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String-averaging algorithms for convex feasibility with infinitely many sets

INVERSE PROBLEMS 2019年第4期35卷 1-1页

作者： Kong, T. Yung Pajoohesh, Homeira Herman, Gabor T. CUNY Queens Coll Comp Sci Dept Flushing NY 11367 USA CUNY Medgar Evers Coll Math Dept Brooklyn NY 11225 USA CUNY Comp Sci PhD Program Grad Ctr New York NY 10016 USA

algorithms for convex feasibility find or approximate a point in the intersection of given closed convex sets. Typically there are only finitely many convex sets, but the case of infinitely many convex sets also has some applications. In this context, a string is a finite sequence of points in which each point after the first is obtained from the previous point by considering one of the convex sets. In a string-averaging algorithm, an iterative step from a first point to a second point computes a number of strings, all starting with the first point, and then calculates a (weighted) average of those string's end-points: this average is that iterative step's second point, which is used as the first point for the next iterative step. For string-averaging algorithms based on strings in which each point either is the projection of the previous point on one of the convex sets or is equal to the previous point, we present theorems that provide answers to the following question: 'How can the iterative steps be specified so that the string-averaging algorithm generates a convergent sequence whose limit lies in the intersection of the sets of a given convex feasibility problem'? This paper focuses on the case where the given collection of convex sets is infinite, whereas prior work on the same question that we are aware of has assumed the collection of convex sets is finite (or has been applicable only to a small subset of the algorithms we consider). The string-averaging algorithms that are shown to generate a convergent sequence whose limit lies in the intersection are also shown to be perturbation resilient, so they can be superiorized to generate sequences that also converge to a point of the intersection but in a manner that is superior with respect to some application-dependent criterion.

关键词： convex feasibility iterative algorithm convergence string-averaging superiorization

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Simple "Residual-Norm" Based algorithms, for the Solution of a Large System of Non-Linear Algebraic Equations, which Converge Faster than the Newton's Method

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CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES 2011年第3期71卷 279-304页

作者： Liu, Chein-Shan Atluri, Satya N. Natl Taiwan Univ Dept Civil Engn Taipei 10764 Taiwan Univ Calif Irvine Ctr Aerosp Res & Educ Irvine CA USA

For solving a system of nonlinear algebraic equations (NAEs) of the type: F(x) = 0, or F(i)(x(j)) = 0, i, j = 1, ..., n, a Newton-like algorithm has several drawbacks such as local convergence, being sensitive to the initial guess of solution, and the time-penalty involved in finding the inversion of the Jacobian matrix partial derivative F(i)/partial derivative x(j). Based-on an invariant manifold defined in the space of (x, t) in terms of the residual-norm of the vector F(x), we can derive a gradient-flow system of nonlinear ordinary differential equations (ODEs) governing the evolution of x with a fictitious time-like variable t as an independent variable. We can prove that in the present novel Residual-Norm Based algorithms (RNBAs), the residual-error is automatically decreased to zero along the path of x(t). More importantly, we have derived three iterative algoritms which do not involve the fictitious time and its stepsize Delta t. We apply the three RNBAs to several numerical examples, revealing exponential convergences with different slopes and displaying the high efficiencies and accuracies of the present iterative algorithms. All the three presently proposed RNBAs: (i) are easy to implement numerically, (ii) converge much faster than the Newton's method, (iii) do not involve the inversion of the Jacobian partial derivative F(i)/partial derivative x(j), (iv) are suitable for solving a large system of NAEs, and (v) are purely iterative in nature.

