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At least 199 records · Page 11

A GENERAL FRAMEWORK FOR ENHANCING SPARSITY OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS

Compressive sensing has become a powerful addition to uncertainty quantification when only limited data are available. In this paper, we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of generalized polynomial chaos expansion. We use an alternating direction method to identify new sets of random variables through iterative rotations so the new representation of the uncertainty is sparser. Consequently, we increase both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the previously developed iterative method to enhance the sparsity of Hermite polynomial expansion is a special case of this general framework. Moreover, we use Legendre and Chebyshev polynomial expansions to demonstrate the effectiveness of this method with applications in solving stochastic partial differential equations and high-dimensional (O(100)) problems.

Yang, Xiu↗

Motion-map constrained image reconstruction (MCIR): Application to four-dimensional cone-beam computed tomography

Purpose: Utilization of respiratory correlated four-dimensional cone-beam computed tomography (4DCBCT) has enabled verification of internal target motion and volume immediately prior to treatment. However, with current standard CBCT scan, 4DCBCT poses challenge for reconstruction due to the fact that multiple phase binning leads to insufficient number of projection data to reconstruct and thus cause streaking artifacts. The purpose of this study is to develop a novel 4DCBCT reconstruction algorithm framework called motion-map constrained image reconstruction (MCIR), that allows reconstruction of high quality and high phase resolution 4DCBCT images with no more than the imaging dose as well as projections used in a standard free breathing 3DCBCT (FB-3DCBCT) scan.Methods: The unknown 4DCBCT volume at each phase was mathematically modeled as a combination of FB-3DCBCT and phase-specific update vector which has an associated motion-map matrix. The motion-map matrix, which is the key innovation of the MCIR algorithm, was defined as the matrix that distinguishes voxels that are moving from stationary ones. This 4DCBCT model was then reconstructed with compressed sensing (CS) reconstruction framework such that the voxels with high motion would be aggressively updated by the phase-wise sorted projections and the voxels with less motion would be minimally updated to preserve the FB-3DCBCT. To evaluate the performance of our proposed MCIR algorithm, we evaluated both numerical phantoms and a lung cancer patient. The results were then compared with the (1) clinical FB-3DCBCT reconstructed using the FDK, (2) 4DCBCT reconstructed using the FDK, and (3) 4DCBCT reconstructed using the well-known prior image constrained compressed sensing (PICCS).Results: Examination of the MCIR algorithm showed that high phase-resolved 4DCBCT with sets of up to 20 phases using a typical FB-3DCBCT scan could be reconstructed without compromising the image quality. Moreover, in comparison with other published algorithms, the image quality of the MCIR algorithm is shown to be excellent.Conclusions: This work demonstrates the potential for providing high-quality 4DCBCT during on-line image-guided radiation therapy (IGRT), without increasing the imaging dose. The results showed that (at least) 20 phase images could be reconstructed using the same projections data, used to reconstruct a single FB-3DCBCT, without streak artifacts that are caused by insufficient projections.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Ghost imaging second harmonic generation microscopy

Second harmonic generation (SHG) microscopy is useful for visualizing interfaces and sub-structures within a wide range of materials due to the propensity for SHG to occur in non-centrosymmetric environments. However, since SHG is a nonlinear process generally necessitating small focal sizes for higher peak powers, a raster scanning approach is usually needed to build an SHG image over a significant sample size. While raster scanning is effective, there is a cost in terms of the time needed to acquire the image and, also, some materials cannot withstand the higher optical intensities within the small focal volume. As such, we describe a SHG microscopy approach based on ghost imaging (GI), which enables imaging data to be collected in parallel rather than sequentially as in raster scanning techniques. We experimentally demonstrate the approach and combine GI-SHG with compressive sensing to make further substantial gains in reducing the amount of sampling required for image reconstruction. Furthermore, GI-SHG is shown to have significant advantages for imaging in highly scattering environments, partly because GI is a background-free approach requiring spatial correlations between photons that travel two paths, with one path entirely devoid of sample interaction. This basic property of GI means that only the photons that travel unimpeded through the sample preserve the spatial correlations needed to reconstruct the image, while more scattered photons do not contribute to the overall GI signal. Finally, we compare the image quality and sampling properties of three different reconstruction algorithms used for compressive sensing.

