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Asymptotically Efficient Recursive Identification of FIR Systems With Binary-Valued Observations

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2021年第5期51卷 2687-2700页

作者： Zhang, Hang Wang, Ting Zhao, Yanlong Chinese Acad Sci Acad Math & Syst Sci Key Lab Syst & Control Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing 100049 Peoples R China

This paper considers the identification problem of finite impulse response (FIR) systems with binary-valued observations under the assumption of fixed threshold and bounded persistently excitations. A recursive projection algorithm is constructed to estimate the unknown parameter. For first-order FIR systems, the convergence properties of the algorithm are analyzed theoretically. With mild conditions on the weight coefficients in the parameter update, the algorithm is proved to be convergent in mean square and the convergence rate can be the reciprocal of the number of observations, which has the same order as the optimal estimation when the system output is exactly known. Furthermore, it is also shown that the Cramer-Rao (CR) lower bound is achieved asymptotically with proper weight coefficients, which indicates that the algorithm is optimal in the sense of asymptotic efficiency. Some numerical examples are simulated to demonstrate the effectiveness of the proposed algorithm in both first-order and high-order FIR systems.

关键词： Finite impulse response filters Convergence Approximation algorithms Adaptive control projection algorithms Estimation Control systems Asymptotic efficiency binary-valued observations convergence Cramé r– Rao (CR) lower bound identification

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Imaging for a Forward Scanning Automotive Synthetic Aperture Radar

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2019年第3期55卷 1420-1434页

作者： Gishkori, Shahzad Daniel, Liam Gashinova, Marina Mulgrew, Bernard Univ Edinburgh Sch Engn Inst Digital Commun Edinburgh EH8 9YL Midlothian Scotland Univ Birmingham Microwave Integrated Syst Lab Sch Elect Elect & Syst Engn Birmingham B15 2TT W Midlands England

In this paper, we propose a forward scanning synthetic aperture radar methodology for a forward-looking automotive (low-terahertz) radar, which combines scene scanning with synthetic aperture processing, resulting in enhanced angular resolution and improved imaging. We propose two algorithms, first, a modified back-projection (BP) algorithm and, second, a compressed sensing-based BP algorithm. We suggest techniques to reduce computational complexity of the proposed algorithms. Results of simulation and real-data experiments corroborate the validity of our proposed methodology and algorithms.

关键词： Radar imaging Synthetic aperture radar Apertures Imaging Radar antennas projection algorithms

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On linear infeasibility arising in intensity-modulated radiation therapy inverse planning

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LINEAR ALGEBRA AND ITS APPLICATIONS 2008年第5-6期428卷 1406-1420页

作者： Censor, Yair Ben-Israel, Adi Xiao, Ying Galvin, James M. Univ Haifa Dept Math IL-31905 Haifa Israel State Univ New Jersey RUTCOR Piscataway NJ 08854 USA Thomas Jefferson Univ Hosp Dept Radiat Oncol Med Phys Div Philadelphia PA 19107 USA

Intensity-modulated radiation therapy (IMRT) gives rise to systems of linear inequalities, representing the effects of radiation on the irradiated body. These systems are often infeasible, in which case one settles for an approximate solution, such as an {alpha, beta}-relaxation, meaning that no more than alpha percent of the inequalities are violated by no more than beta percent. For real-world IMRT problems, there is a feasible {alpha, beta}-relaxation for sufficiently large alpha, beta > 0, however large values of these parameters may be unacceptable medically. The {alpha, beta}-relaxation problem is combinatorial, and for given values of the parameters can be solved exactly by mixed integer programming (MIP), but this may be impractical because of problem size, and the need for repeated solutions as the treatment progresses. As a practical alternative to the MIP approach we present a heuristic non-combinatorial method for finding an approximate relaxation. The method solves a linear program for each pair of values of the parameters {alpha, beta} and progresses through Successively increasing values until an acceptable solution is found, or is determined non-existent. The method is fast and reliable, since it consists of solving a sequence of linear programs. (C) 2007 Elsevier Inc. All rights reserved.

