New hybrid inertial CQ projection algorithms with line-search process for the split feasibility problem

In this paper, we propose two hybrid inertial CQ projection algorithms with linesearch process for the split feasibility problem. Based on the hybrid CQ projection algorithm, we firstly add the inertial term into the iteration to accelerate the convergence of the algorithm, and adopt flexible rules for selecting the stepsize and the shrinking projection region, which makes an optimal stepsize available at each iteration. The shrinking projection region is the intersection of three sets, which are the set C and two hyperplanes. Furthermore, we modify the Armijo-type line-search step in the presented algorithm to get a new algorithm.The algorithms are shown to be convergent under certain mild assumptions. Besides, numerical examples are given to show that the proposed algorithms have better performance than the general CQ algorithm.

Approximate subgradient projection algorithm for convex feasibility problem

An ε-subgradient projection algorithm for solving a convex feasibility problem is presented.Based on the iterative projection methods and the notion of ε-subgradient,a series of special projection hyperplanes is established.Moreover,compared with the existing projection hyperplanes methods with subgradient,the proposed hyperplanes are interactive with ε,and their ranges are more larger.The convergence of the proposed algorithm is given under some mild conditions,and the validity of the algorithm is proved by the numerical test.

Research and Implementation for License Plate Recognition Based on Improved Projection Algorithm

This paper analyzes and dissertates the discrete wavelet transform and improved projection algorithm in four kernel stages （image preprocessing, license plate localization, character segmentation, license plate recognition, i.e.） of license plate recognition system in detail. At last, it gives some conclusions and suggestions on future research.

Hybrid alternate projection algorithm and its application for practical conformal array pattern synthesis

Based on the fabricated 12-element cavity-backed microstrip sector cylinder array,a novel hybrid alternate projection algorithm（HAPA）,which combines analytical method with numerical techniques effectively,is proposed for synthesizing the pattern of practical conformal array.The algorithm applies the variable direction aperture projection method with mutual coupling correction techniques to provide the good initial excitations of elements to the enhanced alternate projection algorithm（EAPA）.In order to do further optimization,which improves the convergent speed of the algorithm significantly.Finally,the HAPA has been applied to the fabricated sector cylinder array with mutual coupling considered.The results of synthesized patterns,such as low sidelobe with null points formed pattern,beam scanning with low sidelobe pattern and the shaped beam pattern are presented.It demonstrates the validity of HAPA in practical conformal array synthesis.

Steady-state weights solution to affine projection algorithm

A new expression of the weights update equation for the affine projection algorithm （APA） is proposed that improves the convergence rate of an adaptive flter, particularly for highly colored input signals, and yields greater details of the internal structure. The steady-state weights solution to the APA algorithm is calculated in different step-sizes, which is significantly different from the iteration method. The weights error in steady-state is proved to be zero as the number of the input direction vector increases to infinity, ensuring that the estimated weights of the APA algorithm in steady-state are unbiased and consistent. The sensitivity of the step-size parameter for the steady-state weights is also analyzed. Simulation results show that the steady-state weights of the APA algorithm, obtained from the proposed method, are closer to the true weights than the estimated steady-state weights as determined by the traditional iteration method.

Non-monotonous Sequential Subgradient Projection Algorithm for Convex Feasibility Problem

The existing methods of projection for solving convex feasibility problem may lead to slow conver- gence when the sequences enter some narrow＂corridor＂ between two or more convex sets. In this paper, we apply a technique that may interrupt the monotonity of the constructed sequence to the sequential subgradient pro- jection algorithm to construct a nommonotonous sequential subgradient projection algorithm for solving convex feasibility problem, which can leave such corridor by taking a big step at different steps during the iteration. Under some suitable conditions, the convergence is proved.We also compare the numerical performance of the proposed algorithm with that of the monotonous algorithm by numerical experiments.

