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A dose-volume constraint (DVC) projection-based algorithm for IMPT inverse planning optimization

MEDICAL PHYSICS 2022年第4期49卷 2699-2708页

作者： Gadoue, Sherif M. Toomeh, Dolla Schultze, Blake E. Schulte, Reinhard W. Karmanos Canc Inst Dept Radiat Oncol Flint MI USA Univ Miami Dept Radiat Oncol Miami FL USA Baylor Univ Dept Elect & Comp Engn Waco TX 76798 USA Loma Linda Univ Dept Basic Sci Div Biomed Engn Sci Loma Linda CA 92350 USA

Purpose Provide a projection-based algorithm to solve the class of optimization problems encountered in intensity modulated proton therapy (IMPT). The algorithm can handle percentage dose-volume constraints (DVCs) that are usually found in such problems. Methods To seek a feasible solution, the automatic relaxation method was used to project the spot weight vector onto the interval defined by lower and upper bound target dose constraints. The obtained solution was optimized separately based on the objective of each organ at risk (OAR) in addition to maximizing the minimum target dose using the bisection search method using a stopping criterion of 10 cGy. The combined weight was used in the CQ algorithm to solve the split feasibility problem but with a special projection technique due to the nonconvexity of DVCs. The algorithm was applied to four clinical IMPT cases (meningioma, prostate, tongue, and oropharynx) and compared to the corresponding treatment plans optimized in Eclipse. Results The treatment plans obtained, for the four cases, using the BCQ-ARM algorithm have dosimetric endpoints that are similar to their counterparts generated from Eclipse. The algorithm worked equally well with all cases, including the complex head and neck ones. The stopping criterion of 10 cGy results in making the generated plans slightly less optimal (epsilon$\epsilon$-optimal) rather than optimal, but with the advantage of the possibility of generating a database of plans. Conclusions The application of the BCQ-ARM algorithm to different cases of IMPT plans with DVCs was demonstrated. The algorithm is successful in generating plans that are dosimetrically equivalent to their corresponding Eclipse plans. Thus, it is suitable to generate optimized treatment plans in a clinically reasonable time frame.

关键词： dose-volume constraints IMPT optimization projection algorithms proton therapy

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A projection Algorithm for Non-Monotone Variational Inequalities

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SET-VALUED AND VARIATIONAL ANALYSIS 2020年第1期28卷 149-166页

作者： Burachik, Regina S. Millan, R. Diaz Univ South Australia Sch Informat Technol & Math Sci Mawson Lakes SA 5095 Australia Fed Inst Goias Rua 7546 Ctr BR-74055110 Goiania Go Brazil

We introduce a projection-type algorithm for solving the variational inequality problem for point-to-set operators, and establish its convergence properties. Namely, we assume that the operator of the variational inequality is continuous in the point-to-set sense, i.e., inner- and outer-semicontinuous. Under the assumption that the dual solution set is not empty, we prove that our method converges to a solution of the variational inequality. Instead of the monotonicity assumption, we require the non-emptiness of the solution set of the dual formulation of the variational inequality. We provide numerical experiments illustrating the behaviour of our iterates. Moreover, we compare our new method with a recent similar one.

关键词： Variational inequality projection algorithms Outer-semicontinuous operator Inner-semicontinuous operator

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ARTIFICIAL NEURAL NETWORKS FOR FEATURE-EXTRACTION AND MULTIVARIATE DATA projection

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IEEE TRANSACTIONS ON NEURAL NETWORKS 1995年第2期6卷 296-317页

