一种改进的偏微分扩散方程的医学超声图像去噪方法

研究了偏微分扩散方程在医学超声图像去噪中的应用。首先对各向异性扩散模型的进行分析,为了更好地去除噪声并保留图像的边缘等重要信息,提出了构造新的各向异性加权系数和优化的迭代次数的改进方法,并通过实验证明可达到更好的去噪效果。     

一种改进型各向异性扩散滤波器

通过分析Perona和Malik(PM)扩散滤波器扩散率函数的统计学意义,提出一种关于扩散率函数的统计学解释模型,即扩散率函数定义了一个以边界估计算子为随机变量的概率密度函数,解决了扩散率函数设计和选择没有统一理论的问题.依据这一解释模型,设计出一种改进型的各向异性扩散滤波器.实验结果显示,改进型扩散滤波器只需要相对于PM方法较少的迭代次数,就能得到预期的图像去噪效果,证明统计学解释模型为各向异性扩散滤波器提供了一种有效的设计方法.     

一种用各向异性扩散方程抑制SAR相干斑噪声的方法

本文提出了一种基于各向异性扩散偏微分方程抑制合成孔径雷达(SAR)图像的相干斑噪声的算法,简称DSADE算法。本算法根据SAR图像的局部特征在均匀区域各向同性扩散,边缘细节区域各向异性扩散,不仅可以很好地保持边缘细节信息,而且可以对其进行增强。实验结果表明,本算法不仅有效抑制了SAR图像的相干斑噪声,保持并增强了边缘细节,而且有着良好的图像视觉效果。     

方向扩散方程与小波变换的相关性研究

方向扩散方程是一种有方向性的扩散,本文基于这一特点,对方向扩散方程与小波分解和重构的相关性作了研究。首先,用小波分解后下层的低频图像作为对上层低频图像的一个初始近似,验证了由上层低频图像经方向扩散方程可逐渐扩散收敛到下层的低频图像;反过来,由下层低频图像经方向扩散方程亦可逐渐扩散恢复到上层低频图像,这正体现了小波分解与重构的渐变过程。因此,由方向扩散方程的迭代扩散可以实现小波变换在相邻两层间的分解与重构,且随着所选扩散时间间隔的减小,可以在越来越细的尺度上观察相邻两层间小波分解与重构的渐变过程。     

方向扩散方程与小波变换的相关性研究

方向扩散方程是一种有方向性的扩散,本文基于这一特点,对方向扩散方程与小波分解和重构的相关性作了研究。首先,用小波分解后下层的低频图像作为对上层低频图像的一个初始近似,验证了由上层低频图像经方向扩散方程可逐渐扩散收敛到下层的低频图像;反过来,由下层低频图像经方向扩散方程亦可逐渐扩散恢复到上层低频图像,这正体现了小波分解与重构的渐变过程。因此,由方向扩散方程的迭代扩散可以实现小波变换在相邻两层间的分解与重构,且随着所选扩散时间间隔的减小,可以在越来越细的尺度上观察相邻两层间小波分解与重构的渐变过程。     

一种非线性复扩散与冲击滤波的图像消噪方法

由于图像复扩散的虚数部分等价于图像高斯卷积后二阶梯度算子,因此利用复扩散的虚部去控制扩散系数可得到前后向复扩散,然而这种选择性的前后向复扩散不能有效消除图像细节区域的噪声。针对前后向复扩散的缺点,提出一种复扩散与冲击滤波相结合的前后向复扩散,利用复扩散去消噪,虚部控制冲击滤波器实现图像边界的锐化。通过实验证明了这种扩散消噪的同时更好的保留图像的细节,且具有更高的峰值信噪比。     

一种改进的反应扩散滤波器图像去噪算法

提出一种基于Nordstrm能量泛函的非线性反应扩散数字滤波模型。数值实验结果表明该模型不仅对高斯噪声、椒盐噪声和Speckle噪声污染的图像去噪效果较好,而且也适合对混合噪声污染的图像去噪。去噪后图像有良好的视觉效果,峰值信噪比较高。     

基于各向异性扩散方程的局部非纹理图像修整与去噪

图像修整(image inpainting)是一种图像插值的方法,它根据丢失信息区域周围的图像信息来猜测和填充这个区域,图像修整属于图像恢复的范畴。利用变分方法导出的各向异性扩散方程对于图像边缘的良好保持特性,而在图像处理中得到了广泛的应用。基于这一思想,本文提出了一种基于各向异性扩散方程的图像修整算法:在填补修整区域的同时,可有效地去除噪声,同时保持边缘信息。理论分析和实验结果表明了这一点。     

一种基于核函数的各向异性扩散图像去噪算法

分析了各向异性扩散去噪模型优缺点,针对PM模型不能有效区分噪声和边缘,提出了一种基于核函数的各向异性扩散去噪模型。在该模型中,把图像中噪声与边缘在低维空间的非线性区分关系转变为高维特征空间的线性关系,利用核函数获得高维空间的扩散函数。实验中分别与PM模型、Cattle模型比较分析,证明基于核函数的扩散模型在去除噪声的同时,更好地保留图像的信息,且峰值信噪比最高,去噪性能最优。     

基于非线性小波阈值的各向异性扩散方程

本文给出了林石算子定义的扩散方程的小波阈值等价形式,并在此基础上对林石算子定义的扩散系数计算公式进行了修改,将其中估计各阶导数时所用的高斯线性滤波图像改成平移不变小波非线性阈值图像,这样避免了高斯滤波引起的过度光滑和边界移动.实验结果表明新的扩散方程在保持边缘位置的同时能更有效地去除噪声.     