47 OTHER INSTRUMENTATION↗

SU-C-207-05: A Comparative Study of Noise-Reduction Algorithms for Low-Dose Cone-Beam Computed Tomography

Purpose: To study different noise-reduction algorithms and to improve the image quality of low dose cone beam CT for patient positioning in radiation therapy. Methods: In low-dose cone-beam CT, the reconstructed image is contaminated with excessive quantum noise. In this study, three well-developed noise reduction algorithms namely, a) penalized weighted least square (PWLS) method, b) split-Bregman total variation (TV) method, and c) compressed sensing (CS) method were studied and applied to the images of a computer–simulated “Shepp-Logan” phantom and a physical CATPHAN phantom. Up to 20% additive Gaussian noise was added to the Shepp-Logan phantom. The CATPHAN phantom was scanned by a Varian OBI system with 100 kVp, 4 ms and 20 mA. For comparing the performance of these algorithms, peak signal-to-noise ratio (PSNR) of the denoised images was computed. Results: The algorithms were shown to have the potential in reducing the noise level for low-dose CBCT images. For Shepp-Logan phantom, an improvement of PSNR of 2 dB, 3.1 dB and 4 dB was observed using PWLS, TV and CS respectively, while for CATPHAN, the improvement was 1.2 dB, 1.8 dB and 2.1 dB, respectively. Conclusion: Penalized weighted least square, total variation and compressed sensing methods were studied and compared for reducing the noise on a simulated phantom and a physical phantom scanned by low-dose CBCT. The techniques have shown promising results for noise reduction in terms of PSNR improvement. However, reducing the noise without compromising the smoothness and resolution of the image needs more extensive research.

60 APPLIED LIFE SCIENCES↗

SU-F-BRB-12: A Novel Haar Wavelet Based Approach to Deliver Non-Coplanar Intensity Modulated Radiotherapy Using Sparse Orthogonal Collimators

Purpose: Existing efforts to replace complex multileaf collimator (MLC) by simple jaws for intensity modulated radiation therapy (IMRT) resulted in unacceptable compromise in plan quality and delivery efficiency. We introduce a novel fluence map segmentation method based on compressed sensing for plan delivery using a simplified sparse orthogonal collimator (SOC) on the 4π non-coplanar radiotherapy platform. Methods: 4π plans with varying prescription doses were first created by automatically selecting and optimizing 20 non-coplanar beams for 2 GBM, 2 head & neck, and 2 lung patients. To create deliverable 4π plans using SOC, which are two pairs of orthogonal collimators with 1 to 4 leaves in each collimator bank, a Haar Fluence Optimization (HFO) method was used to regulate the number of Haar wavelet coefficients while maximizing the dose fidelity to the ideal prescription. The plans were directly stratified utilizing the optimized Haar wavelet rectangular basis. A matching number of deliverable segments were stratified for the MLC-based plans. Results: Compared to the MLC-based 4π plans, the SOC-based 4π plans increased the average PTV dose homogeneity from 0.811 to 0.913. PTV D98 and D99 were improved by 3.53% and 5.60% of the corresponding prescription doses. The average mean and maximal OAR doses slightly increased by 0.57% and 2.57% of the prescription doses. The average number of segments ranged between 5 and 30 per beam. The collimator travel time to create the segments decreased with increasing leaf numbers in the SOC. The two and four leaf designs were 1.71 and 1.93 times more efficient, on average, than the single leaf design. Conclusion: The innovative dose domain optimization based on compressed sensing enables uncompromised 4π non-coplanar IMRT dose delivery using simple rectangular segments that are deliverable using a sparse orthogonal collimator, which only requires 8 to 16 leaves yet is unlimited in modulation resolution. This work is supported in part by Varian Medical Systems, Inc. and NIH R43 CA18339.

60 APPLIED LIFE SCIENCES↗

Systematic parameter inference in stochastic mesoscopic modeling

We propose a method to efficiently determine the optimal coarse-grained force field in mesoscopic stochastic simulations of Newtonian fluid and polymer melt systems modeled by dissipative particle dynamics (DPD) and energy conserving dissipative particle dynamics (eDPD). The response surfaces of various target properties (viscosity, diffusivity, pressure, etc.) with respect to model parameters are constructed based on the generalized polynomial chaos (gPC) expansion using simulation results on sampling points (e.g., individual parameter sets). To alleviate the computational cost to evaluate the target properties, we employ the compressive sensing method to compute the coefficients of the dominant gPC terms given the prior knowledge that the coefficients are “sparse”. The proposed method shows comparable accuracy with the standard probabilistic collocation method (PCM) while it imposes a much weaker restriction on the number of the simulation samples especially for systems with high dimensional parametric space. Fully access to the response surfaces within the confidence range enables us to infer the optimal force parameters given the desirable values of target properties at the macroscopic scale. Moreover, it enables us to investigate the intrinsic relationship between the model parameters, identify possible degeneracies in the parameter space, and optimize the model by eliminating model redundancies. The proposed method provides an efficient alternative approach for constructing mesoscopic models by inferring model parameters to recover target properties of the physics systems (e.g., from experimental measurements), where those force field parameters and formulation cannot be derived from the microscopic level in a straight forward way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Cardiac C-arm computed tomography using a 3D + time ROI reconstruction method with spatial and temporal regularization