关键词： Nonlinear algebraic equations Non-Linear Ordinary Differential Equations Non-Linear Partial Differential Equations Residual-Norm Based algorithms (RNBAs) Fictitious time integration method (FTIM) iterative algorithm

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Using GMDH for Modeling Economical Indices of Mine Opening

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Systems Analysis Modelling Simulation 2003年第10期43卷 1341-1349页

作者： Sarycheva, Ljudmila Institute of Geoinformatics National Mining University of Ukraine Dnepropetrovsk K.Marx av. 19 Ukraine

Dependency of explicit costs index of mining opening on its parameters is modeled. In addition, the problem of structural identification is solved. Models enumeration is realized with the help of group methods of data handling (GMDH). Least-squares and least-modules methods are used for evaluating model parameters. The quality of resulting models is evaluated by the following criteria: (a) remaining sum of squares criteria; (b) 'sliding control' criteria; (c) regularity criteria. [ABSTRACT FROM AUTHOR]

关键词： Economic parameters GMDH-technique iterative algorithm Modeling Nonlinear regress

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Active Polynomial Chaos Expansion for Reliability-Based Design Optimization

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AIAA JOURNAL 2019年第12期57卷 5431-5446页

作者： Zhou, Yicheng Lu, Zhenzhou Northwestern Polytech Univ Sch Aeronaut POB 120 Xian 710072 Shaanxi Peoples R China

The aim of the present paper is to develop a strategy for solving reliability-based design optimization (RBDO) problems by sparse polynomial chaos expansion (PCE). Because classic sparse regression methods cannot provide the surrogate error measure that can be employed to improve the sampling performance for failure probability estimation in RBDO, Bayesian compressed sensing with state-of-the-art performance is employed to build sparse PCE in the paper. In the meanwhile, a new active learning function is proposed to adaptively select new training points. Two goals can be achieved using this criterion;that is, most of the selected training points are selected from the desired regions to approximate limit state surfaces, and these points tend to be far away from the existing points in the current design to avoid the clustering problem. Because the sparse PCEs are built in an augmented space, it is made numerically affordable to solve the RBDO problem with no extra computational cost. The computation capability of the proposed method is demonstrated by several analytical RBDO problems. Meanwhile, the design optimization of a stiffened rib of the wing edge in a certain aircraft also verifies its good engineering applicability.

关键词： Numerical Stability Cumulative Distribution Function Sequential Quadratic Programming Finite Element Modeling Design of Experiments Mathematical Models Monte Carlo Simulation Support Vector Machine Sensitivity Analysis iterative algorithm

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algorithm-enabled exploration of image-quality potential of cone-beam CT in image-guided radiation therapy

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PHYSICS IN MEDICINE AND BIOLOGY 2015年第12期60卷 4601-4633页

作者： Han, Xiao Pearson, Erik Pelizzari, Charles Al-Hallaq, Hania Sidky, Emil Y. Bian, Junguo Pan, Xiaochuan Univ Chicago Dept Radiol Chicago IL 60637 USA Univ Chicago Dept Radiat & Cellular Oncol Chicago IL 60637 USA Massachusetts Gen Hosp Dept Radiol Boston MA 02114 USA

Kilo-voltage (KV) cone-beam computed tomography (CBCT) unit mounted onto a linear accelerator treatment system, often referred to as on-board imager (OBI), plays an increasingly important role in image-guided radiation therapy. While the FDK algorithm is currently used for reconstructing images from clinical OBI data, optimization-based reconstruction has also been investigated for OBI CBCT. An optimization-based reconstruction involves numerous parameters, which can significantly impact reconstruction properties (or utility). The success of an optimization-based reconstruction for a particular class of practical applications thus relies strongly on appropriate selection of parameter values. In the work, we focus on tailoring the constrained-TVminimization- based reconstruction, an optimization-based reconstruction previously shown of some potential for CBCT imaging conditions of practical interest, to OBI imaging through appropriate selection of parameter values. In particular, for given real data of phantoms and patient collected with OBI CBCT, we first devise utility metrics specific to OBI-quality-assurance tasks and then apply them to guiding the selection of parameter values in constrained-TV-minimization-based reconstruction. The study results show that the reconstructions are with improvement, relative to clinical FDK reconstruction, in both visualization and quantitative assessments in terms of the devised utility metrics.