An edge fusion scheme for image denoising based on anisotropic diffusion models

In this paper, we propose an enhanced anisotropic diffusion model. The improved model can classify finely image information as smooth regions, edges, corners and isolated noises by characteristic parameters and gradient variance parameter. And for different image information the eigenvalues of diffusion tensor are designed to conduct adaptive diffusion. Moreover, an edge fusion scheme is posed to preserve edges after denoising by combing different denoising and edge detection methods. Firstly, different denoising methods are applied for noisy image to obtain denoised images, and the best method among them is selected as main method. Then edge images of denoised images are obtained by edge detection methods. Finally, by fusing edge images together more integrated edges can be achieved to replace edges of denoised image obtained by main method. The experimental results show the proposed model can denoise meanwhile preserve edges and corners, and the edge fusion scheme is accurate and effective.     

Spectral-spatial adaptive and well-balanced flow-based anisotropic diffusion for multispectral image denoising

Anisotropic diffusion can provide better compromise between noise reduction and edge preservation. In multispectral images, there exist different spatial local structures in the same band. Therefore, the levels of smoothing of anisotropic diffusion process should conform to both of image spectral and spatial features. In this paper, we present an effective denoising algorithm by integrating the spectral-spatial adaptive mechanism into a well-balanced flow (WBF) based anisotropic diffusion model, in which an adjustable weighted function is introduced to perform the appropriate levels of smoothing and enhancing according to different feature scales. Moreover, we make the fidelity term in the model to be adaptive by replacing the original noisy signal with the last evolution of the smoothed image. Consequently, the proposed algorithm can better control the diffusion behavior than traditional multispectral diffusion-based algorithms. The experimental results verify that our algorithm can improve visual quality of the image and obtain better quality indices.     

Anisotropic diffusion for image denoising based on diffusion tensors

In this paper, the anisotropic diffusion for image denoising is considered. A new method to construct diffusion tensors is proposed. The tensors obtained by our approach depend on four directional derivatives of the intensity of an image, and hence they are adaptively determined by local image structure. It is shown that the proposed diffusion filter is isotropic in the interior of a region, whereas it is anisotropic at edges. This property of tensors allows us to efficiently remove noise in an image, particularly noise at edges. Several numerical experiments are conducted on both synthetic and real images.     

基于NSCT扩散的图像去噪增强方法

本文提出了一种基于非下采样Contourlet变换与非线性各向异性扩散的方法进行含噪图像的去噪和增强。首先对含噪图像进行非下采样Contourlet分解,对每个分解层的各个子带进行非线性收缩和拉伸,以达到抑制噪声和增强图像特征的目的。然后,对去噪增强后图像的Contourlet小系数进行空间域的非线性各向异性扩散,以去除由于进行非下采样Contourlet去噪所造成的为伪Gibbs现象和 side-band效应。实验结果表明,本文方法相比于无扩散的Wavelet和Contourlet方法相比,不仅对图像进行了去噪和增强,而且有效的抑制了伪Gibbs现象和 side-band效应。     

Orthogonal-directional forward diffusion image inpainting and denoising model

In this paper, an orthogonal-directional forward diffusion Partial Differential Equation （PDE） image inpainting and denoising model which processes image based on variation problem is proposed. The novel model restores the damaged information and smoothes the noise in image simultaneously. The model is morphological invariant which processes image based on the geometrical property. The regularization item of it diffuses along and cross the isophote, and then the known image information is transported into the target region through two orthogonal directions. The cross isophote diffusion part is the TV （Total Variation） equation and the along isophote diffusion part is the inviscid Helmholtz vorticity equation. The equivalence between the Helmholtz equation and the inpainting PDEs is proved. The model with the fidelity item which is used in the whole image domain denoises while preserving edges. So the novel model could inpaint and denoise simultaneously. Both theoretical analysis and experiments have verified the validity of the novel model proposed in this paper.     

一种改进的图像中脉冲噪声滤波方法

提出了一种估计脉冲噪声强度的方法,并针对传统中值滤波(MF)法在去除脉冲噪声时存在的不足,给出了一种由噪声检测和噪声滤波2个阶段组成的图像滤波方法.实验结果表明,采用本文估计方法获得的噪声强度偏差较小,噪声滤波方法能在有效去除噪声的同时保持图像的边缘.     

二维扩散方程边界元解法中的四重奇异积分计算

对二维热传导方程的Dirichlet初边值问题,采用带时间变量的基本解,利用基于单层位势的间接边界积分方程及其等价的Galerkin变分形式求解,该方法涉及到与时空相关的四重奇异积分的计算.在采用常单元离散的情况下,推导了具体实施数值计算所需的积分公式,完成了数值实验,验证了该方法的有效性和可行性.     

改进的分布式扩散符号LMS算法

针对无线传感器网络(WSN)中数据运算量大及传输速率受限问题,提出了在分布式扩散LMS算法中先后采用符号函数和改进的符号函数量化策略,实现对误差和估计信号的量化,以减少多节点无线传感器网络的运算量和通信量。仿真结果表明,采用符号函数的量化策略时,误差相对较大;采用改进的符号函数量化策略,在设定适当的量化门限时,所提出的算法性能十分接近非量化的扩散LMS算法,且优于非协作算法。特别对于BPSK信号,相较于传统的扩散LMS算法,性能更为优良。     

An improved finite-difference approximation to the diffusion equation

A higher order approximation to field quantities than the piecewise constant approximation commonly used and implicit in the second-order central difference approximation to the Helmholtz equation is described. The continuous finite-difference (CFD) approximation results in reduced error without an increase in complexity of the associated computational algorithm.