Two novel spline adaptive filtering(SAF)algorithms are proposed by combining different iterative gradient methods,i.e.,Adagrad and RMSProp,named SAF-Adagrad and SAF-RMSProp,in this paper.Detailed convergence performan...Two novel spline adaptive filtering(SAF)algorithms are proposed by combining different iterative gradient methods,i.e.,Adagrad and RMSProp,named SAF-Adagrad and SAF-RMSProp,in this paper.Detailed convergence performance and computational complexity analyses are carried out also.Furthermore,compared with existing SAF algorithms,the influence of step-size and noise types on SAF algorithms are explored for nonlinear system identification under artificial datasets.Numerical results show that the SAF-Adagrad and SAFRMSProp algorithms have better convergence performance than some existing SAF algorithms(i.e.,SAF-SGD,SAF-ARC-MMSGD,and SAF-LHC-MNAG).The analysis results of various measured real datasets also verify this conclusion.Overall,the effectiveness of SAF-Adagrad and SAF-RMSProp are confirmed for the accurate identification of nonlinear systems.展开更多
A spline filter is used to extract roughness profiles for the measurement of surface texture and is useful when sufficient sections before and after a primary profile could not be secured.This is because a spline filt...A spline filter is used to extract roughness profiles for the measurement of surface texture and is useful when sufficient sections before and after a primary profile could not be secured.This is because a spline filter could prevent the end effect,which is the fluctuation of output data that occurs around both ends of the primary profile and depends on the width of the weighting function of a filter.The spline filter is based on the calculation of an inverse matrix instead of the convolution of the weighting function of the filters.When input data include outliers,the output of a spline filter greatly fluctuates.To solve this problem,we propose a robust spline filter.However,output of the robust spline is not in agreement with that of the spline filter when input data do not include outliers.Thus,the robust spline filter has no lower compatibility.In this paper,the"Fast M-estimation Spline Filter(FMSF)"is proposed.FMSF uses the fast M-estimation method.FMGF performs robust to input data including outliers,and gives the same output as that of general spline filters to input data without outliers.The value estimated by this method is in agreement with that estimated by the least squares method if no outlier exists.In order to apply the fast M-estimation method to the spline filter,convolution of weight function is used instead of the inverse matrix.And the input geometry with shear and point-symmetric extensions is pre-processed to prevent the end effect.展开更多
Currently, the approximation methods of the Gaussian filter by some other spline filters have been developed. However, thesc methods are only suitable for the study of one-dimensional filtering, when these methods are...Currently, the approximation methods of the Gaussian filter by some other spline filters have been developed. However, thesc methods are only suitable for the study of one-dimensional filtering, when these methods are used for three-dimensional filtering, it is found that a rounding error and quantization error would be passed to the next in every part. In this paper, a new and high-precision implementation approach for Gaussian filter is described, which is suitable for three-dimensional reference filtering. Based on the theory of generalized B-spline function and the variational principle, the transmission characteristics of a digital filter can be changed through the sensitivity of the parameters （t1, t2）, and which can also reduce the rounding error and quantization error by the filter in a parallel form instead of the cascade form, Finally, the approximation filter of Gaussian filter is obtained. In order to verify the feasibility of the new algorithm, the reference extraction of the conventional methods are also used and compared. The experiments are conducted on the measured optical surface, and the results show that the total calculation by the new algorithm only requires 0.07 s for 480×480 data points; the amplitude deviation between the reference of the parallel form filter and the Gaussian filter is smaller; the new method is closer to the characteristic of the Gaussian filter through the analysis of three-dimensional roughness parameters, comparing with the cascade generalized B-spline approximating Gaussian. So the new algorithm is also efficient and accurate for the implementation of Gaussian filter in the application of surface roughness measurement.展开更多
According to the B-spline convolution mask, first, the contrast sensitiveness （CS） is computed and then is viewed as a noise sensitiveness coeficient （NSC） to adaptively determine a noise-recognized threshold valu...According to the B-spline convolution mask, first, the contrast sensitiveness （CS） is computed and then is viewed as a noise sensitiveness coeficient （NSC） to adaptively determine a noise-recognized threshold value. Based on the noise density function （NDF） in a 3×3 window, the filtering window size is adaptively adjusted, and then a median filter is used to eliminate the noise-marked pixels. The experiment results show that the proposed algorithm can preserve image detail information well and effectively remove the noises, particularly the impulse noises that is also called salt-and-pepper noises superimposed on the computed tomography （CT） and magnetic resonance imaging （MRI） medical images.展开更多
基金supported by the National Natural Science Foundation of China(61871420)the Natural Science Foundation of Sichuan Province,China(23NSFSC2916)the introduction of talent,Southwest MinZu University,China,funding research projects start(RQD2021064).
