图像所包含的信息是通过灰度值在空域的变化呈现的.梯度是度量变化的基本工具,这使得梯度成为了目前大多数图像质量评价算法的重要组成部分.但是梯度只能度量局部变化,而当人类视觉系统(Human visual system,HVS)感知一幅图像时,既能感...图像所包含的信息是通过灰度值在空域的变化呈现的.梯度是度量变化的基本工具,这使得梯度成为了目前大多数图像质量评价算法的重要组成部分.但是梯度只能度量局部变化,而当人类视觉系统(Human visual system,HVS)感知一幅图像时,既能感知到局部变化,也能感知到全局变化.基于HVS的这一特性,本文提出了一种结合全局与局部变化的图像质量评价算法(Global and local variation similarity,GLV-SIM).该算法利用Grünwald-Letnikov分数阶导数来度量图像的全局变化,利用梯度模来度量图像的局部变化.然后结合二者计算参考图像和退化图像之间的相似度谱(Similarity map),进而得到图像的客观评分.在TID2013、TID2008、CSIQ与LIVE四个数据库上的仿真实验表明,较之单一度量局部变化的方法,本文算法能更准确地模拟HVS对图像质量的感知过程,给出的客观评分与主观评分具有较好的一致性.展开更多
The space-time fractional advection dispersion equations are linear partial pseudo-differential equations with spatial fractional derivatives in time and in space and are used to model transport at the earth surface. ...The space-time fractional advection dispersion equations are linear partial pseudo-differential equations with spatial fractional derivatives in time and in space and are used to model transport at the earth surface. The time fractional order is denoted by β∈ and ?is devoted to the space fractional order. The time fractional advection dispersion equations describe particle motion with memory in time. Space-fractional advection dispersion equations arise when velocity variations are heavy-tailed and describe particle motion that accounts for variation in the flow field over entire system. In this paper, I focus on finding the precise explicit discrete approximate solutions to these models for some values of ?with ?, ?while the Cauchy case as ?and the classical case as ?with ?are studied separately. I compare the numerical results of these models for different values of ?and ?and for some other related changes. The approximate solutions of these models are also discussed as a random walk with or without a memory depending on the value of . Then I prove that the discrete solution in the Fourierlaplace space of theses models converges in distribution to the Fourier-Laplace transform of the corresponding fractional differential equations for all the fractional values of ?and .展开更多
文摘图像所包含的信息是通过灰度值在空域的变化呈现的.梯度是度量变化的基本工具,这使得梯度成为了目前大多数图像质量评价算法的重要组成部分.但是梯度只能度量局部变化,而当人类视觉系统(Human visual system,HVS)感知一幅图像时,既能感知到局部变化,也能感知到全局变化.基于HVS的这一特性,本文提出了一种结合全局与局部变化的图像质量评价算法(Global and local variation similarity,GLV-SIM).该算法利用Grünwald-Letnikov分数阶导数来度量图像的全局变化,利用梯度模来度量图像的局部变化.然后结合二者计算参考图像和退化图像之间的相似度谱(Similarity map),进而得到图像的客观评分.在TID2013、TID2008、CSIQ与LIVE四个数据库上的仿真实验表明,较之单一度量局部变化的方法,本文算法能更准确地模拟HVS对图像质量的感知过程,给出的客观评分与主观评分具有较好的一致性.
文摘应用二阶加权移位Grünwald-Letnikov 算子离散Riemann-Liouville型分数阶导数,用中心差分算子离散对流项,并结合非对称迭代技术形成解一维空间分数阶对流扩散的二阶半隐式有限差分格式.此格式形式上是隐式的,而通过在偶数时间层和奇数时间层选择不同的节点模板可以达到显式计算的目的.用Fourier分析方法证明稳定性,并且给出离散解和解析解在 l 2 意义下的误差估计.最后用数值算例验证了理论结果.
文摘The space-time fractional advection dispersion equations are linear partial pseudo-differential equations with spatial fractional derivatives in time and in space and are used to model transport at the earth surface. The time fractional order is denoted by β∈ and ?is devoted to the space fractional order. The time fractional advection dispersion equations describe particle motion with memory in time. Space-fractional advection dispersion equations arise when velocity variations are heavy-tailed and describe particle motion that accounts for variation in the flow field over entire system. In this paper, I focus on finding the precise explicit discrete approximate solutions to these models for some values of ?with ?, ?while the Cauchy case as ?and the classical case as ?with ?are studied separately. I compare the numerical results of these models for different values of ?and ?and for some other related changes. The approximate solutions of these models are also discussed as a random walk with or without a memory depending on the value of . Then I prove that the discrete solution in the Fourierlaplace space of theses models converges in distribution to the Fourier-Laplace transform of the corresponding fractional differential equations for all the fractional values of ?and .