关键词： projection algorithms FEASIBILITY CANCER OPTIMIZATION IMRT inequalities intensity modulated radiation therapy linear programming Radiation Effects

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Adaptive Vector Control of an Induction Motor on the Basis of the Method of Recurrent Objective Inequalities

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AUTOMATION AND REMOTE CONTROL 2010年第9期71卷 1849-1863页

作者： Bondarko, V. A. St Petersburg State Univ St Petersburg Russia

The problem is considered for control of an electromagnetic moment of the induction motor with a squirrel-cage rotor without the measurement of its rotational speed. By means of the principle of vector control, this problem reduces to developing an adaptive observer of values of the vector of the rotor magnetic-flux linkage. The method of recurrent objective inequalities (ROIs) is used, which enables one to reduce adaptation problems to counting systems of inequalities relative to the vector of the parameters estimated. For the control problem under consideration, these inequalities prove to be nonconvex, which makes it impossible to use directly the projection algorithms developed in the framework of the method of ROIs. In this connection, the common method for the stepwise reduction of the dimension of the nonlinear portion of inequalities is suggested in this work. On condition that the processes of a closed system display a certain natural property of nondegeneracy, this method permits reducing nonconvex inequalities to convex ones and ensures the achievement of the control aim on completion of the transient processes.

关键词： Basis rotational speed induction motors squirrel-cage rotor projection algorithms inequalities transient processes

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NONORTHOGONAL SIGNAL REPRESENTATION BY GAUSSIANS AND GABOR FUNCTIONS

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-ANALOG AND DIGITAL SIGNAL PROCESSING 1995年第6期42卷 402-413页

作者： BENARIE, J RAO, KR Department of Electrical and Computer Engineering Illinois Institute of Technology Chicago IL USA Illinois Institute of Technology Chicago IL US Dept. of Electr. & Comput. Eng. Illinois Inst. of Technol. Chicago IL USA

This paper describes a novel approach for nonorthogonal representation of signals using Gaussians and an extension of this method for Gabor representation of signals, based on the equivalence of Gabor expansion to Gaussian expansion in the frequency domain. The Gaussian expansion scheme yields an efficient representation of signals for low number of bits per pixel and is better than the corresponding Discrete Cosine Transform (DCT) representation for very low bit rates, This advantage diminishes gracefully for higher bit rates where the residual approximation error signal to be represented is more random and less structured. It is proved in this paper that a finite number of Gaussians can theoretically approximate sinusoids in a bounded region with arbitrarily small error, and therefore any finite support L(2)(R) signal as well. Two methods for Gaussian representation of signals are outlined, The first, called the Max-Energy paradigm, involves successive extraction of the highest energy Gaussian that best ''fits'' the signal. The second is a parallel approach and uses an adaptive projection algorithm to first derive the Gaussian basis set to be used in parallel, and then optimizes the coefficients for minimum squared error.

关键词： Signal representations Gaussian processes Discrete cosine transforms Polynomials Frequency domain analysis Bit rate Approximation error Gaussian approximation projection algorithms Fourier transforms

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Stable and Robust Geometric Self-Calibration for Cone-Beam CT Using Mutual Information

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IEEE TRANSACTIONS ON NUCLEAR SCIENCE 2014年第1期61卷 202-217页

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

We present a novel geometric calibration method for cone beam computed tomography, which is based on an iterative multiresolution 2-D-3-D image registration framework. Our technique does not require a dedicated calibration phantom or any other specific markers inside the scanned object, so that the geometric parameters can be computed online from the acquired data itself. In contrast to existing registration-based calibration methods, our approach uses the mutual information for maximization of the similarity between the original and the reprojected projections. Furthermore, we incorporated a consistent volume update scheme into our algorithm that supports the registration to accurately retrieve the geometrical misalignment of the scanner. In addition to this, stochastic ray sampling in combination with forward and backprojection operators implemented on the graphics card make the overall runtime comparable to current registration-based approaches. However, we can reach as accurate results as the current phantom-based techniques. Our results will show that our algorithm converges stably to the correct solution, that it is robust against projection noise and that it is independent of the underlying system geometry. It can be applied to circular and to helical trajectories with arbitrary cone angles. Moreover, our studies on simulated and on real data demonstrate that our algorithm can deal with arbitrary imaging objects.

关键词： Calibration computed tomography image reconstruction image registration mutual information (MI) nondestructive testing projection algorithms reconstruction algorithms volume measurement X-ray tomography

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Divide and Concur and Difference-Map BP Decoders for LDPC Codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第2期57卷 786-802页

作者： Yedidia, Jonathan S. Wang, Yige Draper, Stark C. Mitsubishi Elect Res Labs Cambridge MA 02139 USA Univ Wisconsin Dept Elect & Comp Engn Madison WI 53706 USA

