That cycle-slips remain undetected will significantly degrade the accuracy of the navigation solution when using carrier phase measurements in global positioning system(GPS).In this paper,an algorithm based on length-...That cycle-slips remain undetected will significantly degrade the accuracy of the navigation solution when using carrier phase measurements in global positioning system(GPS).In this paper,an algorithm based on length-4 symmetric/anti-symmetric(SA4)orthogonal multi-wavelet is presented to detect and identify cycle-slips in the context of the feature of the GPS zero-differential carrier phase measurements.Associated with the local singularity detection principle,cycle-slips can be detected and located precisely through the modulus maxima of the coefficients achieved by the multi-wavelet transform.Firstly,studies are focused on the feasibility of the algorithm employing the orthogonal multi-wavelet system such as Geronimo-Hardin-Massopust(GHM),Chui-Lian(CL)and SA4.Moreover,the mathematical characterization of singularities with Lipschitz exponents is explained,the modulus maxima from wavelet to multi-wavelet domain is extended and a localization formula is provided from the modulus maxima of the coefficients to the original observation.Finally,field experiments with real receiver are presented to demonstrate the effectiveness of the proposed algorithm.Because SA4 possesses the specific nature of good multi-filter properties(GMPs),it is superior to scalar wavelet and other orthogonal multi-wavelet candidates distinctly,and for the half-cycle slip,it also remains better detection,location ability and the equal complexity of wavelet transform.展开更多
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
Bessel sequence plays an important role in the study of frames for a Hilbert space with the convergence of a frame series, which has been widely studied in the literature. This paper addresses multi-wavelet Bessel seq...Bessel sequence plays an important role in the study of frames for a Hilbert space with the convergence of a frame series, which has been widely studied in the literature. This paper addresses multi-wavelet Bessel sequences in Sobolev spaces setting, the result obtained is useful for the study of multi-wavelet frames in these spaces.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
目的近年来,基于深度学习的水印方法得到了广泛研究。现有方法通常对特征图的低频和高频部分同等对待,忽视了不同频率成分之间的重要差异,导致模型在处理多样化攻击时缺乏灵活性,难以同时实现水印的高保真性和强鲁棒性。为此,本文提出...目的近年来,基于深度学习的水印方法得到了广泛研究。现有方法通常对特征图的低频和高频部分同等对待,忽视了不同频率成分之间的重要差异,导致模型在处理多样化攻击时缺乏灵活性,难以同时实现水印的高保真性和强鲁棒性。为此,本文提出一种频率感知驱动的深度鲁棒图像水印技术(deep robust image watermarking driven by frequency awareness,RIWFP)。方法通过差异化机制处理低频和高频成分,提升水印性能。具体而言,低频成分通过小波卷积神经网络进行建模,利用宽感受野卷积在粗粒度层面高效学习全局结构和上下文信息;高频成分则采用深度可分离卷积和注意力机制组成的特征蒸馏块进行精炼,强化图像细节,在细粒度层面高效捕捉高频信息。此外,本文使用多频率小波损失函数,引导模型聚焦于不同频带的特征分布,进一步提升生成图像的质量。结果实验结果表明,提出的频率感知驱动的深度鲁棒图像水印技术在多个数据集上均表现出优越性能。在COCO(common objects in context)数据集上,RIWFP在随机丢弃攻击下的准确率达到91.4%;在椒盐噪声和中值滤波攻击下,RIWFP分别以100%和99.5%的准确率达到了最高水平,展现了其对高频信息的高效学习能力。在Ima⁃geNet数据集上,RIWFP在裁剪攻击下的准确率为93.4%;在JPEG压缩攻击下的准确率为99.6%,均显著优于其他对比方法。综合来看,RIWFP在COCO和ImageNet数据集上的平均准确率分别为96.7%和96.9%,均高于其他对比方法。结论本文所提方法通过频率感知的粗到细处理策略,显著增强了水印的不可见性和鲁棒性,在处理多种攻击时表现出优越性能。展开更多
针对岩石薄片图像超分辨率重建过程中因纹理复杂导致现有重建方法效果不理想的问题,提出面向岩石薄片图像的超分辨率网络模型(super-resolution denoising diffusion probability model of rock slice,rsDDPMSR).针对传统上采样方法往...针对岩石薄片图像超分辨率重建过程中因纹理复杂导致现有重建方法效果不理想的问题,提出面向岩石薄片图像的超分辨率网络模型(super-resolution denoising diffusion probability model of rock slice,rsDDPMSR).针对传统上采样方法往往会导致伪影和低分辨率图像先验信息利用不充分的问题提出分层特征增强网络(layered feature enhancement network,LFE-Net),利用双通路网络对平稳小波变换分解后的高频与低频分量进行分层特征增强.为引导扩散模型的生成方向并提供丰富先验信息,将经过LFE-Net增强后的低分辨率特征与目标高分辨率加噪图像特征通道拼接作为扩散模型的条件输入.在U-Net的基础上设计了双编码器多尺度噪声预测网络(ACA-U-Net)有效处理岩石薄片多尺度信息并在跳跃连接中引入时间感知的自适应交叉注意力机制适配扩散模型不同去噪阶段的特征分布变化增强模型对关键区域的关注程度,有效提升图像重建细节.实验结果表明,rsDDPMSR在2×、4×、8×放大倍数下,峰值信噪比(PSNR)和结构相似度(SSIM)相比于CAMixerSR、SDFlow、IDM和SR3等主流重建方法具有更优的重建效果.展开更多
The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials and the dilation and translation of a function generator, which consists of a finite n...The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials and the dilation and translation of a function generator, which consists of a finite number of continuous and discontinuous functions. The V-system has interesting properties, such as orthogonality, symmetry, completeness and short compact support. It is shown in this paper that the V-system is essentially a special multi-wavelet basis. As a result, some basic properties of the V-system are established through the well-developed theory of multi-wavelets. From this point of view, more other V-systems are constructed.展开更多
基金National Natural Science Foundation of China(61153002)
文摘That cycle-slips remain undetected will significantly degrade the accuracy of the navigation solution when using carrier phase measurements in global positioning system(GPS).In this paper,an algorithm based on length-4 symmetric/anti-symmetric(SA4)orthogonal multi-wavelet is presented to detect and identify cycle-slips in the context of the feature of the GPS zero-differential carrier phase measurements.Associated with the local singularity detection principle,cycle-slips can be detected and located precisely through the modulus maxima of the coefficients achieved by the multi-wavelet transform.Firstly,studies are focused on the feasibility of the algorithm employing the orthogonal multi-wavelet system such as Geronimo-Hardin-Massopust(GHM),Chui-Lian(CL)and SA4.Moreover,the mathematical characterization of singularities with Lipschitz exponents is explained,the modulus maxima from wavelet to multi-wavelet domain is extended and a localization formula is provided from the modulus maxima of the coefficients to the original observation.Finally,field experiments with real receiver are presented to demonstrate the effectiveness of the proposed algorithm.Because SA4 possesses the specific nature of good multi-filter properties(GMPs),it is superior to scalar wavelet and other orthogonal multi-wavelet candidates distinctly,and for the half-cycle slip,it also remains better detection,location ability and the equal complexity of wavelet transform.