Purpose: Reconstruction of the beating heart in 3D + time in the catheter laboratory using only the available C-arm system would improve diagnosis, guidance, device sizing, and outcome control for intracardiac interventions, e.g., electrophysiology, valvular disease treatment, structural or congenital heart disease. To obtain such a reconstruction, the patient's electrocardiogram (ECG) must be recorded during the acquisition and used in the reconstruction. In this paper, the authors present a 4D reconstruction method aiming to reconstruct the heart from a single sweep 10 s acquisition. Methods: The authors introduce the 4D RecOnstructiOn using Spatial and TEmporal Regularization (short 4D ROOSTER) method, which reconstructs all cardiac phases at once, as a 3D + time volume. The algorithm alternates between a reconstruction step based on conjugate gradient and four regularization steps: enforcing positivity, averaging along time outside a motion mask that contains the heart and vessels, 3D spatial total variation minimization, and 1D temporal total variation minimization. Results: 4D ROOSTER recovers the different temporal representations of a moving Shepp and Logan phantom, and outperforms both ECG-gated simultaneous algebraic reconstruction technique and prior image constrained compressed sensing on a clinical case. It generates 3D + time reconstructions with sharp edges which can be used, for example, to estimate the patient's left ventricular ejection fraction. Conclusions: 4D ROOSTER can be applied for human cardiac C-arm CT, and potentially in other dynamic tomography areas. It can easily be adapted to other problems as regularization is decoupled from projection and back projection.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Remotely sensed image compression based on wavelet transform

In this paper, we present an image compression algorithm that is capable of significantly reducing the vast amount of information contained in multispectral images. The developed algorithm exploits the spectral and spatial correlations found in multispectral images. The scheme encodes the difference between images after contrast/brightness equalization to remove the spectral redundancy, and utilizes a two-dimensional wavelet transform to remove the spatial redundancy. the transformed images are then encoded by Hilbert-curve scanning and run-length-encoding, followed by Huffman coding. We also present the performance of the proposed algorithm with the LANDSAT MultiSpectral Scanner data. The loss of information is evaluated by PSNR (peak signal to noise ratio) and classification capability.

Kim, Seong W.↗

Generalized Optimization of High-Capacity Compressive Imaging Systems

One of the greatest challenges in applying compressive sensing (CS) signal processing techniques to electromagnetic imaging applications is designing a sensing matrix that has good reconstruction capabilities. Compressive reflector antennas (CRAs) are a class of antennas that have been shown to provide enhanced image reconstruction performance over traditional reflector antennas (TRAs) when CS techniques are employed. In this article, we present a unified CRA design method, which considers both the sensing capacity and efficiency of the antenna and can be used for both compressive imaging and multiple-input multiple-output (MIMO) communication applications. The unified design method is assessed for a CRA configuration in which dielectric scatterers are added to the surface of a TRA. The design results demonstrate the ability of the unified design method to enhance the CS reconstruction capabilities of the CRA.

42 ENGINEERING↗

Sparse and Random Sampling Techniques for High-Resolution, Full-Field, BSS-Based Structural Dynamics Identification from Video

Video-based techniques for identification of structural dynamics have the advantage that they are very inexpensive to deploy compared to conventional accelerometer or strain gauge techniques. When structural dynamics from video is accomplished using full-field, high-resolution analysis techniques utilizing algorithms on the pixel time series such as principal components analysis and solutions to blind source separation the added benefit of high-resolution, full-field modal identification is achieved. An important property of video of vibrating structures is that it is particularly sparse. Typically video of vibrating structures has a dimensionality consisting of many thousands or even millions of pixels and hundreds to thousands of frames. However the motion of the vibrating structure can be described using only a few mode shapes and their associated time series. As a result, emerging techniques for sparse and random sampling such as compressive sensing should be applicable to performing modal identification on video. This work presents how full-field, high-resolution, structural dynamics identification frameworks can be coupled with compressive sampling. The techniques described in this work are demonstrated to be able to recover mode shapes from experimental video of vibrating structures when 70% to 90% of the frames from a video captured in the conventional manner are removed.

47 OTHER INSTRUMENTATION↗

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↗

Efficient Network Partitioning: Application for Decentralized State Estimation in Power Distribution Grids: Preprint

Increase in the proliferation of DERs requires real-time situational awareness for efficient grid operations. State estimation plays an important role for real time control and management of the power grid. As the sensing infrastructure grows, aggregating and handling high volumes of data at a centralized location is extremely difficult. To address this challenge, this paper first proposes a novel and efficient hierarchical spectral clustering-based network partition algorithm followed by a decentralized compressive sensing (DCS) based state estimation. The applicability of the proposed network partitioning algorithm is tested on IEEE-123 bus, IEEE-8500 node, and a 6204-node distribution network. The results shows that the proposed approach efficiently divides the network into multiple sub-networks with the minimum edge connections among the neighbors. Then, we perform DCS-based state estimation on the 6204-node distribution network after dividing the network into 18 optimal partitions. Simulation results show that DCS-based state estimation recovers the system states with high accuracy and low complexity.