The continuous wavelet projections algorithm: A practical spectral-feature-mining approach for crop detection

Spectroscopy can be used for detecting crop characteristics. A goal of crop spectrum analysis is to extract effective features from spectral data for establishing a detection model. An ideal spectral feature set should have high sensitivity to target parameters but low information redundancy among features.However, feature-selection methods that satisfy both requirements are lacking. To address this issue,in this study, a novel method, the continuous wavelet projections algorithm(CWPA), was developed,which has advantages of both continuous wavelet analysis(CWA) and the successive projections algorithm(SPA) for generating optimal spectral feature set for crop detection. Three datasets collected for crop stress detection and retrieval of biochemical properties were used to validate the CWPA under both classification and regression scenarios. The CWPA generated a feature set with fewer features yet achieving accuracy comparable to or even higher than those of CWA and SPA. With only two to three features identified by CWPA, an overall accuracy of 98% in classifying tea plant stresses was achieved, and high coefficients of determination were obtained in retrieving corn leaf chlorophyll content(R^(2)= 0.8521)and equivalent water thickness(R^(2)= 0.9508). The mechanism of the CWPA ensures that the novel algorithm discovers the most sensitive features while retaining complementarity among features. Its ability to reduce the data dimension suggests its potential for crop monitoring and phenotyping with hyperspectral data.

BEAM BROADENING SYNTHESIS FOR SAR ANTENNA ARRAY BASED ON PROJECTION MATRIX ALGORITHM

A new beam broadening synthesis technique for Synthetic Aperture Radar(SAR) antenna array, namely Projection Matrix Algorithm(PMA) is presented. The theory of PMA is introduced firstly, and then the iterative renewed manner is improved to resolve the unbalance problem under amplitude and phase control. In order to validate the algorithm correct and effective, an actual engineering application example is investigated. The beam synthesis results of 1.0~4.5 times broadening under the phase only control and the amplitude and phase control using improved PMA are given. The results show that the beam directivity, the beam broadening, and the side-lobe level requirements were met. It is demonstrated that the improved PMA was effective and feasible for SAR application.

Fast motion estimation algorithm of video stabilization system

A real-time electronic image stabilization motion estimation method based on fast sub- block gray projection algorithm is proposed. In the method, each image is divided into a number of sub-blocks, and sub-blocks are sifted with their gray gradients. After removing sub-blocks whose gray gradients are lower than the given threshold, the calculation amount of projection is reduced and the motion estimation accuracy is improved. Then gray projection is done in each remained sub- block, and global motion vector of the image is calculated according to the local motion vectors of sub-blocks and the affine motion model. The drawbacks as the local motions reducing the global mo- tion estimation accuracy and traditional gray projection algorithm could not deal with rotation are re- solved well by this algorithm. The experiment results show that the algorithm is more accurate and efficient than the gray projection algorithm.

Dykstra’s Algorithm for the Optimal Approximate Symmetric Positive Semidefinite Solution of a Class of Matrix Equations

Dykstra’s alternating projection algorithm was proposed to treat the problem of finding the projection of a given point onto the intersection of some closed convex sets. In this paper, we first apply Dykstra’s alternating projection algorithm to compute the optimal approximate symmetric positive semidefinite solution of the matrix equations AXB = E, CXD = F. If we choose the initial iterative matrix X0 = 0, the least Frobenius norm symmetric positive semidefinite solution of these matrix equations is obtained. A numerical example shows that the new algorithm is feasible and effective.

New UWB imaging algorithm for multiple targets detection

Because the conventional ultra wideband（UWB） radar imaging algorithm cannot meet the demand in the capability of multiple targets detection,a novel UWB radar imaging algorithm based on the near field radiation theory of dipole is presented.On the foundation of researching the principle of a time domain imaging algorithm,the back projection（BP） algorithm is derived and analyzed.Firstly,the far field sampling data are transferred to the near field sampling data by using the near field radiation theory of dipole.Then the BP algorithm is applied to target detection.The capability of the new algorithm to detect the multi-target is verified by using the finite-difference time-domain method,and the threedimensional images of targets are obtained.The coupling effect between targets for imaging is analyzed.The simulation results show that the new UWB radar imaging algorithm based on the near field radiation theory of dipole could weaken the coupling effect for imaging,and as a result the quality of imaging is improved.