作者： MAO, JC JAIN, AK MICHIGAN STATE UNIV DEPT COMP SCIE LANSINGMI 48824 IBM CORP ALMADEN RES CTRSAN JOSECA 95120

Classical feature extraction and data projection methods have been well studied in the pattern recognition and exploratory data analysis literature. In this paper, we propose a number of networks and learning algorithms which provide new or alternative tools for feature extraction and data projection. These networks include a network (SAMANN) for Sammon's nonlinear projection, a linear discriminant analysis (LDA) network, a nonlinear discriminant analysis (NDA) network, and a network for nonlinear projection (NP-SOM) based on Kohonen's self-organizing map. A common attribute of these networks id that they all employ adaptive learning algorithms which makes them suitable in some environments where the distribution of patterns in feature space changes with respect to time. The availability of these networks also facilitates hardware implementation of well-known classical feature extraction and projection approaches. Moreover, the SAMANN network offers the generalization ability of projecting new data, which is not present in the original Sammon's projection algorithm;the NDA method and NP-SOM network provide new powerful approaches for visualizing high dimensional data. We evaluate five representative neural networks for feature extraction and data projection based on a visual judgement of the two-dimensional projection maps and three quantitative criteria on eight data sets with various properties. Our conclusions based on analysis and simulations can be used as a guideline for choosing a proper method for a specific application.

关键词： Artificial neural networks Feature extraction projection algorithms Neural networks Data mining Data analysis Linear discriminant analysis Data visualization USA Councils Adaptive systems

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A Reduced-Complexity projection Algorithm for ADMM-Based LP Decoding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第8期66卷 4819-4833页

作者： Gensheimer, Florian Dietz, Tobias Kraft, Kira Ruzika, Stefan Wehn, Norbert Univ Koblenz Landau Math Inst D-56070 Koblenz Germany Tech Univ Kaiserslautern Dept Math D-67663 Kaiserslautern Germany Tech Univ Kaiserslautern Dept Elect & Comp Engn D-67663 Kaiserslautern Germany

The alternating direction method of multipliers has recently been adapted for linear programming decoding of low-density parity-check codes. The computation of the projection onto the parity polytope is the core of this algorithm and usually involves a sorting operation, which is the main effort of the projection. In this paper, we present an algorithm with low complexity to compute this projection. The algorithm relies on new findings in the recursive structure of the parity polytope and iteratively fixes selected components. As shown in our realistic simulation setup, it requires up to 37% less arithmetical operations compared with state-of-the-art projections. Additionally, it does not involve a sorting operation, which is needed in all exact state-of-the-art projection algorithms. These two benefits make it appealing for efficient hardware and software implementations.

关键词： Maximum likelihood decoding Sorting projection algorithms Parity check codes Linear programming Hardware ADMM LP decoding parity polytope projection

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projection-Wise Filter Optimization for Limited-Angle Cone-Beam CT Using the Approximate Inverse

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IEEE TRANSACTIONS ON NUCLEAR SCIENCE 2015年第1期62卷 148-163页

作者： Muders, Jens Hesser, Juergen Heidelberg Univ Univ Med Ctr Mannheim Dept Radiat Oncol Expt Radiat Oncol Grp D-68167 Mannheim Germany

In this paper, we present a novel and efficient approach for the optimization of filters for limited-angle cone beam computed tomography (CBCT). Our method is based on the theory of approximate inverse (AI) and uses a simultaneous iterative reconstruction technique (SIRT) to estimate a view-dependent reconstruction kernel. From this kernel we then derive a set of 2-D filters that can be applied in a filtered backprojection (FBP) algorithm. By construction the resulting filters are independent of the measured data, so that they can be precomputed for a given geometric setup and be reused with different projection datasets. Our approach is the first application of the AI for 3-D limited-angle CBCT supported by iterative reconstruction, such that in comparison to existing methods, it does not rely on additional reference measurements or on the existence of an analytical inversion formula. However, our method reaches results better than standard FBP methods. Additionally, we provide a general scheme that allows the transfer of our method to other system geometries and gives us the ability to extend it with more complex filters. We will conduct several experiments with simulated and real data where we examine the image quality of our method in comparison to standard FBP and SIRT. The results will show that our angle-optimized FBP has a higher contrast-to-artifact ratio than FBP. In addition to this, we analyze the image quality perpendicular to the in-focus plane by the use of the artifact spread function and show that our technique can be employed to reduce the amount of ghosting artifacts.

