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Minimization of the logarithmic function in sparse recovery

NEUROCOMPUTING 2021年 427卷 141-155页

作者： Wang, Changlong Zhou, Feng Ren, Kaiqiang Doctor, Shijie Ren Xidian Univ Minist Educ Key Lab Elect Informat Counter Measure & Simulat 2 South Taibai Rd Xian 710071 Shaanxi Peoples R China Xian Satellite Control Ctr State Key Lab Astronaut Dynam Xian 710043 Shaanxi Peoples R China

In sparse information recovery, the key issue is to solve the l(0)-minimization which is NP-hard. Therefore we consider the logarithmic alternative function to replace 0-norm. In this paper, theoretical analysis of logarithmic alternative model is given in detail. First, we discuss the equivalence between l(0) minimization and the logarithmic function minimization. It is proved that the solution of the alternative model also solves the l(0)-minimization in both noiseless and noisy cases. Second, the recovery condition of logarithmic minimization is presented. By this new condition and a new concept named Logarithms Null Space Constant (L-NSC), we demonstrate the advantages of this model over classical approaches. Third, we study the optimal properties of the alternative model including the analytic property of optimal solution, a fixed point iterative algorithm and the corresponding convergence conclusion. Finally, we use the logarithmic function and the proposed algorithm to solve the multi-source time difference of arrival (TDOA) location problem. Compared with classic approaches, the experimental results demonstrate the effectiveness of the proposed algorithm. (c) 2020 Elsevier B.V. All rights reserved.

关键词： L-0-minimization Sparse recovery Equivalence iterative algorithms

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Efficient Pencil Beam Synthesis in 4-D Antenna Arrays Using an iterative Convex Optimization Algorithm

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2019年第11期67卷 6847-6858页

作者： Yang, Feng Yang, Shiwen Chen, Yikai Qu, Shiwei Hu, Jun UESTC Sch Elect Sci & Engn Chengdu 611731 Sichuan Peoples R China

A novel iterative convex optimization algorithm is proposed for the efficient synthesis of 4-D antenna arrays in this paper. A general nonconvex programming problem in terms of pencil beam synthesis at the center frequency and the suppression of multiple sidebands with different time schemes is first established. In order to decrease the nonconvexity with respect to equivalent excitations, the nonconvex programming problem is then decomposed into a convex optimization problem at the center frequency and a simplified nonconvex optimization problem at sidebands. Based on the optimized results at the center frequency, an iterative convex optimization algorithm that consists in solving a sequence of convex optimization problems is adopted to solve the nonconvex optimization problem efficiently. Because of the introduction of iterative idea and convex optimization, the proposed method achieves a good tradeoff between the optimization time and the optimality of the solution for the synthesis of 4-D antenna arrays of various scales. Numerical examples of uniformly or nonuniformly spaced 4-D antenna arrays are presented to demonstrate the excellent performance of the proposed algorithm in comparison with those of the previously reported methods.

关键词： Antenna arrays Optimization Convex functions Amplitude modulation Switches iterative algorithms Array synthesis convex optimization 4-D antenna arrays iterative convex optimization

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Complex-Variable Weighted Least Modulus State Estimation

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IEEE TRANSACTIONS ON POWER SYSTEMS 2024年第4期39卷 6026-6035页

作者： Jabr, Rabih A. Amer Univ Beirut Dept Elect & Comp Engn Beirut 11072020 Lebanon

The use of the Weighted Least Absolute Value (WLAV) state estimator is especially advantageous in systems that utilize Phasor Measurement Units (PMUs). Although PMU measurements and the phasor state vector are complex-valued, traditional WLAV methods operate solely in the real domain. This paper introduces the Weighted Least Modulus (WLM) state estimator, which is the counterpart of the WLAV method in complex variables. The WLM state estimator exploits the coupling of real and imaginary measurement components for noise filtering and bad data elimination. The paper demonstrates that the WLM state estimator replaces the WLAV linear programs with conic programs. An efficient implementation in complex variables is also derived through the iteratively Reweighted Least Squares (IRLS) technique within the Wirtinger calculus framework. The WLM state estimator is tested on networks with up to 6495 nodes in PMU-only and hybrid measurement scenarios. The results were compared to the IRLS solution using real variables and a traditional linear programming formulation. They show that the IRLS-based WLM state estimator achieves a significant speedup compared to WLAV implementations and, at the same time, gives overall better estimation results.

