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
SPIHT和无链表SPIHT(Not List SPIHT)是高效的图像压缩算法,但是抗误码性差、压缩速度慢等缺点限制了其在航天领域的应用。文章针对上述两个缺点对算法进行了改进,采用Le Gall5/3小波对遥感图像进行小波分解,将小波域系数分家族块进行...SPIHT和无链表SPIHT(Not List SPIHT)是高效的图像压缩算法,但是抗误码性差、压缩速度慢等缺点限制了其在航天领域的应用。文章针对上述两个缺点对算法进行了改进,采用Le Gall5/3小波对遥感图像进行小波分解,将小波域系数分家族块进行索引、扫描和码率分配,按照比特平面或运算进行重要性预测,实现了N个位平面同时编码。改进算法与SPIHT相比易于硬件编程实现,仿真结果显示,解压后图像峰值信噪比(PSNR)提高了0.2～0.6db,压缩速度提高了4～6倍。用硬件实现时如果采用并行和流水线操作,速度还可以进一步提高。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.
文摘SPIHT和无链表SPIHT(Not List SPIHT)是高效的图像压缩算法,但是抗误码性差、压缩速度慢等缺点限制了其在航天领域的应用。文章针对上述两个缺点对算法进行了改进,采用Le Gall5/3小波对遥感图像进行小波分解,将小波域系数分家族块进行索引、扫描和码率分配,按照比特平面或运算进行重要性预测,实现了N个位平面同时编码。改进算法与SPIHT相比易于硬件编程实现,仿真结果显示,解压后图像峰值信噪比(PSNR)提高了0.2～0.6db,压缩速度提高了4～6倍。用硬件实现时如果采用并行和流水线操作,速度还可以进一步提高。
