Wavelet transform is being widely used in the field of information processing.One-dimension and two-dimension quantum wavelet transforms have been investigated as important tool algorithms.However,three-dimensional qu...Wavelet transform is being widely used in the field of information processing.One-dimension and two-dimension quantum wavelet transforms have been investigated as important tool algorithms.However,three-dimensional quantum wavelet transforms have not been reported.This paper proposes a multi-level three-dimensional quantum wavelet transform theory to implement the wavelet transform for quantum videos.Then,we construct the iterative formulas for the multi-level three-dimensional Haar and Daubechies D4 quantum wavelet transforms,respectively.Next,we design quantum circuits of the two wavelet transforms using iterative methods.Complexity analysis shows that the proposed wavelet transforms offer exponential speed-up over their classical counterparts.Finally,the proposed quantum wavelet transforms are selected to realize quantum video compression as a primary application.Simulation results reveal that the proposed wavelet transforms have better compression performance for quantum videos than two-dimension quantum wavelet transforms.展开更多
Quantum watermarking is a technique to embed specific information, usually the owner's identification,into quantum cover data such for copyright protection purposes. In this paper, a new scheme for quantum waterma...Quantum watermarking is a technique to embed specific information, usually the owner's identification,into quantum cover data such for copyright protection purposes. In this paper, a new scheme for quantum watermarking based on quantum wavelet transforms is proposed which includes scrambling, embedding and extracting procedures. The invisibility and robustness performances of the proposed watermarking method is confirmed by simulation technique.The invisibility of the scheme is examined by the peak-signal-to-noise ratio(PSNR) and the histogram calculation.Furthermore the robustness of the scheme is analyzed by the Bit Error Rate(BER) and the Correlation Two-Dimensional(Corr 2-D) calculation. The simulation results indicate that the proposed watermarking scheme indicate not only acceptable visual quality but also a good resistance against different types of attack.展开更多
A rotational parameter R_θ has been introduced to complex wavelet transform (CWT).The rotational CWT(RCWT) corresponds to a matrix element 〈ψ|U_2(θ;μ;k)|F〉 in the context of quantum mechanics,where U_2(θ;μ;k) ...A rotational parameter R_θ has been introduced to complex wavelet transform (CWT).The rotational CWT(RCWT) corresponds to a matrix element 〈ψ|U_2(θ;μ;k)|F〉 in the context of quantum mechanics,where U_2(θ;μ;k) is atwo-mode rotational displacing-squeezing operator in the 〈η| representation.Based on this,the Parseval theorem andthe inversion formula of RCWT have been proved.The concise proof not only manifestly shows the merit of Dirac'srepresentation theory but also leads to a new orthogonal property of complex mother wavelets in parameter space.展开更多
In this paper, we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation. This motivation can let the mother-wavelet-state its...In this paper, we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation. This motivation can let the mother-wavelet-state itself vary from ｜ψ〉 to Ftr, s ｜ψ〉, except for variation within the family of dilations and translations. The Parseval＇s equality, admissibility condition and inverse transform of this continuous Fresnel-wavelet combinatorial transform are analysed. By taking certain parameters and using the admissibility condition of this continuous Fresnel-wavelet combinatorial transform, we obtain some mother wavelets. A comparison between the newly found mother wavelets is presented.展开更多
基金supported by the Science and Technology Project of Guangxi(2020GXNSFDA238023)the National Natural Science Foundation of China(Grant No.61762012).
文摘Wavelet transform is being widely used in the field of information processing.One-dimension and two-dimension quantum wavelet transforms have been investigated as important tool algorithms.However,three-dimensional quantum wavelet transforms have not been reported.This paper proposes a multi-level three-dimensional quantum wavelet transform theory to implement the wavelet transform for quantum videos.Then,we construct the iterative formulas for the multi-level three-dimensional Haar and Daubechies D4 quantum wavelet transforms,respectively.Next,we design quantum circuits of the two wavelet transforms using iterative methods.Complexity analysis shows that the proposed wavelet transforms offer exponential speed-up over their classical counterparts.Finally,the proposed quantum wavelet transforms are selected to realize quantum video compression as a primary application.Simulation results reveal that the proposed wavelet transforms have better compression performance for quantum videos than two-dimension quantum wavelet transforms.
基金Supported by Kermanshah Branch,Islamic Azad University,Kermanshah,Iran
文摘Quantum watermarking is a technique to embed specific information, usually the owner's identification,into quantum cover data such for copyright protection purposes. In this paper, a new scheme for quantum watermarking based on quantum wavelet transforms is proposed which includes scrambling, embedding and extracting procedures. The invisibility and robustness performances of the proposed watermarking method is confirmed by simulation technique.The invisibility of the scheme is examined by the peak-signal-to-noise ratio(PSNR) and the histogram calculation.Furthermore the robustness of the scheme is analyzed by the Bit Error Rate(BER) and the Correlation Two-Dimensional(Corr 2-D) calculation. The simulation results indicate that the proposed watermarking scheme indicate not only acceptable visual quality but also a good resistance against different types of attack.
基金National Natural Science Foundation of China under Grant No.10647133the Research Foundation of the Education Department of Jiangxi Province under Grant No.[2007]22
文摘A rotational parameter R_θ has been introduced to complex wavelet transform (CWT).The rotational CWT(RCWT) corresponds to a matrix element 〈ψ|U_2(θ;μ;k)|F〉 in the context of quantum mechanics,where U_2(θ;μ;k) is atwo-mode rotational displacing-squeezing operator in the 〈η| representation.Based on this,the Parseval theorem andthe inversion formula of RCWT have been proved.The concise proof not only manifestly shows the merit of Dirac'srepresentation theory but also leads to a new orthogonal property of complex mother wavelets in parameter space.
基金supported by the Startup Research Fund for Introducing Talents of Anhui Polytechnic University (Grant No. 2009YQQ006)the Research Foundation of the Education Department of Anhui Province of China (Grant No. KJ2011B031)
文摘In this paper, we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation. This motivation can let the mother-wavelet-state itself vary from ｜ψ〉 to Ftr, s ｜ψ〉, except for variation within the family of dilations and translations. The Parseval＇s equality, admissibility condition and inverse transform of this continuous Fresnel-wavelet combinatorial transform are analysed. By taking certain parameters and using the admissibility condition of this continuous Fresnel-wavelet combinatorial transform, we obtain some mother wavelets. A comparison between the newly found mother wavelets is presented.
