The objective of this paper is to solve the timefractional Schr¨odinger and coupled Schr¨odinger differential equations(TFSE) with appropriate initial conditions by using the Haar wavelet approximation. For ...The objective of this paper is to solve the timefractional Schr¨odinger and coupled Schr¨odinger differential equations(TFSE) with appropriate initial conditions by using the Haar wavelet approximation. For the most part, this endeavor is made to enlarge the pertinence of the Haar wavelet method to solve a coupled system of time-fractional partial differential equations. As a general rule, piecewise constant approximation of a function at different resolutions is presentational characteristic of Haar wavelet method through which it converts the differential equation into the Sylvester equation that can be further simplified easily. Study of the TFSE is theoretical and experimental research and it also helps in the development of automation science,physics, and engineering as well. Illustratively, several test problems are discussed to draw an effective conclusion, supported by the graphical and tabulated results of included examples, to reveal the proficiency and adaptability of the method.展开更多
In this paper, a robust digital watermarking method against shearing based on Haar orthogonal function system was introduced. The proposed method adopted the complete generalized orthogonal properties of Haar ortbogon...In this paper, a robust digital watermarking method against shearing based on Haar orthogonal function system was introduced. The proposed method adopted the complete generalized orthogonal properties of Haar ortbogonal function system to achieve the piece-based orthogonal transform on the image. The significant middle frequency coefficients in the transformation matrix are picked up, based on characteristics of the image visual system and the Haar orthogonal transform. The watermark is adoptively weighed to the middle frequency matrix. The method improves the validity of watermarking and shows excellent advantage against shearing attack. Experimental results show that the Haar orthogonal function system based watermark approach can provide an excellent protection under geometric attacks.展开更多
The performance of OFDM systems may be degraded when intersymbol interference （ISI） channels have spectral nulls. Recently, the precoded OFDM was proposed to combat this problem. However, due to inserting （M- K） z...The performance of OFDM systems may be degraded when intersymbol interference （ISI） channels have spectral nulls. Recently, the precoded OFDM was proposed to combat this problem. However, due to inserting （M- K） zeros between each two sets of K consecutive information symbols, the average transmitting power of the precoded OFDM system reduces by 10log10（M/K） dB compared with the conventional OFDM system. Under the same points inverse fast Fourier transformation （IFFF）, the precoded OFDM system has a higher peak-to-average power ratio （PAPR） compared with the conventional OFDM system. This paper proposes a novel precoded BPSK-OFDM system based on Haar wavelet transformation. The Haar wavelet transformation operating decomposition over the vector information symbols produced by a precoder shows that half of the information symbols are zeros and the rest are either √2- or √2. Then, we have the peak power and PAPR reduced by 10log1002=3dB at most compared with the precoded OFDM system. Finally, we compare PAPR of the proposed OFDM system with the precoded OFDM and the conventional OFDM system.展开更多
Contactless verification is possible with iris biometric identification,which helps prevent infections like COVID-19 from spreading.Biometric systems have grown unsteady and dangerous as a result of spoofing assaults ...Contactless verification is possible with iris biometric identification,which helps prevent infections like COVID-19 from spreading.Biometric systems have grown unsteady and dangerous as a result of spoofing assaults employing contact lenses,replayed the video,and print attacks.The work demonstrates an iris liveness detection approach by utilizing fragmental coefficients of Haar transformed Iris images as signatures to prevent spoofing attacks for the very first time in the identification of iris liveness.Seven assorted feature creation ways are studied in the presented solutions,and these created features are explored for the training of eight distinct machine learning classifiers and ensembles.The predicted iris liveness identification variants are evaluated using recall,F-measure,precision,accuracy,APCER,BPCER,and ACER.Three standard datasets were used in the investigation.The main contribution of our study is achieving a good accuracy of 99.18%with a smaller feature vector.The fragmental coefficients of Haar transformed iris image of size 8∗8 utilizing random forest algorithm showed superior iris liveness detection with reduced featured vector size(64 features).Random forest gave 99.18%accuracy.Additionally,conduct an extensive experiment on cross datasets for detailed analysis.The results of our experiments showthat the iris biometric template is decreased in size tomake the proposed framework suitable for algorithmic verification in real-time environments and settings.展开更多
This paper proposes a method combining blue the Haar wavelet and the least square to solve the multi-dimensional stochastic Ito-Volterra integral equation.This approach is to transform stochastic integral equations in...This paper proposes a method combining blue the Haar wavelet and the least square to solve the multi-dimensional stochastic Ito-Volterra integral equation.This approach is to transform stochastic integral equations into a system of algebraic equations.Meanwhile,the error analysis is proven.Finally,the effectiveness of the approach is verified by two numerical examples.展开更多
文摘The objective of this paper is to solve the timefractional Schr¨odinger and coupled Schr¨odinger differential equations(TFSE) with appropriate initial conditions by using the Haar wavelet approximation. For the most part, this endeavor is made to enlarge the pertinence of the Haar wavelet method to solve a coupled system of time-fractional partial differential equations. As a general rule, piecewise constant approximation of a function at different resolutions is presentational characteristic of Haar wavelet method through which it converts the differential equation into the Sylvester equation that can be further simplified easily. Study of the TFSE is theoretical and experimental research and it also helps in the development of automation science,physics, and engineering as well. Illustratively, several test problems are discussed to draw an effective conclusion, supported by the graphical and tabulated results of included examples, to reveal the proficiency and adaptability of the method.