The study and application of PTR algorithm on recognizing various structure samples

In this paper,four pattern recognition methods are set forth.Based on plane projection of samples and analysis of typical samples along with the few pattern recognition methods,the PTR algorithm for recognizing various structure samples is proposed.Also two examples are given and these show the PTR algorithm is effective.

Bus frequency optimization in a large-scale multi-modal transportation system:integrating 3D-MFD and dynamic traffic assignment

A properly designed public transport system is expected to improve traffic efficiency.A high-frequency bus service would decrease the waiting time for passengers,but the interaction between buses and cars might result in more serious congestion.On the other hand,a low-frequency bus service would increase the waiting time for passengers and would not reduce the use of private cars.It is important to strike a balance between high and low frequencies in order to minimize the total delays for all road users.It is critical to formulate the impacts of bus frequency on congestion dynamics and mode choices.However,as far as the authors know,most proposed bus frequency optimization formulations are based on static demand and the Bureau of Public Roads function,and do not properly consider the congestion dynamics and their impacts on mode choices.To fill this gap,this paper proposes a bi-level optimization model.A three-dimensional Macroscopic Fundamental Diagram based modeling approach is developed to capture the bi-modal congestion dynamics.A variational inequality model for the user equilibrium in mode choices is presented and solved using a double projection algorithm.A surrogate model-based algorithm is used to solve the bi-level programming problem.

Low Complexity Adaptive Equalizers for Underwater Acoustic Communications

Interference signals due to scattering from surface and reflecting from bottom is one of the most important problems of reliable communications in shallow water channels. To solve this problem, one of the best suggested ways is to use adaptive equalizers. Convergence rate and misadjustment error in adaptive algorithms play important roles in adaptive equalizer performance. In this paper, affine projection algorithm （APA）, selective regressor APA（SR-APA）, family of selective partial update （SPU） algorithms, family of set-membership （SM） algorithms and selective partial update selective regressor APA （SPU-SR-APA） are compared with conventional algorithms such as the least mean square （LMS） in underwater acoustic communications. We apply experimental data from the Strait of Hormuz for demonstrating the efficiency of the proposed methods over shallow water channel. We observe that the values of the steady-state mean square error （MSE） of SR-APA, SPU-APA0 SPU-normalized least mean square （SPU-NLMS）, SPU-SR-APA0 SM-APA and SM-NLMS algorithms decrease in comparison with the LMS algorithm. Also these algorithms have better convergence rates than LMS type algorithm.

Model⁃Free Predictive Control for a Kind of High Order Nonlinear Systems

For a type of high⁃order discrete⁃time nonlinear systems(HDNS)whose system models are undefined,a model⁃free predictive control(MFPC)algorithm is proposed in this paper.At first,an estimation model is given by the improved projection algorithm to approach the controlled nonlinear system.Then,on the basis of the estimation model,a predictive controller is designed by solving the finite time domain rolling optimization quadratic function,and the controller’s explicit analytic solution is also obtained.Furthermore,the closed⁃loop system's stability can be ensured.Finally,the results of simulation reveal that the presented control strategy has a faster convergence speed as well as more stable dynamic property compared with the model⁃free sliding mode control(MFSC).