文摘Two novel spline adaptive filtering(SAF)algorithms are proposed by combining different iterative gradient methods,i.e.,Adagrad and RMSProp,named SAF-Adagrad and SAF-RMSProp,in this paper.Detailed convergence performance and computational complexity analyses are carried out also.Furthermore,compared with existing SAF algorithms,the influence of step-size and noise types on SAF algorithms are explored for nonlinear system identification under artificial datasets.Numerical results show that the SAF-Adagrad and SAFRMSProp algorithms have better convergence performance than some existing SAF algorithms(i.e.,SAF-SGD,SAF-ARC-MMSGD,and SAF-LHC-MNAG).The analysis results of various measured real datasets also verify this conclusion.Overall,the effectiveness of SAF-Adagrad and SAF-RMSProp are confirmed for the accurate identification of nonlinear systems.
基金This study is supported by a Grant-in-Aid for Scientific Research No.20K04202 from Japan Society for the Promotion of Science(JSPS).We would like to thank Editage(www.editage.com)for English language editing.
文摘A spline filter is used to extract roughness profiles for the measurement of surface texture and is useful when sufficient sections before and after a primary profile could not be secured.This is because a spline filter could prevent the end effect,which is the fluctuation of output data that occurs around both ends of the primary profile and depends on the width of the weighting function of a filter.The spline filter is based on the calculation of an inverse matrix instead of the convolution of the weighting function of the filters.When input data include outliers,the output of a spline filter greatly fluctuates.To solve this problem,we propose a robust spline filter.However,output of the robust spline is not in agreement with that of the spline filter when input data do not include outliers.Thus,the robust spline filter has no lower compatibility.In this paper,the"Fast M-estimation Spline Filter(FMSF)"is proposed.FMSF uses the fast M-estimation method.FMGF performs robust to input data including outliers,and gives the same output as that of general spline filters to input data without outliers.The value estimated by this method is in agreement with that estimated by the least squares method if no outlier exists.In order to apply the fast M-estimation method to the spline filter,convolution of weight function is used instead of the inverse matrix.And the input geometry with shear and point-symmetric extensions is pre-processed to prevent the end effect.
基金Supported by National Natural Science Foundation of China(Grant Nos51175085,51375094)Fujian Provincial Education Department Foundation of China(Grant No.JA13059)+1 种基金Open Fund of State Key Laboratory of Tribology of Tsinghua University,China(Grant No.SKLTKF13B02)Fuzhou Science and Technology plan Fund of China(Grant No.2014-G-74)
文摘Currently, the approximation methods of the Gaussian filter by some other spline filters have been developed. However, thesc methods are only suitable for the study of one-dimensional filtering, when these methods are used for three-dimensional filtering, it is found that a rounding error and quantization error would be passed to the next in every part. In this paper, a new and high-precision implementation approach for Gaussian filter is described, which is suitable for three-dimensional reference filtering. Based on the theory of generalized B-spline function and the variational principle, the transmission characteristics of a digital filter can be changed through the sensitivity of the parameters （t1, t2）, and which can also reduce the rounding error and quantization error by the filter in a parallel form instead of the cascade form, Finally, the approximation filter of Gaussian filter is obtained. In order to verify the feasibility of the new algorithm, the reference extraction of the conventional methods are also used and compared. The experiments are conducted on the measured optical surface, and the results show that the total calculation by the new algorithm only requires 0.07 s for 480×480 data points; the amplitude deviation between the reference of the parallel form filter and the Gaussian filter is smaller; the new method is closer to the characteristic of the Gaussian filter through the analysis of three-dimensional roughness parameters, comparing with the cascade generalized B-spline approximating Gaussian. So the new algorithm is also efficient and accurate for the implementation of Gaussian filter in the application of surface roughness measurement.
基金supported by Foundation of 11th Five-year Plan for Key Construction Academic Subject (Optics) of Hunan Province,PRC, Outstanding Young Scientific Research Fund of Hunan Provincial Education Department, PRC (No. 09B071)Scientific Research Fund of Hunan Provincial Education Department, PRC(No. 06C581)
文摘According to the B-spline convolution mask, first, the contrast sensitiveness （CS） is computed and then is viewed as a noise sensitiveness coeficient （NSC） to adaptively determine a noise-recognized threshold value. Based on the noise density function （NDF） in a 3×3 window, the filtering window size is adaptively adjusted, and then a median filter is used to eliminate the noise-marked pixels. The experiment results show that the proposed algorithm can preserve image detail information well and effectively remove the noises, particularly the impulse noises that is also called salt-and-pepper noises superimposed on the computed tomography （CT） and magnetic resonance imaging （MRI） medical images.
