Nonlinear scale-space filtering and multiresolution system

We derive and demonstrate a nonlinear scale-space filter and its application in generating a nonlinear multiresolution system. For each datum in a signal, a neighborhood of weighted data is used for clustering. The cluster center becomes the filter output. The filter is governed by a single scale parameter that dictates the spatial extent of nearby data used for clustering. This, together with the local characteristic of the signal, determines the scale parameter in the output space, which dictates the influences of these data on the output. This filter is thus adaptive and data driven. It provides a mechanism for (a) removing impulsive noise, (b) improved smoothing of nonimpulsive noise, and (c) preserving edges. Comparisons with Gaussian scale-space filtering and median filters are made using real images. Using the architecture of the Laplacian pyramid and this nonlinear filter for interpolation, we construct a nonlinear multiresolution system that has two features: (1) edges are well preserved at low resolutions, and (2) difference signals are small and spatially localized. This filter implicitly presents a new mechanism for detecting discontinuities differing from techniques based on local gradients and line processes. This work shows that scale-space filtering, nonlinear filtering, and scale-space clustering are closely related and provides a framework within which further image processing, image coding, and computer vision problems can be investigated.     

一种小波域与空域相结合的图像滤波方法

利用小波阈值去噪方法和传统空间域Lee 滤波的特点, 提出了一种图像去噪的的组合滤波方案。首先在小波域对图像阈值去噪, 得到预去噪图像; 再在空间域上利用自适应Wiener 滤波器进一步提高恢复图像的精度。为了保证小波域和空间域两种算法之间的匹配, 对预去噪图像中残留噪声的分布进行了研究, 对其噪声方差估计做了改进, 提出了一种估计噪声方差的近似最优公式。仿真实验表明, 与单独的在小波域或空域去噪相比, 该方法的均方误差和信噪比指标均得到了改善。     

一种小波域与空域相结合的图像滤波方法

利用小波阈值去噪方法和传统空间域Lee滤波的特点,提出了一种图像去噪的的组合滤波方案。首先在小波域对图像阈值去噪,得到预去噪图像;再在空间域上利用自适应Wiener滤波器进一步提高恢复图像的精度。为了保证小波域和空间域两种算法之间的匹配,对预去噪图像中残留噪声的分布进行了研究,对其噪声方差估计做了改进,提出了一种估计噪声方差的近似最优公式。仿真实验表明,与单独的在小波域或空域去噪相比,该方法的均方误差和信噪比指标均得到了改善。     

A spatially adaptive nonparametric regression image deblurring.

We propose a novel nonparametric regression metthod for deblurring noisy images. The method is based on the local polynomial approximation (LPA) of the image and the paradigm of intersecting confidence intervals (ICI) that is applied to define the adaptive varying scales (window sizes) of the LPA estimators. The LPA-ICI algorithm is nonlinear and spatially adaptive with respect to smoothness and irregularities of the image corrupted by additive noise. Multiresolution wavelet algorithms produce estimates which are combined from different scale projections. In contrast to them, the proposed ICI algorithm gives a varying scale adaptive estimate defining a single best scale for each pixel. In the new algorithm, the actual filtering is performed in signal domain while frequency domain Fourier transform operations are applied only for calculation of convolutions. The regularized inverse and Wiener inverse filters serve as deblurring operators used jointly with the LPA-design directional kernel filters. Experiments demonstrate the state-of-art performance of the new estimators which visually and quantitatively outperform some of the best existing methods.     

一种基于小波变换的雷达图像边缘提取方法

图像最基本的特征是边缘,边缘特征提取是多传感器信息融合与景象匹配中的重要内容.合成孔径雷达图像通常带有较强的相干斑噪声,用传统的边缘检测算法效果很不理想.本文针对合成孔径雷达自身的特点,利用小波变换的特性,提出一种将小波变换的多尺度分析与模糊加权中值滤波相结合的边缘特征提取方法.实验证明方法有效,边缘定位准确,并对噪声有抑制作用,将提取结果用于匹配,定位精度达到1个象素.     

Speckle filtering of SAR images based on adaptive windowing

Speckle noise usually occurs in synthetic aperture radar (SAR) images owing to coherent processing of SAR data. The most well-known image domain speckle filters are the adaptive filters using local statistics such as the mean and standard deviation. The local statistics filters adapt the filter coefficients based on data within a fixed running window. In these schemes, depending on the window size, there exists trade-off between the extent of speckle noise suppression and the capability of preserving fine details. The authors propose a new adaptive windowing algorithm for speckle noise suppression which solves the problem of window size associated with the local statistics adaptive filters. In the algorithm, the window size is automatically adjusted depending on regional characteristics to suppress speckle noise as much as possible while preserving fine details. Speckle noise suppression gets stronger in homogeneous regions as the window size increases succeedingly. In fine detail regions, by reducing the window size successively, edges and textures are preserved. The fixed-window filtering schemes and the proposed one are applied to both a simulated SAR image and an ERS-1 SAR image to demonstrate the excellent performance of the proposed adaptive windowing algorithm for speckle noise     

