基于PDE的非线性图像去噪与增强

应用偏微分理论,提出一种改进的基于偏微分方程的非线性图像去噪与增强方法,对传统的P-M非线性扩散模型进行改进。首先将图像变换到梯度域,然后通过改变梯度域扩散函数来达到去噪和增强的目的。与以往的时域和频域图像去噪方法相比,本文方法不仅能有效去除噪声,还能很好地保留图像的纹理细节。文章采用有限差分法将偏微分方程离散化,并结合热方程简化计算复杂度,从而实现简单快速的计算过程,为实时的图像去噪与增强处理提供保证。     

A new adaptive coupled diffusion PDE for MRI Rician noise

Among different methods of image de-noising, partial differential equation (PDE)-based de-noising attracted much attention in the field of medical image processing. The benefit of PDE-based de-noising methods is the ability to smooth image in a nonlinear way, which effectively removes the noise as well as preserving edge through anisotropic diffusion (AD) controlled by the diffusive function. Today, AD filtering such as Perona and Malik (P–M) model is widely used for MR Image enhancement. However, the AD filter is non-optimal for MR images that have Rician noise. Originally, the PDE-based de-noising designed for additive Gaussian distributed noise was signal independent, but the Rician noise was signal dependent. In this paper, we proposed a new adaptive coupled diffusion PDE fitted with MRI Rician noise which not only preserved the edges and fine structures, but also performed efficient de-noising. Our method was an improved version of AADM (automatic parameter selection anisotropic diffusion for MR Images). For this purpose, we have presented a new adaptive method to estimate the standard deviation of noise. As the simulation results showed, our proposed diffusion effectively improved the improved signal-to-noise ratio (ISNR) and preserved edges more than P–M, AADM and unbiased NLM (UNLM—unbiased non-local means) methods to remove Rician noise in MR Images.     

基于二维小波收缩与非线性扩散的混合图像去噪算法

研究自适应滤波算法对改善图像质量具有重要意义.本文分析了非线性扩散和二维Haar小波收缩去噪方法之间的关系,从本质上说明了非线性扩散方法优于Haar小波收缩去噪方法.然后,给出了一种基于图像全变差(TV)模型的非线性扩散与二维Haar小波收缩相结合的混合图像去噪算法.该算法在图像小波分解的低频部分采用全变差扩散,在高频部分采用小波收缩方法.实验结果表明,混合去噪算法在计算复杂性与滤波效果上具有更好的综合性能.     

基于总变分和中值滤波的图像去噪方法

总变分图像去噪方法是一种经典的图像去噪算法,但是在噪声水平较高时容易产生虚假边缘,从而影响了去噪效果。为了克服总变分去噪算法容易产生虚假边缘的不足并有效地去除噪声,在此利用噪声的无方向性这一与边缘特性不同的特点,提出了一种结合中值滤波和总变分的图像去噪方法。为了说明该去噪算法的有效性,进行了大量的仿真实验。实验结果表明,该方法降噪效果明显,人眼能直观感受到图像质量的改善,在高噪声水平下,其峰值信噪比至少提高了1．2dB左右。     

Edge-forming methods for color image zooming.

This paper introduces edge-forming schemes for image zooming of color images by general magnification factors. In order to remove/reduce artifacts arising in image interpolation, such as image blur and the checkerboard effect, an edge-forming method is suggested to be applied as a postprocess of standard interpolation methods. The method is based on nonconvex nonlinear partial differential equations. The equations are carefully discretized, incorporating numerical schemes of anisotropic diffusion, to be able to form reliable edges satisfactorily. The alternating direction implicit (ADI) method is employed for an efficient simulation of the model. It has been numerically verified that the resulting algorithm can form clear edges in 2 to 3 ADI iterations. Various results are given to show th eeffectiveness and reliability of the algorithm.     

基于结构成分双向扩散的图像插值算法

该文提出一种基于结构成分双向扩散的插值方法,有效地减小了插值图像的边缘扩散,从而获得更为清晰的边缘。该方法采用改进的耦合双向扩散滤波器对轮廓模板插值图像进行边缘增强。其中,为了使滤波器更精确地作用于边缘轮廓,利用形态成分分析(MCA)分离出初始插值图像中的结构分量再实行滤波;同时,改进双向扩散模型,使其能够根据边缘梯度自适应地调整边缘扩散程度,且更加柔和地控制梯度方向的像素值变化。实验结果表明,对比传统的插值方法、相关的边缘自适应插值方法以及几种应用普遍的商用软件,该方法获得的插值图像主、客观质量均有明显提升,不仅有效提高图像锐度,且边缘光滑、过渡自然,避免产生边缘锯齿和过度的人工效应。     

基于B样条小波的偏微分方程图像去噪方法

提出一种基于B样条小波的偏微分方程图像去噪方法.先对图像进行B样条小波变换,将得到的高频系数采用偏微分方程方法去噪,迭代次数采用去相关最优停止准则进行控制;将得到的低频系数进行阈值处理,阈值选取采用基于信息熵的阈值选择策略,然后对处理后的小波系数进行B样条小波逆变换,得到去噪后的图像.数值实验表明,改进算法能克服B样条小波变换与偏微分方程去噪的不足,增强去噪能力,同时有效保护图像边缘和细节信息.     

