The single 2 dilation orthogonal wavelet multipliers in one dimensional case and single A-dilation(where A is any expansive matrix with integer entries and|det A|=2) wavelet multipliers in high dimensional case were c...The single 2 dilation orthogonal wavelet multipliers in one dimensional case and single A-dilation(where A is any expansive matrix with integer entries and|det A|=2) wavelet multipliers in high dimensional case were completely characterized by the Wutam Consortium(1998) and Z. Y. Li, et al.(2010). But there exist no more results on orthogonal multivariate wavelet matrix multipliers corresponding integer expansive dilation matrix with the absolute value of determinant not 2 in L~2(R~2). In this paper, we choose 2I2=(~2~0)as the dilation matrix and consider the 2 I2-dilation orthogonal multivariate waveletΨ = {ψ, ψ, ψ},(which is called a dyadic bivariate wavelet) multipliers. We call the3 × 3 matrix-valued function A(s) = [ f(s)], where fi, jare measurable functions, a dyadic bivariate matrix Fourier wavelet multiplier if the inverse Fourier transform of A(s)( ψ(s), ψ(s), ψ(s)) ~T=( g(s), g(s), g(s))~ T is a dyadic bivariate wavelet whenever(ψ, ψ, ψ) is any dyadic bivariate wavelet. We give some conditions for dyadic matrix bivariate wavelet multipliers. The results extended that of Z. Y. Li and X. L.Shi(2011). As an application, we construct some useful dyadic bivariate wavelets by using dyadic Fourier matrix wavelet multipliers and use them to image denoising.展开更多
The discrete scalar data need prefiltering when transformed by discrete multi-wavelet, but prefiltering will make some properties of multi-wavelets lost. Balanced multi-wavelets can avoid prefiltering. The sufficient ...The discrete scalar data need prefiltering when transformed by discrete multi-wavelet, but prefiltering will make some properties of multi-wavelets lost. Balanced multi-wavelets can avoid prefiltering. The sufficient and necessary condition of p-order balance for multi-wavelets in time domain, the interrelation between balance order and approximation order and the sampling property of balanced multi-wavelets are investigated. The algorithms of 1-order and 2-order balancing for multi-wavelets are obtained. The two algorithms both preserve the orthogonal relation between multi-scaling function and multi-wavelets. More importantly, balancing operation doesnt increase the length of filters, which suggests that a relatively short balanced multi-wavelet can be constructed from an existing unbalanced multi-wavelet as short as possible.展开更多
高光谱遥感图像中不仅存在空间域噪声而且存在光谱域噪声.传统的图像滤波仅对图像空间域噪声进行处理,而不能去除光谱域噪声,为改进这种状况,提出了DSGF(Derivative based Savitzky-Golay F ilter)方法.首先,基于反射率光谱的二阶导数...高光谱遥感图像中不仅存在空间域噪声而且存在光谱域噪声.传统的图像滤波仅对图像空间域噪声进行处理,而不能去除光谱域噪声,为改进这种状况,提出了DSGF(Derivative based Savitzky-Golay F ilter)方法.首先,基于反射率光谱的二阶导数对反射率光谱各波段噪声大小进行判定,然后用不同大小平滑窗的Savitzky-Golay滤波器对反射率光谱作两步滤波.对高光谱图像进行的逐像元DSGF滤波,在去除光谱域中噪声的同时,保留了图像反射率光谱的大部分细微特征.展开更多
基金partially supported by the National Natural Science Foundation of China (Grant No. 11101142 and No. 11571107)
文摘The single 2 dilation orthogonal wavelet multipliers in one dimensional case and single A-dilation(where A is any expansive matrix with integer entries and|det A|=2) wavelet multipliers in high dimensional case were completely characterized by the Wutam Consortium(1998) and Z. Y. Li, et al.(2010). But there exist no more results on orthogonal multivariate wavelet matrix multipliers corresponding integer expansive dilation matrix with the absolute value of determinant not 2 in L~2(R~2). In this paper, we choose 2I2=(~2~0)as the dilation matrix and consider the 2 I2-dilation orthogonal multivariate waveletΨ = {ψ, ψ, ψ},(which is called a dyadic bivariate wavelet) multipliers. We call the3 × 3 matrix-valued function A(s) = [ f(s)], where fi, jare measurable functions, a dyadic bivariate matrix Fourier wavelet multiplier if the inverse Fourier transform of A(s)( ψ(s), ψ(s), ψ(s)) ~T=( g(s), g(s), g(s))~ T is a dyadic bivariate wavelet whenever(ψ, ψ, ψ) is any dyadic bivariate wavelet. We give some conditions for dyadic matrix bivariate wavelet multipliers. The results extended that of Z. Y. Li and X. L.Shi(2011). As an application, we construct some useful dyadic bivariate wavelets by using dyadic Fourier matrix wavelet multipliers and use them to image denoising.
基金Supported by the Scientific Research Foundation for Returned Overseas Chinese Scholars from the State Education Ministry (No. [2002]247) and the Young Key Teachers Foundation of Chongqing University.
文摘The discrete scalar data need prefiltering when transformed by discrete multi-wavelet, but prefiltering will make some properties of multi-wavelets lost. Balanced multi-wavelets can avoid prefiltering. The sufficient and necessary condition of p-order balance for multi-wavelets in time domain, the interrelation between balance order and approximation order and the sampling property of balanced multi-wavelets are investigated. The algorithms of 1-order and 2-order balancing for multi-wavelets are obtained. The two algorithms both preserve the orthogonal relation between multi-scaling function and multi-wavelets. More importantly, balancing operation doesnt increase the length of filters, which suggests that a relatively short balanced multi-wavelet can be constructed from an existing unbalanced multi-wavelet as short as possible.
基金国家自然科学基金(the National Natural Science Foundation of China under Grant No.40571109)广西省科学基金资助项目(the Sci-ence Foundation of Guangxi Province of China under Grant No.桂科基 0448035No.桂科自 0339036)
文摘高光谱遥感图像中不仅存在空间域噪声而且存在光谱域噪声.传统的图像滤波仅对图像空间域噪声进行处理,而不能去除光谱域噪声,为改进这种状况,提出了DSGF(Derivative based Savitzky-Golay F ilter)方法.首先,基于反射率光谱的二阶导数对反射率光谱各波段噪声大小进行判定,然后用不同大小平滑窗的Savitzky-Golay滤波器对反射率光谱作两步滤波.对高光谱图像进行的逐像元DSGF滤波,在去除光谱域中噪声的同时,保留了图像反射率光谱的大部分细微特征.
