基于边缘定向扩散方程的图像复原方法

讨论了光学图像中同时存在噪声与模糊时的复原问题。采用一种能根据边缘方向自适应选取扩散系数的各向异性扩散方程来约束复原后的图像的光滑性质,将其和图像复原模型一起使用,得到了一种图像复原的正则化模型,并利用Eluer方程将该模型转换成一种可以快速求解的各向异性非线性扩散模型。在光滑性约束项的构造上,构造了一种基于边缘定向扩散的各向异性张量型扩散方程,能有效地根据边缘的方向确定是增强边缘还是滤除噪声。相比图像复原的迭代正则化方法,新方法能在复原图像的同时有效地抑制噪声,并有效地减轻边缘处的振铃效应。数值计算结果表明,新方法在整幅图像的复原效果上明显强于迭代正则化方法,尤其在对背景噪声的抑制上效果更明显,峰值信噪比（PSNR）也比迭代正则化方法平均提高了约2dB。     

泊松噪声模糊图像的边缘保持变分复原算法

从贝叶斯估计出发,构造了一种新的变分模型,用于复原被泊松噪声污染的模糊图像.首先讨论了模型正则化项中具有边缘保持能力的函数选取以及模型求解的相关问题,然后将变分模型的求解转化为可快速求解的非线性扩散方程,给出了正则化参数选取的初步空间自适应方法,可以区分平滑区域和图像边缘自适应的调节参数.实验结果表明,本文方法的复原效果整体上优于传统的迭代正则化方法,复原图像的边缘得到了有效的保护,泊松噪声的抑制效果明显,复原图像提高的改进信噪比(ISNR)要比迭代正则化方法平均提高1 dB以上.     

基于正则化变分模型的SAR图像增强方法

讨论合成孔径雷达（SAR）图像的噪声抑制与分辨率增强问题.建立偏微分方程抑噪方法与正则化点增强方法相结合的正则化变分模型,该模型同时具有偏微分方程模型的抑噪优势和正则化模型的分辨率增强优势.在图像的背景区域采用偏微分方程模型进行噪声抑制,而在图像的目标区域,先采用后向扩散方程进行锐化,然后再采用正则化模型进行分辨率增强,使整幅图像的处理结果均得到优化.此外,在偏微分方程抑噪模型的构造上,结合SAR成像的工程背景,提出了基于SAR图像幅度信息的前向-后向扩散方程,使方程能有效抑制图像背景区域的噪声并锐化目标边缘.大量的试验结果表明该方法能有效增强目标的强散射点,显著抑制噪杂波区的噪声.     

基于边缘定向增强的各向异性扩散抑噪方法

本文提出了一个新的边缘定向增强扩散模型.针对现有各向异性扩散方程中,边缘增强扩散模型不能正确地对边缘定向,而相干增强扩散模型易在光滑处产生虚假边缘的缺点,本文的模型采用基于非线性光滑算子的边缘定向算子对边缘定向,并根据边缘的位置和方向设置扩散张量的特征根,使其在光滑区域沿边缘方向和垂直边缘方向均具有较大值,而在边缘区域垂直边缘方向值小,沿边缘方向值大,从而达到既保护边缘又去除噪声的目的,在整幅图像上均具有较好的去噪效果.理论分析和数值计算结果均表明,本文方法具有比现有扩散去噪方法更好的去噪效果,同时在峰值信噪比和边缘保护指数方面具有显著优势.     

高阶正则逆扩散变分图像增强模型

利用逆扩散方程增强图像是对图像退化过程的逆处理,但由于逆扩散方程对图像高频信息敏感,极易造成噪声的放大和振荡的产生.针对以上问题,提出了一种引入高阶正则项约束的逆扩散变分图像增强模型.新模型由逆扩散项及高频抑制项组成,高频抑制项通过最小化图像高频信息能量能够有效减少逆扩散方程产生的噪声放大和振荡.用该模型增强图像,图像的边缘和纹理信息更加清晰,同时能够有效抑制高频噪声的产生.     

一种改进的方向扩散方程滤波方法

利用方向扩散方程去噪时,噪声滤除的同时边缘也很快模糊了.基于这一缺陷,本文用各向异性扩散算子代替了方向扩散方程第一项中的拉普拉斯算子,并在方程的两个扩散项前加上了不同的扩散系数,以保证算法既能快速扩散去除噪声,又能较好保留边缘.而且,当新模型中的初始逼近图像退化为常数时,本文模型就退化为Perona-Malik扩散方程,因此Perorm-Malik扩散方程是本文新模型的一个特例.实验结果和客观数据分析均表明本文算法在保留边缘方面具有明显的效果.     

有效保持细节特征的图像椒盐噪声滤除方法

 论文结合几种去噪方法,提出一种统一的图像去噪模型.该模型通过一个统一的目标函数将图像去噪问题转化为最优化问题,目标函数的构造主要包括估计残差惩罚函数、局部权函数及正则化项三个方面.随后基于此模型提出一种新的去除椒盐噪声的非线性滤波方法,其中估计残差惩罚函数采用L1范数形式,局部权函数采用自适应高斯核函数,正则化项则利用图像的小波域稀疏性作为先验约束来构造.由于充分融合了图像的全局和局部统计特性,因而在抑制噪声的同时能够更好地保持图像边缘等细节特征,相关去噪实验结果证实了本文方法的有效性.     

基于模糊增强信息的图像边缘检测改进算法

针对经典的Pal和King模糊增强算法存在的固有缺陷,提出改进的模糊增强算法;为增强图像的对比度而获取更多的图像边缘细节信息,提出基于模糊对比度的图像增强算法;结合全局模糊增强与局部模糊对比度增强两种算法思想,提出基于模糊增强信息的图像边缘检测改进算法,由于该算法在增强图像边缘细节信息的同时也增强了噪声,因此,采用中值平滑滤波方法消除噪声.实验证明,该算法取得了良好的边缘检测效果.     