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 Doctoral Research Project of Yan’an University(Grant No.YDBK2017-21)the Foundation of Yan’an University(Grant No.YDQ2018-09)
文摘Bessel sequence plays an important role in the study of frames for a Hilbert space with the convergence of a frame series, which has been widely studied in the literature. This paper addresses multi-wavelet Bessel sequences in Sobolev spaces setting, the result obtained is useful for the study of multi-wavelet frames in these spaces.
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.
文摘目的近年来,基于深度学习的水印方法得到了广泛研究。现有方法通常对特征图的低频和高频部分同等对待,忽视了不同频率成分之间的重要差异,导致模型在处理多样化攻击时缺乏灵活性,难以同时实现水印的高保真性和强鲁棒性。为此,本文提出一种频率感知驱动的深度鲁棒图像水印技术(deep robust image watermarking driven by frequency awareness,RIWFP)。方法通过差异化机制处理低频和高频成分,提升水印性能。具体而言,低频成分通过小波卷积神经网络进行建模,利用宽感受野卷积在粗粒度层面高效学习全局结构和上下文信息;高频成分则采用深度可分离卷积和注意力机制组成的特征蒸馏块进行精炼,强化图像细节,在细粒度层面高效捕捉高频信息。此外,本文使用多频率小波损失函数,引导模型聚焦于不同频带的特征分布,进一步提升生成图像的质量。结果实验结果表明,提出的频率感知驱动的深度鲁棒图像水印技术在多个数据集上均表现出优越性能。在COCO(common objects in context)数据集上,RIWFP在随机丢弃攻击下的准确率达到91.4%;在椒盐噪声和中值滤波攻击下,RIWFP分别以100%和99.5%的准确率达到了最高水平,展现了其对高频信息的高效学习能力。在Ima⁃geNet数据集上,RIWFP在裁剪攻击下的准确率为93.4%;在JPEG压缩攻击下的准确率为99.6%,均显著优于其他对比方法。综合来看,RIWFP在COCO和ImageNet数据集上的平均准确率分别为96.7%和96.9%,均高于其他对比方法。结论本文所提方法通过频率感知的粗到细处理策略,显著增强了水印的不可见性和鲁棒性,在处理多种攻击时表现出优越性能。
文摘针对岩石薄片图像超分辨率重建过程中因纹理复杂导致现有重建方法效果不理想的问题,提出面向岩石薄片图像的超分辨率网络模型(super-resolution denoising diffusion probability model of rock slice,rsDDPMSR).针对传统上采样方法往往会导致伪影和低分辨率图像先验信息利用不充分的问题提出分层特征增强网络(layered feature enhancement network,LFE-Net),利用双通路网络对平稳小波变换分解后的高频与低频分量进行分层特征增强.为引导扩散模型的生成方向并提供丰富先验信息,将经过LFE-Net增强后的低分辨率特征与目标高分辨率加噪图像特征通道拼接作为扩散模型的条件输入.在U-Net的基础上设计了双编码器多尺度噪声预测网络(ACA-U-Net)有效处理岩石薄片多尺度信息并在跳跃连接中引入时间感知的自适应交叉注意力机制适配扩散模型不同去噪阶段的特征分布变化增强模型对关键区域的关注程度,有效提升图像重建细节.实验结果表明,rsDDPMSR在2×、4×、8×放大倍数下,峰值信噪比(PSNR)和结构相似度(SSIM)相比于CAMixerSR、SDFlow、IDM和SR3等主流重建方法具有更优的重建效果.
基金Supported by National Natural Science Foundation of China (Grant Nos.11071261,60873088 and 10911120394)
文摘The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials and the dilation and translation of a function generator, which consists of a finite number of continuous and discontinuous functions. The V-system has interesting properties, such as orthogonality, symmetry, completeness and short compact support. It is shown in this paper that the V-system is essentially a special multi-wavelet basis. As a result, some basic properties of the V-system are established through the well-developed theory of multi-wavelets. From this point of view, more other V-systems are constructed.
