstrate that this allows for more accurate reconstruction of a broader class of images – even those for which TV was designed for – particularly when dealing with pragmatic tomographic sampling patterns and very fine image features. In conclusion, we develop results for an electron tomography data set as well as a phantom example, and we also make comparisons with discrete tomography approaches.

47 OTHER INSTRUMENTATION↗
DOE OSTI2014

SU-E-I-93: Improved Imaging Quality for Multislice Helical CT Via Sparsity Regularized Iterative Image Reconstruction Method Based On Tensor Framelet

Purpose: Inspired by compressive sensing, sparsity regularized iterative reconstruction method has been extensively studied. However, its utility pertinent to multislice helical 4D CT for radiotherapy with respect to imaging quality, dose, and time has not been thoroughly addressed. As the beginning of such an investigation, this work carries out the initial comparison of reconstructed imaging quality between sparsity regularized iterative method and analytic method through static phantom studies using a state-of-art 128-channel multi-slice Siemens helical CT scanner. Methods: In our iterative method, tensor framelet (TF) is chosen as the regularization method for its superior performance from total variation regularization in terms of reduced piecewise-constant artifacts and improved imaging quality that has been demonstrated in our prior work. On the other hand, X-ray transforms and its adjoints are computed on-the-fly through GPU implementation using our previous developed fast parallel algorithms with O(1) complexity per computing thread. For comparison, both FDK (approximate analytic method) and Katsevich algorithm (exact analytic method) are used for multislice helical CT image reconstruction. Results: The phantom experimental data with different imaging doses were acquired using a state-of-art 128-channel multi-slice Siemens helical CT scanner. The reconstructed image quality was compared between TF-based iterative method, FDK and Katsevich algorithm with the quantitative analysis for characterizing signal-to-noise ratio, image contrast, and spatial resolution of high-contrast and low-contrast objects. Conclusion: The experimental results suggest that our tensor framelet regularized iterative reconstruction algorithm improves the helical CT imaging quality from FDK and Katsevich algorithm for static experimental phantom studies that have been performed.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Anisotropic seismic-waveform inversion: Application to a seismic velocity model from Eleven-Mile Canyon in Nevada

Accurate imaging and characterization of fracture zones is crucial for geothermal energy exploration. Aligned fractures within fracture zones behave as anisotropic media for seismic-wave propagation. The anisotropic properties in fracture zones introduce extra difficulties for seismic imaging and waveform inversion. We have recently developed a new anisotropic elastic-waveform inversion method using a modified total-variation regularization scheme and a wave-energy-base preconditioning technique. Our new inversion method uses the parameterization of elasticity constants to describe anisotropic media, and hence it can properly handle arbitrary anisotropy. We apply our new inversion method to a seismic velocity model along a 2D-line seismic data acquired at Eleven-Mile Canyon located at the Southern Dixie Valley in Nevada for geothermal energy exploration. Our inversion results show that anisotropic elastic-waveform inversion has potential to reconstruct subsurface anisotropic elastic parameters for imaging and characterization of fracture zones.

15 GEOTHERMAL ENERGY↗
DOE OSTI2014

Sampling-based Uncertainty Quantification in Deconvolution of X-ray Radiographs

In imaging applications that focus on quantitative analysis{such as X-ray radiography in the security sciences--it is necessary to be able to reliably estimate the uncertainties in the processing algorithms applied to the image data, and deconvolving the system blur out of the image is usually an essential step. In this work we solve the deconvolution problem within a Bayesian framework for edge-enhancing reconstruction with uncertainty quantification. The likelihood is a normal approximation to the Poisson likelihood, and the prior is generated from a classical total variation regularized Poisson deconvolution. Samples from the corresponding posterior distribution are computed using a Markov chain Monte Carlo approach, giving a pointwise measure of uncertainty in the final, deconvolved signal. We demonstrate the results on real data used to calibrate a high-energy X-ray source and show that this approach gives reconstructions as good as classical regularization methods, while mitigating many of their drawbacks.

Deconvolution, Inverse Problems, Markov Chain Mont↗
DOE OSTI2015

Dose domain regularization of MLC leaf patterns for highly complex IMRT plans

Purpose: The advent of automated beam orientation and fluence optimization enables more complex intensity modulated radiation therapy (IMRT) planning using an increasing number of fields to exploit the expanded solution space. This has created a challenge in converting complex fluences to robust multileaf collimator (MLC) segments for delivery. A novel method to regularize the fluence map and simplify MLC segments is introduced to maximize delivery efficiency, accuracy, and plan quality. Methods: In this work, we implemented a novel approach to regularize optimized fluences in the dose domain. The treatment planning problem was formulated in an optimization framework to minimize the segmentation-induced dose distribution degradation subject to a total variation regularization to encourage piecewise smoothness in fluence maps. The optimization problem was solved using a first-order primal-dual algorithm known as the Chambolle-Pock algorithm. Plans for 2 GBM, 2 head and neck, and 2 lung patients were created using 20 automatically selected and optimized noncoplanar beams. The fluence was first regularized using Chambolle-Pock and then stratified into equal steps, and the MLC segments were calculated using a previously described level reducing method. Isolated apertures with sizes smaller than preset thresholds of 1–3 bixels, which are square units of an IMRT fluence map from MLC discretization, were removed from the MLC segments. Performance of the dose domain regularized (DDR) fluences was compared to direct stratification and direct MLC segmentation (DMS) of the fluences using level reduction without dose domain fluence regularization. Results: For all six cases, the DDR method increased the average planning target volume dose homogeneity (D95/D5) from 0.814 to 0.878 while maintaining equivalent dose to organs at risk (OARs). Regularized fluences were more robust to MLC sequencing, particularly to the stratification and small aperture removal. The maximum and mean aperture sizes using the DDR were consistently larger than those from DMS for all tested number of segments. Conclusions: The fluence map to MLC segmentation conversion problem was formulated as a secondary optimization problem in the dose domain to minimize the smoothness-regularized dose discrepancy. The large scale optimization problem was solved using a primal-dual algorithm that transformed complicated fluences into maps that were more robust to the MLC segmentation and sequencing, affording fewer and larger segments with minimal degradation to dose distribution.

60 APPLIED LIFE SCIENCES↗