关键词： cone-beam CT image reconstruction optimization iterative algorithm

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Practical snapshot hyperspectral imaging with DOE

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OPTICS AND LASERS IN ENGINEERING 2022年 156卷

作者： Hu, Haiquan Zhou, Hao Xu, Zhihai Li, Qi Feng, Huajun Chen, Yueting Jiang, Tingting Xu, Wenbin Zhejiang Univ Coll Opt Sci & Engn State Key Lab Modern Opt Instrumentat Hangzhou 310027 Peoples R China Res Ctr Intelligent Sensing Syst Zhejiang Lab Hangzhou 311100 Peoples R China Sci & Technol Opt Radiat Lab Beijing 100854 Peoples R China

As the pursuit of snapshot spectral imaging continued to grow, traditional hyperspectral imaging systems have been too enormous and too slow to implement in real scenarios. Considering the portability and the demand for snapshots, in this study, we proposed a practical hyperspectral camera with a designed diffractive optical element (DOE). The designed DOE distinguished the incident spectrums and converged them into different point spread functions (PSFs) on the imaging plane. Utilizing the spectrally-varying PSF information, we engaged the iterative algorithm with the deep-learning model to reconstruct hyperspectral data. Experimental results demonstrated that the proposed system performed at least as well as the current methods and could achieve great spatial resolution and spectral accuracy in spectral imaging. This proposed system had good potential in portable hyperspectral imaging system.

关键词： Hyperspectral imaging Diffractive optical element iterative algorithm Neural network Snapshot

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iterative Component Mode Synthesis Using a Priori and a Posteriori Criteria

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AIAA JOURNAL 2019年第5期57卷 2145-2157页

作者： Kim, Soo Min Kim, Jin-Gyun Park, K. C. Chae, Soo-Won Korea Univ Dept Mech Engn 145 Anam Ro Seoul 02841 South Korea Kyung Hee Univ Dept Mech Engn 1732 Deogyeong Daero Yongin 17104 Gyeonggi Do South Korea Univ Colorado Dept Aerosp Engn Sci Campus Box 429 Boulder CO 80309 USA Univ Colorado Ctr Aerosp Struct Campus Box 429 Boulder CO 80309 USA

An iterative algorithm of component mode synthesis for a rational reduced-order modeling is proposed. The present algorithm consists of three steps: initial mode selection with a priori criterion, model reduction using the selected modes, and a posteriori error evaluation. The algorithm is based on the Craig-Bampton method, which is one of the most widely used techniques. Specifically, the present algorithm uses, in a judicious manner, both an a priori mode selection criterion employing the moment-matching strategy and an a posteriori error estimation technique in evaluating the relative eigenvalue errors. If desired, an optional step of boundary interface reduction offers an additional possibility of obtaining a more compact model. The proposed iterative algorithm is recommended to researchers as well as commercialized software users in developing linear reduced-order structural dynamics models. Numerical examples are presented for its practical usage and performance.

关键词： iterative algorithm Structural Dynamics Aeroplane Flexibility Matrix Elastic Modulus Frequency Response Functions Material Properties Computing Tetrahedral Element Free Vibrations

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A KRASNOSELSKII-TYPE algorithm FOR APPROXIMATING ZEROS OF MONOTONE MAPS IN BANACH SPACES WITH APPLICATIONS

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS

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JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS 2018年第3期2卷 305-315页

作者： Romanus, Ogonnaya M. Nnakwe, Monday O. Nnyaba, Ukamaka V. African Univ Sci & Technol Abuja Nigeria

In this paper, a Krasnoselskii-type algorithm that approximates the unique zero of a Holder continuous and strongly monotone map is constructed. Strong convergence of the sequence generated by this algorithm is established in strictly convex, reflexive and smooth real Banach spaces. Results obtained in this paper are applied to approximate a minimizer of some convex functionals and a solution of a Hammerstein integral equation.