基于熵变分的图像放大模型

针对传统图像放大处理过程中出现的边缘模糊和噪声干扰问题,分析了Tikhonov正则化模型对带噪图像放大处理的缺陷.在最大后验估计(MAP)和熵理论基础上,提出了一种基于熵变分的带噪图像放大模型及其算法.该算法利用图像像素点梯度信息自适应的各向异性滤波处理,在较好的保持图像边缘锐度的同时有效地克服了图像噪声的影响,理论分析和实验结果皆表明此算法的有效性.     

基于BTV正则项的图像超分辨率重建改进算法

文章在最大后验概率(MAP)随机正则化理论框架下,采用L1范数来构造数据保真项,同时为了更好的保持重建图像边缘,在结合双边滤波(BTV)正则项的基础上,提出了一种能有效利用图像梯度大小和方向信息的正则化模型.实验结果表明,此方法与L1范数结合BTV正则项经典算法相比,能更好的抑制噪声和保持边缘,且在视觉效果和客观评价两...     

Anisotropic nonlinear diffusion approach to single image resolution enhancement

In many image resolution enhancement applications, the blurring process of the imaging system is unknown. This paper discusses the problem of single image blind resolution enhancement without estimating the point spread function （PSF）. A regularization model is constructed for image enhancement based on the prior informaton of image error and image gray value,which does not need any prior in- formation of PSF. Moreover, through the solution of Euler equations, an an isotropic nonlinear diffusion equation are obtained,which can avoid the high computational cost of regularization model. Furthermore,in order to get sub-pixel superresolved image, the regularization model for image enhancement is extended to the enlargement of image, which can enlarge and enhance image at the same time. Last,to get clearer edges, a high frequency enhancement filter is used on the superresolved image. Numerical results show that the new model can get much clearer super-resolution images than traditional methods, and the peak signal to noise ratios （PSNRs） are also higher than traditional methods.     

一种改进的图像去噪与增强模型

图像的去噪和增强越来越成为制约后续图像一系列处理的瓶颈,为此提出一种图像去噪与增强的混合模型。该模型在各向异性扩散模型的基础上引入边缘指示函数,达到快速识别边缘的目的;在冲击滤波器的基础上,引入含有时间变量的边缘判定函数,适时控制冲击幅度的大小。而后将上述两个模型结合起来,克服了扩散模型仅依赖梯度信息来控制扩散进程的弊端,也适时地锐化了边缘。实验表明该混合模型不仅可以很好地去除图像的斑点噪声,并且可以达到图像增强效果。     

Despeckling low SNR, low contrast ultrasound images via anisotropic level set diffusion

Speckle is a form of multiplicative and locally correlated noise which degrades the signal-to-noise ratio (SNR) and contrast resolution of ultrasound images. This paper presents a new anisotropic level set method for despeckling low SNR, low contrast ultrasound images. The coefficient of variation, a speckle-robust edge detector is embedded in the well known geodesic “snakes” model to smooth the image level sets, while preserving and sharpening edges of a speckled image. The method achieves much better speckle suppression and edge preservation compared to the traditional anisotropic diffusion based despeckling filters. In addition, the performance of the filter is less sensitive to the speckle scale of the image and edge contrast parameter, which makes it more suitable for the detection of low contrast features in an ultrasound image. We validate the method using both synthetic and real ultrasound images and quantify the performance improvement over other state-of-the-art algorithms in terms of speckle noise reduction and edge preservation indices.     

一种改进的各向异性扩散模型

各项异性扩散方程是一种经典的图像去噪方法,但该方法在去除噪声的过程中会造成一定程度的模糊边缘。对此文中提出了一种基于改进的各向异性扩散方程的图像去噪方法,通过在其能量泛函的目标函数中添加残差项,使能量泛函的极小解更加接近原始的函数,可取得比其更好的去噪效果。文中方法可看作是各项异性扩散方程和全变差模型的结合。实验表明,新提出的方程相对经典的方程有较好的边界处理效果和更高的信噪比。     

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.     

非线性扩散方程在SAR图像噪声抑制中的应用

将光学图像加性噪声抑制的非线性扩散方程引入到SAR图像相干斑抑制中，通过分析SAR图像的相干斑噪声模型在功率图像域以及功率图像的对数域上的表现特性，说明了基于加性噪声模型的非线性扩散方程在SAR图像噪声抑制中的应用可能性，并由此设计了基于非线性扩散方程的SAR图像噪声抑制算法。计算结果表明，与现有的SAR噪声抑制方法相比，非线性扩散方程方法具有更强的对背景区域的噪声抑制能力，且能更好地保持目标特征。     

Smoothing low-SNR molecular images via anisotropic median-diffusion

We propose a new anisotropic diffusion filter for denoising low-signal-to-noise molecular images. This filter, which incorporates a median filter into the diffusion steps, is called an anisotropic median-diffusion filter. This hybrid filter achieved much better noise suppression with minimum edge blurring compared with the original anisotropic diffusion filter when it was tested on an image created based on a molecular image model. The universal quality index, proposed in this paper to measure the effectiveness of denoising, suggests that the anisotropic median-diffusion filter can retain adherence to the original image intensities and contrasts better than other filters. In addition, the performance of the filter is less sensitive to the selection of the image gradient threshold during diffusion, thus making automatic image denoising easier than with the original anisotropic diffusion filter. The anisotropic median-diffusion filter also achieved good denoising results on a piecewise-smooth natural image and real Raman molecular images.