The "Divide and Concur" (DC) algorithm introduced by Gravel and Elser can be considered a competitor to the belief propagation (BP) algorithm, in that both algorithms can be applied to a wide variety of constraint satisfaction, optimization, and inference problems. We show that DC can be interpreted as a message-passing algorithm on a "normal" factor graph. The "difference-map" dynamics of the DC algorithm enables it to avoid "traps" which may be related to the "trapping sets" or "pseudo-codewords" that plague BP decoders of low-density parity check (LDPC) codes in the error-floor regime. We investigate two decoders for LDPC codes based on these ideas. The first decoder is based directly on DC, while the second decoder borrows the important "difference-map" concept from the DC algorithm and translates it into a BP-like decoder. We show that this "difference-map belief propagation" (DMBP) decoder has dramatically improved error-floor performance compared to standard BP decoders, while maintaining a similar computational complexity. We present simulation results for LDPC codes comparing DC and DMBP decoders with other decoders based on sum-product BP, linear programming, and mixed-integer linear programming. We also describe the close relation of the DMBP decoder to reweighted min-sum algorithms, including those recently proposed by Ruozzi and Tatikonda.

关键词： Belief propagation (BP) error floors graphical models iterative algorithms low-density parity check (LDPC) decoding projection algorithms reweighted max-product reweighted min-sum

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INVERSE HALF-TONING AND KERNEL ESTIMATION FOR ERROR DIFFUSION

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IEEE TRANSACTIONS ON IMAGE PROCESSING 1995年第4期4卷 486-498页

作者： WONG, PW Hewlett-Packard Co. Palo Alto CA.

Two different approaches in the inverse halftoning of error-diffused images are considered. The first approach uses linear filtering and statistical smoothing that reconstructs a gray-scale image from a given error-diffused image. The second approach can be viewed as a projection operation, where one assumes the error diffusion kernel is known, and finds a gray-scale image that will be halftoned into the same binary image. Two projection algorithms, viz., minimum mean square error (MMSE) projection and maximum a posteriori probability (MAP) projection, that differ on the way an inverse quantization step is performed, are developed, Among the filtering and the two projection algorithms, MAP projection provides the best performance for inverse halftoning. Using techniques from adaptive signal processing, we suggest a method for estimating the error diffusion kernel from the given halftone. This means that the projection algorithms can be applied in the inverse halftoning of any error-diffused image without requiring any a priori information on the error diffusion kernel, It is shown that the kernel estimation algorithm combined with MAP projection provide the same performance in inverse halftoning compared to the case where the error diffusion kernel is known.

关键词： Inverse Error diffusion linear filters projection algorithms map projections halftones grayscale images

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Multipath Suppression for Continuous Wave Radar via Slepian Sequences

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2020年第0期68卷 548-557页

作者： Day, Brian Evers, Aaron Hack, Daniel Matrix Res Dayton OH 45432 USA Radial Res & Dev Dayton OH 45432 USA

In continuous wave (CW) radar systems, multiple signal copies impinge the receiver simultaneously. Often, undesired multipath and direct-path copies are many times stronger than potential targets. When applying matched filter signal processing techniques, the undesired signal components can mask weaker targets and decrease performance of post-processing techniques, such as target indication or estimation. In this manuscript, we propose a method of rejecting multipath-scattered returns over a continuous region in range and Doppler. We explore the computational cost of this method and additionally propose an approximate method of rejection which leverages the well-known discrete prolate spheroidal sequences (DPSS) typically referred to as Slepian sequences to gain a computational advantage. Results are shown to decrease the effective noise floor when applying matched filtering techniques as well as increase target signal-to-interference-plus-noise ratio (SINR) outside of an undesired multipath region. Comparisons are shown to traditional CW multipath removal in terms of rejection performance and run-time.

关键词： Radar clutter projection algorithms least squares approximation RF signals

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An iterative algorithm for finding a nearest pair of points in two convex subsets of Rⁿ

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2000年第8-9期40卷 971-983页

作者： Llanas, B de Sevilla, MF Feliu, V ETSI Caminos Dpto Matemat & Informat Madrid 28040 Spain ETSI Ind Dpto Ingn Elect Real 13071 Spain

We present an algorithm for finding a nearest pair of points in two convex sets of Rn, and therefore, their distance. The algorithm is based on the fixed-point theory of nonexpansive operators on a Hilbert space. Its practical implementation requires a fast projection algorithm. We introduce such a procedure for convex polyhedra. This algorithm effects a local search in the faces using visibility as a guide for finding the global minimum. After studying the convergence of both algorithms, we detail computer experiments on polyhedra (projection and distance). In the case of distances, these experiments show a sublinear time complexity relative to the total number of vertices. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： polyhedra local search projection algorithms euclidean distance nonexpansive operators

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