With the increasing availability of precipitation radar data from space,enhancement of the resolution of spaceborne precipitation observations is important,particularly for hazard prediction and climate modeling at lo...With the increasing availability of precipitation radar data from space,enhancement of the resolution of spaceborne precipitation observations is important,particularly for hazard prediction and climate modeling at local scales relevant to extreme precipitation intensities and gradients.In this paper,the statistical characteristics of radar precipitation reflectivity data are studied and modeled using a hidden Markov tree(HMT)in the wavelet domain.Then,a high-resolution interpolation algorithm is proposed for spaceborne radar reflectivity using the HMT model as prior information.Owing to the small and transient storm elements embedded in the larger and slowly varying elements,the radar precipitation data exhibit distinct multiscale statistical properties,including a non-Gaussian structure and scale-to-scale dependency.An HMT model can capture well the statistical properties of radar precipitation,where the wavelet coefficients in each sub-band are characterized as a Gaussian mixture model(GMM),and the wavelet coefficients from the coarse scale to fine scale are described using a multiscale Markov process.The state probabilities of the GMM are determined using the expectation maximization method,and other parameters,for instance,the variance decay parameters in the HMT model are learned and estimated from high-resolution ground radar reflectivity images.Using the prior model,the wavelet coefficients at finer scales are estimated using local Wiener filtering.The interpolation algorithm is validated using data from the precipitation radar onboard the Tropical Rainfall Measurement Mission satellite,and the reconstructed results are found to be able to enhance the spatial resolution while optimally reproducing the local extremes and gradients.展开更多
Shearlet变换作为后小波时代的一个重要的多尺度几何分析工具具有良好的各向异性和方向捕捉性,同时它也可以对诸如图像等多维信号进行一种近最优的稀疏表示.非下采样Shearlet变换(NSST)在保持Shearlet变换特性的同时还具有平移不变特性...Shearlet变换作为后小波时代的一个重要的多尺度几何分析工具具有良好的各向异性和方向捕捉性,同时它也可以对诸如图像等多维信号进行一种近最优的稀疏表示.非下采样Shearlet变换(NSST)在保持Shearlet变换特性的同时还具有平移不变特性,这在具有丰富纹理和细节信息的图像处理中发挥着重要作用.该文首先对图像NSST方向子带内系数的概率密度分布进行分析,获得系数的稀疏统计特性和Cauchy分布拟合子带内系数的有效性;其次对NSST方向子带间系数的联合概率分布进行分析,获得方向子带系数间所具有的持续和传递特性,确定了一种NSST子带间树形架构的系数对应关系,进而提出一种NSST域隐马尔可夫模树模型(C-NSSTHMT),该模型通过Cauchy分布来拟合NSST系数,更好地揭示图像NSST变换后相同尺度子带内和不同尺度子带间系数的相关性.进一步提出一种基于所提出C-NSST-HMT模型的图像去噪算法,该算法对于含噪声方差为30和40的噪声图像,其去噪后的PSNR(Peak Signal to Noise Ratio)较NSCT-HMT方法分别提高了1.995dB和1.193dB.特别对纹理和细节丰富的图像,该算法在去噪的同时,有效地保留了图像的几何信息.展开更多
Wavelet transformation and hidden Markov model are used in wavelet-based HMT model for analyzing andprocessing images. Expected Maximization(EM) algorithm used in training model results in slow convergence. Thepersist...Wavelet transformation and hidden Markov model are used in wavelet-based HMT model for analyzing andprocessing images. Expected Maximization(EM) algorithm used in training model results in slow convergence. Thepersistence, exponential decay characteristics of wavelet coefficient are analyzed. A model parameter initializationmethod is proposed. This method provides reasonable initial model value, reduces training time greatly. Its applica-tion in image de-noising demonstrates is validity.展开更多
基金This study was funded by the National Natural Science Foundation of China(Grant No.41975027)the Natural Science Foundation of Jiangsu Province(Grant No.BK20171457)the National Key R&D Program on Monitoring,Early Warning and Prevention of Major Natural Disasters(Grant No.2017YFC1501401).
文摘With the increasing availability of precipitation radar data from space,enhancement of the resolution of spaceborne precipitation observations is important,particularly for hazard prediction and climate modeling at local scales relevant to extreme precipitation intensities and gradients.In this paper,the statistical characteristics of radar precipitation reflectivity data are studied and modeled using a hidden Markov tree(HMT)in the wavelet domain.Then,a high-resolution interpolation algorithm is proposed for spaceborne radar reflectivity using the HMT model as prior information.Owing to the small and transient storm elements embedded in the larger and slowly varying elements,the radar precipitation data exhibit distinct multiscale statistical properties,including a non-Gaussian structure and scale-to-scale dependency.An HMT model can capture well the statistical properties of radar precipitation,where the wavelet coefficients in each sub-band are characterized as a Gaussian mixture model(GMM),and the wavelet coefficients from the coarse scale to fine scale are described using a multiscale Markov process.The state probabilities of the GMM are determined using the expectation maximization method,and other parameters,for instance,the variance decay parameters in the HMT model are learned and estimated from high-resolution ground radar reflectivity images.Using the prior model,the wavelet coefficients at finer scales are estimated using local Wiener filtering.The interpolation algorithm is validated using data from the precipitation radar onboard the Tropical Rainfall Measurement Mission satellite,and the reconstructed results are found to be able to enhance the spatial resolution while optimally reproducing the local extremes and gradients.
文摘Shearlet变换作为后小波时代的一个重要的多尺度几何分析工具具有良好的各向异性和方向捕捉性,同时它也可以对诸如图像等多维信号进行一种近最优的稀疏表示.非下采样Shearlet变换(NSST)在保持Shearlet变换特性的同时还具有平移不变特性,这在具有丰富纹理和细节信息的图像处理中发挥着重要作用.该文首先对图像NSST方向子带内系数的概率密度分布进行分析,获得系数的稀疏统计特性和Cauchy分布拟合子带内系数的有效性;其次对NSST方向子带间系数的联合概率分布进行分析,获得方向子带系数间所具有的持续和传递特性,确定了一种NSST子带间树形架构的系数对应关系,进而提出一种NSST域隐马尔可夫模树模型(C-NSSTHMT),该模型通过Cauchy分布来拟合NSST系数,更好地揭示图像NSST变换后相同尺度子带内和不同尺度子带间系数的相关性.进一步提出一种基于所提出C-NSST-HMT模型的图像去噪算法,该算法对于含噪声方差为30和40的噪声图像,其去噪后的PSNR(Peak Signal to Noise Ratio)较NSCT-HMT方法分别提高了1.995dB和1.193dB.特别对纹理和细节丰富的图像,该算法在去噪的同时,有效地保留了图像的几何信息.
文摘Wavelet transformation and hidden Markov model are used in wavelet-based HMT model for analyzing andprocessing images. Expected Maximization(EM) algorithm used in training model results in slow convergence. Thepersistence, exponential decay characteristics of wavelet coefficient are analyzed. A model parameter initializationmethod is proposed. This method provides reasonable initial model value, reduces training time greatly. Its applica-tion in image de-noising demonstrates is validity.
