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.

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.

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.

A SVD-based ensemble projection algorithm for calculating the conditional nonlinear optimal perturbation

Conditional nonlinear optimal perturbation(CNOP) is an extension of the linear singular vector technique in the nonlinear regime.It represents the initial perturbation that is subjected to a given physical constraint,and results in the largest nonlinear evolution at the prediction time.CNOP-type errors play an important role in the predictability of weather and climate.Generally,when calculating CNOP in a complicated numerical model,we need the gradient of the objective function with respect to the initial perturbations to provide the descent direction for searching the phase space.The adjoint technique is widely used to calculate the gradient of the objective function.However,it is difficult and cumbersome to construct the adjoint model of a complicated numerical model,which imposes a limitation on the application of CNOP.Based on previous research,this study proposes a new ensemble projection algorithm based on singular vector decomposition(SVD).The new algorithm avoids the localization procedure of previous ensemble projection algorithms,and overcomes the uncertainty caused by choosing the localization radius empirically.The new algorithm is applied to calculate the CNOP in an intermediate forecasting model.The results show that the CNOP obtained by the new ensemble-based algorithm can effectively approximate that calculated by the adjoint algorithm,and retains the general spatial characteristics of the latter.Hence,the new SVD-based ensemble projection algorithm proposed in this study is an effective method of approximating the CNOP.

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.

Fast Affine Projection Algorithm for Adaptive Noise Canceling and Its Application on the Fetal Electrocardiogram Extraction

Aimed at the problem of adaptive noise canceling(ANC),three implementary algorithms which are least mean square(LMS) algorithm,recursive least square(RLS) algorithm and fast affine projection(FAP) algorithm,have been researched.The simulations were made for the performance of these algorithms.The extraction of fetal electrocardiogram(FECG) is applied to compare the application effect of the above algorithms.The proposed FAP algorithm has obvious advantages in computational complexity,convergence speed and steadystate error.

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.

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

Improving numerical forecasting skill in the atmospheric and oceanic sciences by solving optimization problems is an important issue. One such method is to compute the conditional nonlinear optimal perturbation(CNOP), which has been applied widely in predictability studies. In this study, the Differential Evolution(DE) algorithm, which is a derivative-free algorithm and has been applied to obtain CNOPs for exploring the uncertainty of terrestrial ecosystem processes, was employed to obtain the CNOPs for finite-dimensional optimization problems with ball constraint conditions using Burgers' equation. The aim was first to test if the CNOP calculated by the DE algorithm is similar to that computed by traditional optimization algorithms, such as the Spectral Projected Gradient(SPG2) algorithm. The second motive was to supply a possible route through which the CNOP approach can be applied in predictability studies in the atmospheric and oceanic sciences without obtaining a model adjoint system, or for optimization problems with non-differentiable cost functions. A projection skill was first explanted to the DE algorithm to calculate the CNOPs. To validate the algorithm, the SPG2 algorithm was also applied to obtain the CNOPs for the same optimization problems. The results showed that the CNOPs obtained by the DE algorithm were nearly the same as those obtained by the SPG2 algorithm in terms of their spatial distributions and nonlinear evolutions. The implication is that the DE algorithm could be employed to calculate the optimal values of optimization problems, especially for non-differentiable and nonlinear optimization problems associated with the atmospheric and oceanic sciences.

NEW ALGORITHM FOR FIR FILTER DESIGN WITH DISCRETE COEFFICIENTS

This paper develops a new algorithm based on the Projected Gradient Algorithm (PGA) for the design of FIR digital filters with "sum of power of two" coefficients. It is shown that the integer programming involved in the FIR filter design can be solved by this algorithm. It is compared with the reported method for a SemiDefinite Programming (SDP) relaxation- based design. The simulations demonstrate that the new algorithm often yields the similar error performances of the FIR filter design, but the average CPU time of this approach is significantly reduced.

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.

Research of Large Field of View Scan Mode for Industrial CT

For industrial computed tomography systems, generation II scan mode has a large field of view but time consuming and generation III has a small field of view but fast. In order to realize the rapid ICT test of large objects, a scan mode based on generation III called large field of view scan was discussed and its reconstruction algorithm based on FBP was deduced. The validity of the algorithm was verified by the results of computer simulation and experiments. Analysis showed that the effective scan field of view could be improved by more than 90% compared with that of generation III.