Feature preserving image interpolation by adaptive bidirectional flow

Most image interpolation algorithms currently used suffer visually to some extent the effects of blurred edges and jagged artifacts in the image. This letter presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to enhance edges along the normal directions to the isophote lines （edges）, while a normal diffusion is done to remove artifacts （＂jaggies＂） along the tangent directions. In order to preserve image features such as edges, angles and textures, the nonlinear diffusion coefficients are locally adjusted according to the first order and the second order directional derivatives of the image. Experimental results on the Lena image demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.     

A Multi-Scale Gradient Algorithm Based on Morphological Operators

1 Introduction The performance of a watershed-based image segmentation method depends largely on the algorithm used to compute the gradient. Conventional morphological gradient operators[2~3] produce too many local minima because of noise and quantization…     

A Multi-Scale Gradient Algorithm Based on Morphological Operators

Watershed transformation is a powerful morphological tool for image segmentation. However, the performance of the image segmentation methods based on watershed transformation depends largely on the algorithm for computing the gradient of the image to be segmented. In this paper, we present a multi-scale gradient algorithm based on morphological operators for watershed-based image segmentation, with effective handling of both step and blurred edges. We also present an algorithm to eliminate the local minima produced by noise and quantization errors. Experimental results indicate that watershed transformation with the algorithms proposed in this paper produces meaningful segmentations, even without a region-merging step.     

多尺度形态梯度算法及其在图像分割中的应用

分水岭变换是一种适用于图像分割的强有力的形态工具.然而,基于分水岭变换的图像分割方法的性能在很大程度上依赖于用来计算待分割图像梯度的算法.本文首先提出了一种计算图像形态梯度的多尺度算法,对阶跃边缘和"模糊"边缘进行了有效的处理其次,提出了一种去除因噪声或量化误差造成的局部"谷底"的算法.实验结果表明,采用本文算法后进行分水岭变换,即使不进行区域合并也能产生有意义的分割,极大地减轻了计算负担.     

基于边缘特征的SAR图像目标检测方法

如何快速而准确地检测出SAR图像中的目标是一个极富挑战性的课题.利用图像边缘特征和模糊集理论设计了一种快速有效的SAR图像目标检测算法.该算法先利用模糊软阈值小波降噪方法去除相干斑噪声,然后用模糊边缘检测器检测出降噪图像的边缘,最后利用形态学操作算子提取出边缘图中的目标区域.与基于亮度特征以及基于纹理特征的检测算法相比,提出的检测算法能够快速、准确地检测出目标,而且产生的虚警数量较少.SAR实测数据的实验结果表明,提出的算法是有效的且具有很好的应用前景.     

基于总体变差模型的数字滤波器设计及其性能研究

根据经典总体变差恢复模型,设计了一种新型的应用于图像去噪的数字TV滤波器的一种算法。该新型滤波器是绝对稳定的低通滤波器,在抑制噪声的同时能够很好的保留图像的细节信息。与一般的统计滤波器不同,该滤波器充分利用了局部数据的梯度信息精确计算滤波器系数,滤波过程是图像自适应的。文中直接给出了新型滤波器固定的模板形式,使滤波过程简单易行。最后将新型滤波器与中值滤波器、均值滤波器、高斯滤波器等进行性能比较,效果更好。     

Robust anisotropic diffusion

Relations between anisotropic diffusion and robust statistics are described in this paper. Specifically, we show that anisotropic diffusion can be seen as a robust estimation procedure that estimates a piecewise smooth image from a noisy input image. The "edge-stopping" function in the anisotropic diffusion equation is closely related to the error norm and influence function in the robust estimation framework. This connection leads to a new "edge-stopping" function based on Tukey's biweight robust estimator that preserves sharper boundaries than previous formulations and improves the automatic stopping of the diffusion. The robust statistical interpretation also provides a means for detecting the boundaries (edges) between the piecewise smooth regions in an image that has been smoothed with anisotropic diffusion. Additionally, we derive a relationship between anisotropic diffusion and regularization with line processes. Adding constraints on the spatial organization of the line processes allows us to develop new anisotropic diffusion equations that result in a qualitative improvement in the continuity of edges.     