Application Test of Anti-Interference Electrical Method Instrument to Urban Geophysical Prospecting in Tongzhou, Beijing

With the rapid development of the city, it is necessary to obtain geological information within 500 meters. Electrical prospecting is not only low cost and simple operation, but also solves the problem of insufficient drilling density in a survey. However, due to the dense urban buildings and strong electromagnetic interference, it is difficult for traditional electrical instruments to obtain effective data. An anti-interference electrical method instrument is designed. In the application test of Tongzhou core area in Beijing, the resistivity sounding data collected by anti-interference electrical method instrument is stable and reliable;inversion results of sounding are basically consistent with borehole data;the known Zhangjiawan fault and Yaoxinzhuang fault are obvious;basement karst collapse area inferred is basically coincident with the historical collapse area. It is proved that the anti-interference electrical method instrument is effective and can be applied to the geological survey of underground space in other cities.

A novel NIRS modelling method with OPLS-SPA and MIX-PLS for timber evaluation

The identification of timber properties is important for safe application.Near Infrared Spectroscopy(NIRS)technology is widely-used because of its simplicity,efficiency,and positive environmental attributes.However,in its application,weak signals are extracted from complex,overlapping and changing information.This study focused on the stability of NIR modeling.The Orthogonal Partial Least Squares(OPLS)and Successive Projections Algorithm(SPA)eliminates noise and extracts effective spectra,and an ensemble learning method MIX-PLS,is applied to establish the model.The elastic modulus of timber is taken as an example,and 201 wood samples of three species,Xylosmacongesta(Lour.)Merr.,Acer pictum subsp.mono,and Betula pendula,samples were divided into three groups to investigate modelling performance.The results show that OPLS can preprocess the near-infrared spectroscopy information according to the target object in the face of the system error and reduce errors to minimum.SPA finally selects 13 spectral bands,simplifies the NIR spectral data and improves model accuracy.The Pearson's correlation coefficient of Calibration(Rc)and the Pearson's correlation coefficient of Prediction(Rp)of Mix Partial Least Squares(MIX-PLS)were 0.95 and 0.90,and Root Mean Square Error of Calibration(RMSEC)and Root Mean Square Error of Prediction(RMSEP)are 2.075 and 6.001,respectively,which shows the model has good generalization abilities.

Distributed projection subgradient algorithm for two-network zero-sum game with random sleep scheme

In this paper,a zero-sum game Nash equilibrium computation problem with a common constraint set is investigated under two time-varying multi-agent subnetworks,where the two subnetworks have opposite payoff function.A novel distributed projection subgradient algorithm with random sleep scheme is developed to reduce the calculation amount of agents in the process of computing Nash equilibrium.In our algorithm,each agent is determined by an independent identically distributed Bernoulli decision to compute the subgradient and perform the projection operation or to keep the previous consensus estimate,it effectively reduces the amount of computation and calculation time.Moreover,the traditional assumption of stepsize adopted in the existing methods is removed,and the stepsizes in our algorithm are randomized diminishing.Besides,we prove that all agents converge to Nash equilibrium with probability 1 by our algorithm.Finally,a simulation example verifies the validity of our algorithm.

Full-color and less-speckled modified Gerchberg–Saxton algorithm computer-generated hologram floating in a dual-parabolic projection system

This Letter proposes to apply full-color computer-generated holograms to the virtual image projection system so that the viewers can comfortably view floating images. Regarding the spatial division and distribution operation,a modified Gerchberg–Saxton algorithm is used for acquiring the phase infographics, which are input into the spatial light modulator for the reconstructed projection. Such a virtual image projection system could reach the vertical angle of view of 15°–75° and the horizontal angle of view 360°, and the mixed-light modulating proportion contains a 3 m W red light laser, a 2 m W green light laser, and a 2.6 m W blue light laser to achieve the full-color mixed-light proportion with a speckle contrast of 6.65%. The relative diffraction efficiency and root mean square error of the reconstructed image are 95.3% and 0.0524, respectively.

Iterative analytic extension in tomographic imaging

If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood.Trying to obtain such an exact Taylor expansion is difficult.This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions.Computer simulations show that the proposed algorithm converges very slowly,indicating that the problem is too ill-posed to be practically solvable using available methods.