关键词： Holder continuous map iterative algorithm Lipschitz map Monotone map Strong convergence

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Sparse-view proton computed tomography using modulated proton beams

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MEDICAL PHYSICS 2015年第2期42卷 1129-1137页

作者： Lee, Jiseoc Kim, Changhwan Min, Byungjun Kwak, Jungwon Park, Seyjoon Lee, Se Byeong Park, Sungyong Cho, Seungryong Korea Adv Inst Sci & Technol Dept Nucl & Quantum Engn Taejon 305701 South Korea Kangbuk Samsung Hosp Dept Radiat Oncol Seoul 110746 South Korea Asan Med Ctr Dept Radiat Oncol Asan 138736 South Korea Natl Canc Ctr Proton Therapy Ctr Seoul 410769 South Korea McLaren Canc Inst Proton Therapy Ctr Flint MI 48532 USA

Purpose: Proton imaging that uses a modulated proton beam and an intensity detector allows a relatively fast image acquisition compared to the imaging approach based on a trajectory tracking detector. In addition, it requires a relatively simple implementation in a conventional proton therapy equipment. The model of geometric straight ray assumed in conventional computed tomography (CT) image reconstruction is however challenged by multiple-Coulomb scattering and energy straggling in the proton imaging. Radiation dose to the patient is another important issue that has to be taken care of for practical applications. In this work, the authors have investigated iterative image reconstructions after a deconvolution of the sparsely view-sampled data to address these issues in proton CT. Methods: Proton projection images were acquired using the modulated proton beams and the EBT2 film as an intensity detector. Four electron-density cylinders representing normal soft tissues and bone were used as imaged object and scanned at 40 views that are equally separated over 360 degrees. Digitized film images were converted to water-equivalent thickness by use of an empirically derived conversion curve. For improving the image quality, a deconvolution-based image deblurring with an empirically acquired point spread function was employed. They have implemented iterative image reconstruction algorithms such as adaptive steepest descent-projection onto convex sets (ASD-POCS), superiorization method-projection onto convex sets (SM-POCS), superiorization method-expectation maximization (SM-EM), and expectation maximization-total variation minimization (EM-TV). Performance of the four image reconstruction algorithms was analyzed and compared quantitatively via contrast-to- noise ratio (CNR) and root-mean-square-error (RMSE). Results: Objects of higher electron density have been reconstructed more accurately than those of lower density objects. The bone, for example, has been reconstructed

关键词： proton computed tomography modulated proton beam image reconstruction iterative algorithm

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An improved algorithm for fast resonant Mie scatter correction of infrared spectra of cells and tissues

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JOURNAL OF BIOPHOTONICS 2018年第1期11卷 2018 Jan;11(1)页

作者： Konevskikh, Tatiana Lukacs, Rozalia Kohler, Achim Norwegian Univ Life Sci Dept Math Sci & Technol IMT N-1430 Trondheim Norway

Mie scattering effects create serious problems for the interpretation of Fourier-transform infrared spectroscopy spectra of single cells and tissues. During recent years, different techniques were proposed to retrieve pure absorbance spectra from spectra with Mie distortions. Recently, we published an iterative algorithm for correcting Mie scattering in spectra of single cells and tissues, which we called the fast resonant Mie scatter correction algorithm. The algorithm is based on extended multiplicative signal correction (EMSC) and employs a meta-model for a parameter range of refractive index and size parameters. In the present study, we suggest several improvements of the algorithm. We demonstrate that the improved algorithm reestablishes chemical features of the measured spectra, and show that it tends away from the reference spectrum employed in the EMSC. We suggest strategies for choosing parameter ranges and other model parameters such as the number of principal components of the meta-model and the number of iterations. We demonstrate that the suggested algorithm optimizes an error function of the refractive index in a forward Mie model. We suggest a stop criterion for the iterative algorithm based on the error function of the forward model.

关键词： complex refractive index extended multiplicative signal correction Hilbert transform infrared microscopy iterative algorithm Mie scattering

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