关键词： Phasor measurement units State estimation Voltage measurement Power measurement Weight measurement Calculus Time measurement iterative algorithms L-1-norm least squares approximation optimization phasor measurement units (PMUs) power system analysis computing state estimation Wirtinger calculus

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Attenuation and scatter correction of list-mode data driven iterative and analytic image reconstruction algorithms for rotating 3D PET systems

Attenuation and scatter correction of list-mode data driven ...

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IEEE Symposium on Nuclear Science (NSS/MIC)

作者： A.J. Reader K. Erlandsson R.J. Ott M.A. Flowers Joint Department of Physics Institute of Cancer Research Royal Marsden NHS Foundation Trust Sutton Surrey UK

Image reconstruction directly from list-mode data requires different data correction techniques to standard projection-data based reconstruction, particularly in the case of iterative reconstruction. Attenuation and scatter correction techniques have been developed for two list-mode data driven reconstruction algorithms (FAIR-B (iterative) and Atrax (analytic/iterative)) recently proposed by the authors, and the results compared with two popular projection-data based algorithms (FORE+OSEM (iterative) and FORE+FBP (analytic)). List-mode data driven algorithms require event-by-event correction schemes, or alternatively image space procedures, as no direct operations to the completely sampled projection data set can be practically carried out. The methods developed in this work allow correction of list-mode data driven EM-ML type algorithms, such as FAIR, as well as analytic list-mode algorithms. The correction schemes have been applied to simulated data from various activity and attenuating medium distributions for a rotating 3D PET system. Both list-mode algorithms show improvements over the projection-data based methods in some situations.

关键词： Attenuation Scattering Image analysis Image reconstruction iterative algorithms iterative methods Positron emission tomography Reconstruction algorithms Algorithm design and analysis Bayesian methods

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iterative signal extrapolation algorithms with wavelets

Iterative signal extrapolation algorithms with wavelets

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IEEE International Symposium on Circuits and Systems (ISCAS)

作者： Li-Chien Lin C.-C.J. Kuo Department of Electrical Engineering Systems University of Southern California Los Angeles CA USA

A generalized Papoulis-Gerchberg (PG) algorithm for signal extrapolation based on the wavelet representation has been recently proposed by Xia, Kuo and Zhang. In this research, we first show that the generalized PG algorithm converges to the minimum norm solution when the wavelet bases are semi-orthogonal (or known as the prewavelet). However, the generalized PG algorithm converges slowly in numerical implementation. To accelerate the convergence rate, we formulate the discrete signal extrapolation problem os a two-step process and apply the steepest descent and conjugate gradient methods for its solution. Numerical experiments are given to illustrate the performance of the proposed algorithms.< >

关键词： Extrapolation iterative algorithms Frequency domain analysis Convergence Wavelet coefficients Acceleration Signal processing Gradient methods Signal reconstruction Time frequency analysis

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Comparative Study on iterative-Optimization-Based Image Registration algorithms

Comparative Study on Iterative-Optimization-Based Image Regi...

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Computer Science and Information Engineering, CSIE, WRI World Congress on FLAGGED

作者： N. Ye L.Y. Zhang H.T. Wang H. Zhang College of Mechanical and Electronic Engineering Nanjing University of Aeronautics and Astronautics Nanjing P.R. China

A detail comparative study is carried out on three representative iterative-optimization-based image registration methods, namely digital image correlation using Newton-Raphson iteration, iterative gray-gradient algorithm and least square image matching, which are originated and developed in the fields of optical experimental mechanics and stereo vision respectively. The mathematical consistency of the three algorithms is first demonstrated. Analysis and comparison of some further conclusions drawn from the three methods are then conducted. As the analysis and comparison show, these further conclusions can explain each other and can be mutually employed among the three methods. However, in view of algorithm implementation and extension, image correlation using Newton-Raphson iteration is more adaptable and flexible.

关键词： Image registration iterative algorithms Digital images iterative methods Least squares methods Optical films Pixel Image matching Stereo vision Computer science

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Discrete-time cellular neural networks for associative memories: a new design method via iterative learning and forgetting algorithms

Discrete-time cellular neural networks for associative memor...

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Midwest Symposium on Circuits and Systems (MWSCAS)

作者： M. Brucoli L. Carnimeo G. Grassi Dipartimento di Elettrotecnica ed Elettronica Politecnico di Bari Bari Italy

In this paper a synthesis procedure of discrete-time Cellular Neural Networks (DTCNN's) for associative memories with iterative learning and forgetting algorithms is developed, by which each pattern to be stored is learnt one at a time and each pattern to be forgotten is deleted one at a time. The proposed approach exploits the properties of pseudo inverse matrices and preserves the local connection feature of DTCNN's.