一维小波变换在时域光学相干层析成像中的应用

时域光学相干层析(OCT)系统通常采用短时傅里叶变换(STFT)完成干涉信号的解调和图像重构。短时傅里叶变换算法简单,但是在干涉信号解调时难以获得好的去噪效果,通常还需在二维(2D)图像域对重构图像进行去噪。该方法数据运算量大,集成度不高。将一维(1D)小波变换(WT)应用于时域光学相干层析成像技术,同时实现干涉信号解调、去噪和图像重构。算法将时域光学相干层析的干涉信号分解到各个不同的频率空间,保留包含调制频率的频率空间的小波系数,对保留的小波系数进行滤波去噪后进行逆变换即可实现对干涉信号的解调和去噪,对解调信号等间距采样实现图像重构。该方法数据运算量小,集成度高,结合先进的小波去噪技术可以大大提高重构图像的分辨率,具有良好的应用前景。     

连续和离散各向异性扩散方程行为的数值模拟

采用数值模拟的方法研究一维连续和离散各向异性扩散方程的行为差异.研究结果表明:当没有逆向扩散时,连续和离散方程的演化方式类似;当有逆向扩散时,连续方程不收敛,但其相对应的离散方程会在图像灰度函数的拐点处形成阶梯边缘.揭示了离散逆向扩散的一个重要特性:其扩散结果由图像灰度函数拐点的初始分布预先确定,而虚假阶梯边缘的形成是由于计算噪声引起了假拐点.提出了用约束图像灰度函数凸凹性的方法来避免由计算噪声引起的虚假阶梯边缘.该方法仅对计算噪声引起的虚假阶梯边缘有效,不能避免由观测/量化噪声或图像纹理拐点形成的虚假阶梯边缘.     

Fourth-order partial differential equations for noise removal

A class of fourth-order partial differential equations (PDEs) are proposed to optimize the trade-off between noise removal and edge preservation. The time evolution of these PDEs seeks to minimize a cost functional which is an increasing function of the absolute value of the Laplacian of the image intensity function. Since the Laplacian of an image at a pixel is zero if the image is planar in its neighborhood, these PDEs attempt to remove noise and preserve edges by approximating an observed image with a piecewise planar image. Piecewise planar images look more natural than step images which anisotropic diffusion (second order PDEs) uses to approximate an observed image. So the proposed PDEs are able to avoid the blocky effects widely seen in images processed by anisotropic diffusion, while achieving the degree of noise removal and edge preservation comparable to anisotropic diffusion. Although both approaches seem to be comparable in removing speckles in the observed images, speckles are more visible in images processed by the proposed PDEs, because piecewise planar images are less likely to mask speckles than step images and anisotropic diffusion tends to generate multiple false edges. Speckles can be easily removed by simple algorithms such as the one presented in this paper.     

一种适用于稀疏多径信道的自适应均衡算法

针对传统的自适应均衡算法在稀疏多径信道下性能表现不佳的问题,提出了一种基于基追踪降噪的自适应均衡算法。该算法利用稀疏多径信道下均衡器权值的稀疏性,将自适应均衡器的训练过程看作压缩感知理论中稀疏信号对字典的加权求和,并利用重构算法直接对稀疏权值进行求解,解决了迭代参数设置和收敛慢的问题。采用基追踪降噪作为重构算法并选用变量分离近似稀疏重构对该最优化问题进行求解,既提高了权值的重构精度又降低了计算的复杂度。仿真结果表明,所提算法能够以较低的计算量和较少的训练序列达到更优性能,这对提升系统的通信性能具有参考价值。     

基于变步长约瑟夫遍历和DNA动态编码的图像加密算法的安全性分析

近年来,不断有新的图像加密算法被提出,其安全性却未得到充分的分析和验证。该文对一种最新报道的图像加密算法的安全性进行了分析。所分析算法通过基于变步长约瑟夫遍历的像素置乱、基于DNA动态编码的像素替换及像素行列扩散来完成图像加密。分析表明,该算法的秘密密钥设计不具有实用性,加密过程也存在缺陷。在选择明文攻击条件下,对该算法的加密过程进行了密码分析,并提出了相应的攻击算法。仿真实验和理论分析确认了所提攻击算法的有效性与可行性。最后,针对所分析算法及部分图像加密算法中存在的问题,提出了改进建议。     

一种利用图像角点和边缘信息的阈值分割方法

阈值化算法是图像区域分割的一个基本算法.提出一种利用角点和边缘点的像素灰度值均值和全图像像素点灰度值均值加权相加的阈值选取方法.实验表明,该方法能对具有大面积目标的图像进行很好的分割.