Recently, a two-dimensional (2-D) Tsallis entropy thresholding method has been proposed as a new method for image segmentation. But the computation complexity of 2-D Tsallis entropy is very large and becomes an obst...Recently, a two-dimensional (2-D) Tsallis entropy thresholding method has been proposed as a new method for image segmentation. But the computation complexity of 2-D Tsallis entropy is very large and becomes an obstacle to real time image processing systems. A fast recursive algorithm for 2-D Tsallis entropy thresholding is proposed. The key variables involved in calculating 2-D Tsallis entropy are written in recursive form. Thus, many repeating calculations are avoided and the computation complexity reduces to O(L2) from O(L4). The effectiveness of the proposed algorithm is illustrated by experimental results.展开更多
Nonextensive statistical mechanics as in Tsallis formalism was used in this study, along with the dynamical Hamiltonian rod-like DNA model and the maximum entropy criteria for Tsallis’ entropy, so as to obtain length...Nonextensive statistical mechanics as in Tsallis formalism was used in this study, along with the dynamical Hamiltonian rod-like DNA model and the maximum entropy criteria for Tsallis’ entropy, so as to obtain length distribution of plasmid fragments, after irradiation with very high doses, assuming that the system reaches metaequilibrium. By intensively working out the Grand Canonical Ensemble (used to take into account the variation of the number of base pairs) a simplified expression for Fragment Size Distribution Function (FSDF) was obtained. This expression is dependent on two parameters only, the Tsallis q value and the minimal length of the fragments. Results obtained from fittings to available experimental data were adequate and the characteristic behavior of the shortest fragments was clearly documented and reproduced by the model, a circumstance never verified from theoretical distributions. The results point to the existence of an entropy which characterizes fragmentation processes and depending only on the q entropic index.展开更多
In this paper, we present a new technique for mammogram enhancement using fast dyadic wavelet transform (FDyWT) based on lifted spline dyadic wavelets and normalized Tsallis entropy. First, a mammogram image is deco...In this paper, we present a new technique for mammogram enhancement using fast dyadic wavelet transform (FDyWT) based on lifted spline dyadic wavelets and normalized Tsallis entropy. First, a mammogram image is decom- posed into a multiscale hierarchy of low-subband and high-subband images using FDyWT. Then noise is suppressed using normalized Tsallis entropy of the local variance of the modulus of oriented high-subband images. After that, the wavelet coefficients of high-subbands are modified using a non-linear operator and finally the low-subband image at the first scale is modified with power law transformation to suppress background. Though FDyWT is shift-invariant and has better poten- tial for detecting singularities like edges, its performance depends on the choice of dyadic wavclcts. On the other hand, the nulnber of vanishing moments is an important characteristic of dyadic wavelets for singularity analysis because it provides an upper bound measurement for singularity characterization. Using lifting dyadic schemes, we construct lifted spline dyadic wavelets of different degrees with increased number of vanishing moments. We also examine the effect of these wavelets on mammogram enhancement. The method is tested on mammogram images, taken from MIAS (Mammographic Image Analysis Society) database, having various background tissue types and containing different abnormalities. The comparison with tile state-of-the-art contrast enhancement methods reveals that the proposed method performs better and the difference is statistically significant.展开更多
The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The e...The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The existing two-dimensional Tsallis cross entropy method is not the strict two-dimensional extension. Thus two new methods of image thresholding using two-dimensional Tsallis cross entropy based on either Chaotic Particle Swarm Optimization (CPSO) or decomposition are proposed. The former uses CPSO to find the optimal threshold. The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure. The computing speed is improved greatly. The latter converts the two-dimensional computation into two one-dimensional spaces, which makes the computational complexity further reduced from O(L2) to O(L). The experimental results show that, compared with the proposed recently two-dimensional Shannon or Tsallis cross entropy method, the two new methods can achieve superior segmentation results and reduce running time greatly.展开更多
Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing.By generalizing the resource theory of coherence from von Neumann measurements to positive o...Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing.By generalizing the resource theory of coherence from von Neumann measurements to positive operatorvalued measures(POVMs),POVM-based coherence measures have been proposed with respect to the relative entropy of coherence,the l_(1) norm of coherence,the robustness of coherence and the Tsallis relative entropy of coherence.We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state in terms of the POVM-based coherence of the states in superposition.Our results can be used to estimate range of quantum coherence of superposed states.Detailed examples are presented to verify our analytical bounds.展开更多