关键词： Computed tomography (CT) digital filters filtering algorithms image reconstruction iterative algorithms nondestructive testing projection algorithms reconstruction algorithms volume measurement X-ray tomography

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Shift-invariant, DWT-based "projection" method for estimation of ultrasound pulse power spectrum

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IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL 2002年第8期49卷 1060-1072页

作者： Michailovich, O Adam, D Technion Israel Inst Technol Dept Biomed Engn IL-32000 Haifa Israel

An approach to computing estimates of the ultrasound pulse spectrum from echo-ultrasound RF sequences, measured from biological tissues, is proposed. It is computed by a "projection" algorithm based on the Discrete Wavelet Transform (DWT) using averaging over a range of linear shifts. It is shown that the robust, shift invariant estimate of the ultrasound pulse power spectrum can be obtained by the projection of RF line log spectrum on an appropriately chosen subspace of L-2(R) (i.e., the space of square-integrable functions) that is spanned by a redundant collection of compactly supported, scaling functions. This redundant set is formed from the traditional (in Wavelet analysis) orthogonal set of scaling functions and also by all its linear (discrete) shifts. A proof is given that the estimate, so obtained, could be viewed as the average of the orthogonal projections of the RF line log spectrum, computed for all significant linear shifts of the RF line log spectrum in frequency domain. It implies that the estimate is shift-invariant. A computationally efficient scheme is presented for calculating the estimate. Proof is given that the averaged, shift-invariant estimate can be obtained simply by a convolution with a kernel, which can be viewed as the discretized auto-correlation function of the scaling function, appropriate to the particular subspace being considered. It implies that the computational burden is at most O(n log(2)n), where n is the problem size, making the estimate quite suitable for real-time processing. Because of the property of the wavelet transform to suppress polynomials of orders lower than the number of the vanishing moments of the wavelet used, the presented approach can be considered as a local polynomial fitting. This locality plays a crucial role in the performance of the algorithm, improving the robustness of the estimation. Moreover, it is shown that the "averaging" nature of the proposed estimation allows using (relatively) poorly regul

关键词： Discrete wavelet transforms Ultrasonic imaging Radio frequency Biology computing Pulse measurements Robustness Polynomials Ultrasonic variables measurement Biological tissues projection algorithms

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Robustification of the least absolute value estimator by means of projection statistics - Discussion

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IEEE TRANSACTIONS ON POWER SYSTEMS 1996年第1期11卷 224-225页

作者： Mili, L Cheniae, MG Vichare, NS Rousseeuw, PJ Abur, A Kumar, V Department of Electrical Engineering Virginia Polytechnic Institute and State University Blacksburg VA USA Mathematics Department Universitaire Instelling Antwerpen Antwerp Belgium

This paper describes a fast and robust method for identifying the leverage points of a linearized power system state estimation model. These are measurements whose projections on the space spanned by the row vectors of the weighted Jacobian matrix, the so-called factor space, do not follow the pattern of the bulk of the point cloud. In other words, their projections are outliers in the factor space. The proposed method is implemented through a new version of the projection algorithm that accounts for the sparsity of the Jacobian matrix. It assigns to each data point a projection statistic defined as the maximum of the standardized projections of the point cloud on some directions passing through the origin. By comparing these projection statistics to cutoff values, one can identify the outliers in the factor space and thereby pinpoint the leverage points. The projection statistics are also used to derive weights for robustifying the weighted least absolute value estimator. The computational efficiency and the robustness of the method are demonstrated on the IEEE-14 bus and 118-bus systems.

关键词： Robustness Statistics Clouds Power system modeling State estimation Jacobian matrices Power system measurements Pollution measurement projection algorithms Computational efficiency

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IUAV Path Planning Using a Multiobjective projection Algorithm

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2024年第11期20卷 13069-13076页

作者： Gan, Jianyuan Li, Mingchu Li, Qing Zhang, Runfa Zheng, Xiao Dalian Univ Technol Sch Software Technol Dalian 116024 Peoples R China Jiangxi Normal Univ Nanchang 330022 Peoples R China Shandong Univ Sch Management Jinan 250100 Peoples R China Shanxi Univ Sch Automat & Software Engn Taiyuan 030006 Peoples R China Shandong Univ Technol Sch Comp Sci & Technol Zibo 255049 Peoples R China

For intelligent unmanned aerial vehicles working in complex environments, it is necessary to have a certain autonomous flight control decision-making ability to adapt to complex and changeable environments. In order to realize the rapid path planning of intelligent unmanned aerial vehicle in complex flight environment and ensure its accurate positioning, we consider the constraints of error correction and turning radius and so on, and establish a multiobjective optimization model with the shortest path and the least correction times. In addition, a novel projection algorithm is proposed to solve this model. The evaluation of our proposed method is done from a dataset. We clearly show its effectiveness and its superiority compared to several state-of-the art approaches.