关键词： Cellular neural networks Design methodology iterative methods Associative memory iterative algorithms Network synthesis Vectors Sparse matrices Asymptotic stability Large-scale systems

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A FAST NEW ALGORITHM FOR TRAINING FEEDFORWARD NEURAL NETWORKS

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 1992年第1期40卷 202-210页

作者： SCALERO, RS TEPEDELENLIOGLU, N FLORIDA INST TECHNOL DEPT ELECT & COMP ENGNMELBOURNEFL 32901

A fast new algorithm is presented for training multilayer perceptrons as an alternative to the backpropagation algorithm. The number of iterations required by the new algorithm to converge is less than 20% of what is required by the backpropagation algorithm. Also, it is less affected by the choice of initial weights and setup parameters. The algorithm uses a modified form of the backpropagation algorithm to minimize the mean-squared error between the desired and actual outputs with respect to the inputs to the nonlinearities. This is in contrast to the standard algorithm which minimizes the mean-squared error with respect to the weights. Error signals, generated by the modified backpropagation algorithm, are used to estimate the inputs to the nonlinearities, which along with the input vectors to the respective nodes, are used to produce an updated set of weights through a system of linear equations at each node. These systems of linear equations are solved using a Kalman filter at each layer.

关键词： Neural networks Feedforward neural networks Backpropagation algorithms Signal generators Vectors iterative algorithms Linearity Error correction Nonlinear equations Speech

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iterative Algorithm Induced Deep-Unfolding Neural Networks: Precoding Design for Multiuser MIMO Systems

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2021年第2期20卷 1394-1410页

作者： Hu, Qiyu Cai, Yunlong Shi, Qingjiang Xu, Kaidi Yu, Guanding Ding, Zhi Zhejiang Univ Coll Informat Sci & Elect Engn Hangzhou 310027 Peoples R China Tongji Univ Sch Software Engn Shanghai 201804 Peoples R China Univ Calif Davis Dept Elect & Comp Engn Davis CA 95616 USA

Optimization theory assisted algorithms have received great attention for precoding design in multiuser multiple-input multiple-output (MU-MIMO) systems. Although the resultant optimization algorithms are able to provide excellent performance, they generally require considerable computational complexity, which gets in the way of their practical application in real-time systems. In this work, in order to address this issue, we first propose a framework for deep-unfolding, where a general form of iterative algorithm induced deep-unfolding neural network (IAIDNN) is developed in matrix form to better solve the problems in communication systems. Then, we implement the proposed deep-unfolding framework to solve the sum-rate maximization problem for precoding design in MU-MIMO systems. An efficient IAIDNN based on the structure of the classic weighted minimum mean-square error (WMMSE) iterative algorithm is developed. Specifically, the iterative WMMSE algorithm is unfolded into a layer-wise structure, where a number of trainable parameters are introduced to replace the high-complexity operations in the forward propagation. To train the network, a generalized chain rule of the IAIDNN is proposed to depict the recurrence relation of gradients between two adjacent layers in the back propagation. Moreover, we discuss the computational complexity and generalization ability of the proposed scheme. Simulation results show that the proposed IAIDNN efficiently achieves the performance of the iterative WMMSE algorithm with reduced computational complexity.

关键词： iterative algorithms Precoding Artificial neural networks Computational complexity Optimization Approximation algorithms Deep-unfolding neural network machine learning multiuser MIMO precoding design weighted MMSE

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Application of iterative Learning Genetic algorithms for PID Parameters Auto-Optimization of Missile controller

Application of Iterative Learning Genetic Algorithms for PID...

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World Congress on Intelligent Control and Automation (WCICA)

作者： Hu Yunan Bin Qu Department of Control Engineering Naval Aeronautical Engineering Academy Yantai Shandong China

Aiming at the problem of a great deal of blindly searching the proportional, differential, integral parameters in the process of designing PID controller, the new algorithm combining genetic algorithm with iterative learning algorithm is named as an iterative learning genetic algorithm (ILGA), which can be used to optimize three controller parameters, thus the optimal parameters can be achieved swiftly by virtue of less iterative learning times, and the design of the PID controller is simplified. As the simulation results shown, the effectiveness of the method is verified in optimizing the PID controller parameters

关键词： Genetic algorithms Three-term control Missiles Optimal control Pi control Proportional control Algorithm design and analysis iterative algorithms Process design Design optimization

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