Quantum coherence plays a central role in Grover’s search algorithm.We study the Tsallis relative a entropy of coherence dynamics of the evolved state in Grover’s search algorithm.We prove that the Tsallis relative ...Quantum coherence plays a central role in Grover’s search algorithm.We study the Tsallis relative a entropy of coherence dynamics of the evolved state in Grover’s search algorithm.We prove that the Tsallis relative a entropy of coherence decreases with the increase of the success probability,and derive the complementarity relations between the coherence and the success probability.We show that the operator coherence of the first H■relies on the size of the database N,the success probability and the target states.Moreover,we illustrate the relationships between coherence and entanglement of the superposition state of targets,as well as the production and deletion of coherence in Grover iterations.展开更多
In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums...In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums of coherence are obtained.However,the above results cannot be verified directly for any α∈(0,1/2).Hence,we only consider the special case of α=1/n+1,where n is a positive integer,and we obtain the upper and lower bounds.By comparing the upper and lower bounds,we find that the upper bound is equal to the lower bound for the special α=1/2,and the differences between the upper and the lower bounds will increase as α increases.Furthermore,we discuss the tendency of the sum of coherence,and find that it has the same tendency with respect to the different θ or φ,which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.展开更多
In this paper, we investigate the cohering and decohering power of the one-qubit Markovian channels with respect to coherence measures based on the l1-norm, the R′enyi α-relative entropy and the Tsallis α-relative ...In this paper, we investigate the cohering and decohering power of the one-qubit Markovian channels with respect to coherence measures based on the l1-norm, the R′enyi α-relative entropy and the Tsallis α-relative entropy of coherence, respectively. The amplitude damping channel, phase damping channel, depolarizing channel, and flip channels are analytically calculated. It shows that the decohering power of the amplitude damping channel on the x, y, and z basis is equal to each other. The same phenomenon can be seen for the phase damping channel and the flip channels.The cohering power for the phase damping channel and the flip channels on the x, y basis also equals to that on the z basis. However, the cohering and decohering power of the depolarizing channel is independent to the reference basises.And the cohering power of the amplitude damping channel on the x, y basis is different to that on the z basis.展开更多
基金supported by the National Natural Science Foundation of China for Distinguished Young Scholars(60525303)Doctoral Foundation of Yanshan University(B243).
文摘Recently, a two-dimensional (2-D) Tsallis entropy thresholding method has been proposed as a new method for image segmentation. But the computation complexity of 2-D Tsallis entropy is very large and becomes an obstacle to real time image processing systems. A fast recursive algorithm for 2-D Tsallis entropy thresholding is proposed. The key variables involved in calculating 2-D Tsallis entropy are written in recursive form. Thus, many repeating calculations are avoided and the computation complexity reduces to O(L2) from O(L4). The effectiveness of the proposed algorithm is illustrated by experimental results.
文摘Nonextensive statistical mechanics as in Tsallis formalism was used in this study, along with the dynamical Hamiltonian rod-like DNA model and the maximum entropy criteria for Tsallis’ entropy, so as to obtain length distribution of plasmid fragments, after irradiation with very high doses, assuming that the system reaches metaequilibrium. By intensively working out the Grand Canonical Ensemble (used to take into account the variation of the number of base pairs) a simplified expression for Fragment Size Distribution Function (FSDF) was obtained. This expression is dependent on two parameters only, the Tsallis q value and the minimal length of the fragments. Results obtained from fittings to available experimental data were adequate and the characteristic behavior of the shortest fragments was clearly documented and reproduced by the model, a circumstance never verified from theoretical distributions. The results point to the existence of an entropy which characterizes fragmentation processes and depending only on the q entropic index.
基金supported by the National Science,Technology and Innovation Plan(NSTIP)Strategic Technologies Programs of the Kingdom of Saudi Arabia under Grant No.08-INF325-02
文摘In this paper, we present a new technique for mammogram enhancement using fast dyadic wavelet transform (FDyWT) based on lifted spline dyadic wavelets and normalized Tsallis entropy. First, a mammogram image is decom- posed into a multiscale hierarchy of low-subband and high-subband images using FDyWT. Then noise is suppressed using normalized Tsallis entropy of the local variance of the modulus of oriented high-subband images. After that, the wavelet coefficients of high-subbands are modified using a non-linear operator and finally the low-subband image at the first scale is modified with power law transformation to suppress background. Though FDyWT is shift-invariant and has better poten- tial for detecting singularities like edges, its performance depends on the choice of dyadic wavclcts. On the other hand, the nulnber of vanishing moments is an important characteristic of dyadic wavelets for singularity analysis because it provides an upper bound measurement for singularity characterization. Using lifting dyadic schemes, we construct lifted spline dyadic wavelets of different degrees with increased number of vanishing moments. We also examine the effect of these wavelets on mammogram enhancement. The method is tested on mammogram images, taken from MIAS (Mammographic Image Analysis Society) database, having various background tissue types and containing different abnormalities. The comparison with tile state-of-the-art contrast enhancement methods reveals that the proposed method performs better and the difference is statistically significant.