ADMM↗

Efficient Network Partitioning: Application for Decentralized State Estimation in Power Distribution Grids

Increase in the proliferation of distributed energy resources require real-time situational awareness for efficient grid operations. State estimation plays an important role for the real-time control and management of the power grid. As the sensing infrastructure grows, aggregating and handling high volumes of data at a centralized location is extremely difficult. To address this challenge, this paper first proposes a novel and efficient hier-archical spectral clustering-based network partitioning algorithm followed by a decentralized compressive sensing (DCS)-based state estimation. The applicability of the proposed network partitioning algorithm is tested on an IEEE 123-bus network, an IEEE 8,500-node system, and a 6,000+ node distribution network. The results shows that the proposed approach efficiently divides the network into multiple sub-networks with the minimum number of edge connections among the neighbors. Then, we perform DCS-based state estimation on the 6,000+ node distribution network after dividing the network into 18 optimal partitions. Simulation results show that the DCS-based state estimation recovers the system states with high accuracy and low complexity.

alternating direction method of multipliers↗

Compressed Optimization of Device Architectures for Semiconductor Quantum Devices

Recent advances in nanotechnology have enabled researchers to manipulate small collections of quantum-mechanical objects with unprecedented accuracy. In semiconductor quantum-dot qubits, this manipulation requires controlling the dot orbital energies, the tunnel couplings, and the electron occupations. These properties all depend on the voltages placed on the metallic electrodes that define the device, the positions of which are fixed once the device is fabricated. While there has been much success with small numbers of dots, as the number of dots grows, it will be increasingly useful to control these systems with as few electrode voltage changes as possible. Here, we introduce a protocol, which we call the "compressed optimization of device architectures" (CODA), in order both to efficiently identify sparse sets of voltage changes that control quantum systems and to introduce a metric that can be used to compare device designs. As an example of the former, we apply this method to simulated devices with up to 100 quantum dots and show that CODA automatically tunes devices more efficiently than other common nonlinear optimizers. To demonstrate the latter, we determine the optimal lateral scale for a triple quantum dot, yielding a simulated device that can be tuned with small voltage changes on a limited number of electrodes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Compressed optimization of device architectures

Recent advances in nanotechnology have enabled researchers to control individual quantum mechanical objects with unprecedented accuracy, opening the door for both quantum and extreme- scale conventional computation applications. As these devices become more complex, designing for facility of control becomes a daunting and computationally infeasible task. Here, motivated by ideas from compressed sensing, we introduce a protocol for the Compressed Optimization of Device Architectures (CODA). It leads naturally to a metric for benchmarking and optimizing device designs, as well as an automatic device control protocol that reduces the operational complexity required to achieve a particular output. Because this protocol is both experimentally and computationally efficient, it is readily extensible to large systems. For this paper, we demonstrate both the bench- marking and device control protocol components of CODA through examples of realistic simulations of electrostatic quantum dot devices, which are currently being developed experimentally for quantum computation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection

This work proposes a hyperspherical sparse approximation framework for detecting jump discontinuities in functions in high-dimensional spaces. The need for a novel approach results from the theoretical and computational inefficiencies of well-known approaches, such as adaptive sparse grids, for discontinuity detection. Our approach constructs the hyperspherical coordinate representation of the discontinuity surface of a function. Then sparse approximations of the transformed function are built in the hyperspherical coordinate system, with values at each point estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. Several approaches are used to approximate the transformed discontinuity surface in the hyperspherical system, including adaptive sparse grid and radial basis function interpolation, discrete least squares projection, and compressed sensing approximation. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. In conclusion, rigorous complexity analyses of the new methods are provided, as are several numerical examples that illustrate the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗

Automated piezoresponse force microscopy domain tracking during fast thermally stimulated phase transition in CuInP 2 S 6

Real-time tracking of dynamic nanoscale processes such as phase transitions by scanning probe microscopy is a challenging task, typically requiring extensive and laborious human supervision. Smart strategies to track specific regions of interest (ROI) in the system during such transformations in a fast and automated manner are necessary to study the evolution of the microscopic changes in such dynamic systems. In this work, we realize automated ROI tracking in piezoresponse force microscopy during a fast (≈0.8 °C s –1 ) thermally stimulated ferroelectric-to-paraelectric phase transition in CuInP 2 S 6 . We use a combination of fast (1 frame per second) sparse scanning with compressed sensing image reconstruction and real-time offset correction via phase cross correlation. The applied methodology enables in situ fast and automated functional nanoscale characterization of a certain ROI during external stimulation that generates sample drift and changes local functionality.

36 MATERIALS SCIENCE↗