A multi-objective model for cordon-based congestion pricing schemes with nonlinear distance tolls

Congestion pricing is an important component of urban intelligent transport system.The efficiency,equity and the environmental impacts associated with road pricing schemes are key issues that should be considered before such schemes are implemented.This paper focuses on the cordon-based pricing with distance tolls,where the tolls are determined by a nonlinear function of a vehicles' travel distance within a cordon,termed as toll charge function.The optimal tolls can give rise to:1) higher total social benefits,2) better levels of equity,and 3) reduced environmental impacts(e.g.,less emission).Firstly,a deterministic equilibrium(DUE) model with elastic demand is presented to evaluate any given toll charge function.The distance tolls are non-additive,thus a modified path-based gradient projection algorithm is developed to solve the DUE model.Then,to quantitatively measure the equity level of each toll charge function,the Gini coefficient is adopted to measure the equity level of the flows in the entire transport network based on equilibrium flows.The total emission level is used to reflect the impacts of distance tolls on the environment.With these two indexes/measurements for the efficiency,equity and environmental issues as well as the DUE model,a multi-objective bi-level programming model is then developed to determine optimal distance tolls.The multi-objective model is converted to a single level model using the goal programming.A genetic algorithm(GA) is adopted to determine solutions.Finally,a numerical example is presented to verify the methodology.

ROBUST ACOUSTIC SOURCE LOCALIZATION FOR DIGITAL HEARING AIDS IN NOISE AND REVERBERANT ENVIRONMENT

A new method in digital hearing aids to adaptively localize the speech source in noise and reverberant environment is proposed. Based on the room reverberant model and the multichannel adaptive eigenvalue decomposition （MCAED） algorithm, the proposed method can iteratively estimate impulse response coefficients between the speech source and microphones by the adaptive subgradient projection method. Then, it acquires the time delays of microphone pairs, and calculates the source position by the geometric method. Compared with the traditional normal least mean square （NLMS） algorithm, the adaptive subgradient projection method achieves faster and more accurate convergence in a low signal-to-noise ratio （SNR） environment. Simulations for glasses digital hearing aids with four-component square array demonstrate the robust performance of the proposed method.

A NOVEL DIRECTION OF ARRIVAL ESTIMATOR

A Direction Of Arrival(DOA) estimator based on the signal separation principle is introduced, and one of representative multidimensional estimators is established by introducing Matrix Operator projection signal steering Vector Excision(MOVE) operation. Thanks to Alternating Separation (AS) technique, the multidimensional problem is transformed into a series of one-dimensional optimal ones. Furthermore, an equivalent simplified implementation of the AS is obtained. Finally the definiteness and uniqueness of the estimator are analyzed.

Nonparametric VSS-APA based on precise background noise power estimate

The adaptive algorithm used for echo cancellation(EC) system needs to provide 1) low misadjustment and 2) high convergence rate. The affine projection algorithm(APA) is a better alternative than normalized least mean square(NLMS) algorithm in EC applications where the input signal is highly correlated. Since the APA with a constant step-size has to make compromise between the performance criteria 1) and 2), a variable step-size APA(VSS-APA) provides a more reliable solution. A nonparametric VSS-APA(NPVSS-APA) is proposed by recovering the background noise within the error signal instead of cancelling the a posteriori errors. The most problematic term of its variable step-size formula is the value of background noise power(BNP). The power difference between the desired signal and output signal, which equals the power of error signal statistically, has been considered the BNP estimate in a rough manner. Considering that the error signal consists of background noise and misalignment noise, a precise BNP estimate is achieved by multiplying the rough estimate with a corrective factor. After the analysis on the power ratio of misalignment noise to background noise of APA, the corrective factor is formulated depending on the projection order and the latest value of variable step-size. The new algorithm which does not require any a priori knowledge of EC environment has the advantage of easier controllability in practical application. The simulation results in the EC context indicate the accuracy of the proposed BNP estimate and the more effective behavior of the proposed algorithm compared with other versions of APA class.