文摘In this paper, a robust digital watermarking method against shearing based on Haar orthogonal function system was introduced. The proposed method adopted the complete generalized orthogonal properties of Haar ortbogonal function system to achieve the piece-based orthogonal transform on the image. The significant middle frequency coefficients in the transformation matrix are picked up, based on characteristics of the image visual system and the Haar orthogonal transform. The watermark is adoptively weighed to the middle frequency matrix. The method improves the validity of watermarking and shows excellent advantage against shearing attack. Experimental results show that the Haar orthogonal function system based watermark approach can provide an excellent protection under geometric attacks.
文摘The performance of OFDM systems may be degraded when intersymbol interference （ISI） channels have spectral nulls. Recently, the precoded OFDM was proposed to combat this problem. However, due to inserting （M- K） zeros between each two sets of K consecutive information symbols, the average transmitting power of the precoded OFDM system reduces by 10log10（M/K） dB compared with the conventional OFDM system. Under the same points inverse fast Fourier transformation （IFFF）, the precoded OFDM system has a higher peak-to-average power ratio （PAPR） compared with the conventional OFDM system. This paper proposes a novel precoded BPSK-OFDM system based on Haar wavelet transformation. The Haar wavelet transformation operating decomposition over the vector information symbols produced by a precoder shows that half of the information symbols are zeros and the rest are either √2- or √2. Then, we have the peak power and PAPR reduced by 10log1002=3dB at most compared with the precoded OFDM system. Finally, we compare PAPR of the proposed OFDM system with the precoded OFDM and the conventional OFDM system.
基金supported by theResearchers Supporting Project No.RSP-2021/14,King Saud University,Riyadh,Saudi Arabia.
文摘Contactless verification is possible with iris biometric identification,which helps prevent infections like COVID-19 from spreading.Biometric systems have grown unsteady and dangerous as a result of spoofing assaults employing contact lenses,replayed the video,and print attacks.The work demonstrates an iris liveness detection approach by utilizing fragmental coefficients of Haar transformed Iris images as signatures to prevent spoofing attacks for the very first time in the identification of iris liveness.Seven assorted feature creation ways are studied in the presented solutions,and these created features are explored for the training of eight distinct machine learning classifiers and ensembles.The predicted iris liveness identification variants are evaluated using recall,F-measure,precision,accuracy,APCER,BPCER,and ACER.Three standard datasets were used in the investigation.The main contribution of our study is achieving a good accuracy of 99.18%with a smaller feature vector.The fragmental coefficients of Haar transformed iris image of size 8∗8 utilizing random forest algorithm showed superior iris liveness detection with reduced featured vector size(64 features).Random forest gave 99.18%accuracy.Additionally,conduct an extensive experiment on cross datasets for detailed analysis.The results of our experiments showthat the iris biometric template is decreased in size tomake the proposed framework suitable for algorithmic verification in real-time environments and settings.
基金Supported by the NSF of Hubei Province(2022CFD042)。
文摘This paper proposes a method combining blue the Haar wavelet and the least square to solve the multi-dimensional stochastic Ito-Volterra integral equation.This approach is to transform stochastic integral equations into a system of algebraic equations.Meanwhile,the error analysis is proven.Finally,the effectiveness of the approach is verified by two numerical examples.