关键词： Path planning Error correction projection algorithms Task analysis Informatics Complexity theory Turning Intelligent unmanned aerial vehicle (IUAV) multiobjective path planning projection algorithm

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Set-membership affine projection algorithm based on the percentage change of the error signal and variable projection order

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IEEE LATIN AMERICA TRANSACTIONS 2022年第3期20卷 496-502页

作者： Trejo, Carlos Maya, Xochitl Martinez, Rene Sanchez, Gabriel Perez, Hector Avalos, Juan Sanchez, Giovanny Inst Politecn Nacl ESIME Mexico City DF Mexico

Nowadays, the use of adaptive filters plays an important role in multiple signal processing applications, such as active noise control, acoustic echo cancellers, system identifiers, channel equalizer, among others. Until date, many of the existing adaptive algorithms such as affine projection algorithms offer a high convergence speed. However, its computational cost is also high. Currently, several authors make extraordinary efforts to reduce its computational cost to be used in practical applications. In this paper, we propose a new set-membership affine projection algorithm based on the percentage change of the error signal and variable projection order (SMAP-PC-VO). Specifically, we propose two techniques to create this algorithm;1) the new algorithm uses an error bound, which is obtained by calcuting the percentage change of the error signal, to avoid the computation of the variance of additive noise, since in existing approaches this parameter determines the error bound. In practical applications, the computation of the variance of additive noise is infeasible since this signal is not available;2) we propose a new method to dynamically modify the projection order in the new algorithm. As a consequence, its computational cost is reduced. To demonstrate its performance, the proposed algorithm was successfully tested in different environments for system identification and active noise control for headphone applications. The simulation results demonstrate that the proposed algorithm presents good convergence properties. In addition, the proposed algorithm exhibits a low overall computational complexity.

关键词： projection algorithms Signal processing algorithms Internet of Things Computational efficiency IEEE transactions Heuristic algorithms Convergence set-membership algorithm affine projection algorithm data selective algorithms variable projection order

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A FAST MAXIMUM-INTENSITY projection ALGORITHM FOR GENERATING MAGNETIC-RESONANCE ANGIOGRAMS

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IEEE TRANSACTIONS ON MEDICAL IMAGING 1993年第1期12卷 50-57页

作者： SCHREINER, S GALLOWAY, RL VANDERBILT UNIV DEPT NEUROL SURGNASHVILLETN 37235

Maximum-intensity projection (MIP) algorithms are one class of algorithms currently used for construction of magnetic resonance (MR) angiograms. The blood flow in a volume of interest is represented by bright intensities in the MR data volume. MIP algorithms search for the maximum intensity along parallel rays cast through the MR image volume. A projection image is formed from these maximum intensity values. Thus, the flow within the vasculature shows up in the projection plane. This research strives to discover methods of reducing the time required to produce the projections, thereby making the technology more accessible to users of less powerful systems. A novel approach was developed for calculating projections in which each image slice was presorted into bins of intensities. By relating the intensities of the pixels to their location in the slice, the total number of pixels considered for the projection plane was reduced, thus saving calculation time. Only those brighter intensities that relate to flow are used in the projection. Additional time savings resulted from precalculating projection ''templates'' and filling multiple projection planes at the same time. The algorithm was written in C on a 80386-based system. The new algorithm demonstrated over a six-fold increase in projection calculation speed over a benchmark algorithm.

关键词： projection algorithms Magnetic resonance Blood flow Angiography Magnetic resonance imaging Magnetic field measurement Optical imaging X-ray imaging Biomedical engineering Biomedical measurements

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