基金supported by National Natural Science Foundation of China under Grant No.60872065Open Foundation of State Key Laboratory for Novel Software Technology at Nanjing University under Grant No.KFKT2010B17
文摘The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The existing two-dimensional Tsallis cross entropy method is not the strict two-dimensional extension. Thus two new methods of image thresholding using two-dimensional Tsallis cross entropy based on either Chaotic Particle Swarm Optimization (CPSO) or decomposition are proposed. The former uses CPSO to find the optimal threshold. The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure. The computing speed is improved greatly. The latter converts the two-dimensional computation into two one-dimensional spaces, which makes the computational complexity further reduced from O(L2) to O(L). The experimental results show that, compared with the proposed recently two-dimensional Shannon or Tsallis cross entropy method, the two new methods can achieve superior segmentation results and reduce running time greatly.
基金the National Natural Science Foundation of China(Grant Nos.12075159,12171044,and 12175147)the Natural Science Foundation of Beijing(Grant No.Z190005)+2 种基金the Academician Innovation Platform of Hainan ProvinceShenzhen Institute for Quantum Science and EngineeringSouthern University of Science and Technology(Grant No.SIQSE202001)。
文摘Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing.By generalizing the resource theory of coherence from von Neumann measurements to positive operatorvalued measures(POVMs),POVM-based coherence measures have been proposed with respect to the relative entropy of coherence,the l_(1) norm of coherence,the robustness of coherence and the Tsallis relative entropy of coherence.We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state in terms of the POVM-based coherence of the states in superposition.Our results can be used to estimate range of quantum coherence of superposed states.Detailed examples are presented to verify our analytical bounds.
基金supported by the National Natural Science Foundation of China(Grant Nos.12161056,12075159,12171044)Beijing Natural Science Foundation(Grant No.Z190005)the Academician Innovation Platform of Hainan Province。
文摘Quantum coherence plays a central role in Grover’s search algorithm.We study the Tsallis relative a entropy of coherence dynamics of the evolved state in Grover’s search algorithm.We prove that the Tsallis relative a entropy of coherence decreases with the increase of the success probability,and derive the complementarity relations between the coherence and the success probability.We show that the operator coherence of the first H■relies on the size of the database N,the success probability and the target states.Moreover,we illustrate the relationships between coherence and entanglement of the superposition state of targets,as well as the production and deletion of coherence in Grover iterations.
基金This paper is supported by Startup Foundation for Doctors of Nanchang Hangkong University(No.EA201907210).
文摘In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums of coherence are obtained.However,the above results cannot be verified directly for any α∈(0,1/2).Hence,we only consider the special case of α=1/n+1,where n is a positive integer,and we obtain the upper and lower bounds.By comparing the upper and lower bounds,we find that the upper bound is equal to the lower bound for the special α=1/2,and the differences between the upper and the lower bounds will increase as α increases.Furthermore,we discuss the tendency of the sum of coherence,and find that it has the same tendency with respect to the different θ or φ,which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11271237,11671244the Higher School Doctoral Subject Foundation of Ministry of Education of China under Grant No.20130202110001the Central Universities under Grants Nos.2016TS060 and 2016CBY003
文摘In this paper, we investigate the cohering and decohering power of the one-qubit Markovian channels with respect to coherence measures based on the l1-norm, the R′enyi α-relative entropy and the Tsallis α-relative entropy of coherence, respectively. The amplitude damping channel, phase damping channel, depolarizing channel, and flip channels are analytically calculated. It shows that the decohering power of the amplitude damping channel on the x, y, and z basis is equal to each other. The same phenomenon can be seen for the phase damping channel and the flip channels.The cohering power for the phase damping channel and the flip channels on the x, y basis also equals to that on the z basis. However, the cohering and decohering power of the depolarizing channel is independent to the reference basises.And the cohering power of the amplitude damping channel on the x, y basis is different to that on the z basis.