一种图像去噪的小波相位滤波改进算法

大多数的小波去噪方法都是基于图像小波幅度信息的,但对于低SNR图像来说,其小波域中的图像边缘信息被噪声掩盖,所以有人提出了对幅度不敏感的小波相位滤波算法,利用含噪图像分解后的相位信息来恢复图像,本文对这种算法作出了一些改进。在相位滤波的基础上,考虑Laplace邻域,试验结果表明比原算法效果好。     

Noise reduction for magnetic resonance images via adaptive multiscale products thresholding

Edge-preserving denoising is of great interest in medical image processing. This paper presents a wavelet-based multiscale products thresholding scheme for noise suppression of magnetic resonance images. A Canny edge detector-like dyadic wavelet transform is employed. This results in the significant features in images evolving with high magnitude across wavelet scales, while noise decays rapidly. To exploit the wavelet interscale dependencies we multiply the adjacent wavelet subbands to enhance edge structures while weakening noise. In the multiscale products, edges can be effectively distinguished from noise. Thereafter, an adaptive threshold is calculated and imposed on the products, instead of on the wavelet coefficients, to identify important features. Experiments show that the proposed scheme better suppresses noise and preserves edges than other wavelet-thresholding denoising methods.     

Noise adaptive soft-switching median filter

Existing state-of-the-art switching-based median filters are commonly found to be nonadaptive to noise density variations and prone to misclassifying pixel characteristics at high noise density interference. This reveals the critical need of having a sophisticated switching scheme and an adaptive weighted median filter. We propose a novel switching-based median filter with incorporation of fuzzy-set concept, called the noise adaptive soft-switching median (NASM) filter, to achieve much improved filtering performance in terms of effectiveness in removing impulse noise while preserving signal details and robustness in combating noise density variations. The proposed NASM filter consists of two stages. A soft-switching noise-detection scheme is developed to classify each pixel to be uncorrupted pixel, isolated impulse noise, nonisolated impulse noise or image object's edge pixel. "No filtering" (or identity filter), standard median (SM) filter or our developed fuzzy weighted median (FWM) filter will then be employed according to the respective characteristic type identified. Experimental results show that our NASM filter impressively outperforms other techniques by achieving fairly close performance to that of ideal-switching median filter across a wide range of noise densities, ranging from 10% to 70%     

基于复小波方向信息的SAR图像斑点噪声抑制

针对一般小波去噪方法在去除合成孔径雷达(Synthetic Aperture Radar-SAR)图像斑点噪声时不能有效保持图像边缘信息的问题,提出结合双密度双树复小波变换（Double-Density Dual Tree Complex Wavelet Transform –DD_DTCWT）方向信息进行边缘检测的SAR图像噪声抑制算法。本文对边缘检测指标进行改进,利用DD_DTCWT方向复小波系数的相对方差作为边缘检测指标,通过相对方差分布密度函数获取阈值处理的自适应门限,由此实现SAR图像的自适应滤波。实验结果表明,本文提出的边缘检测和主方向高频复系数提升方法可以有效保持并增强图像的边缘信息。与SRAD算法和基于DD_DTCWT的双变量收缩函数（Bivariate Shrinkage Function--BSF）算法相比较,本文算法具有更好的边缘保持能力。      

基于多尺度边缘响应函数的自适应阈值边缘检测算法

该文提出了一种基于多尺度边缘响应函数的自适应阈值边缘检测算法。首先分析二进小波变换,根据边缘和噪声随尺度变化的不同特性,设计了多尺度边缘响应函数(MERF)。通过MERF中的乘积放大作用,增大了边缘响应的幅度,同时也抑制了噪声产生的伪边缘。然后利用小波变换多尺度之间的联合分布关系,计算自适应阈值,检测MERF的梯度模值形成多尺度边缘。该算法直接在小波特征上进行多尺度合成,避免了多个边缘图合成过程的病态问题。实验表明,与LOG,Canny以及Mallat多尺度小波检测方法相比,该算法在检测和定位之间能够达到更好的平衡,既能够实现小尺度下的精确定位,也可以保留大尺度下对噪声的抑制作用。     

同态非局部滤波在激光主动成像散斑抑制中的应用研究

传统的激光主动成像散斑抑制方法中,局部单像素滤波和变换域滤波难以取得良好的抑制效果,同时容易导致边缘展宽,对图像信息造成破坏。鉴于非局部滤波对加性噪声的优异去噪性能,本文研究了三种具有代表性的非局部滤波方法,并使用半导体泵浦固体脉冲激光器搭建主动成像系统,进行散斑噪声抑制性能的比较。实验表明,采用同态FMPatchGP不仅能够有效抑制散斑噪声,而且能很好地保持边缘信息,同时满足实时性处理的要求,在激光主动照明系统中具有良好的应用前景。     

基于双正交小波域的SAR图像滤波方法

将E-lee、E-Kuan、GammaMap、wiener等经典滤波算法和双正交小波变换相结合,提出了基于双正交小波变换域的局部统计特性SAR图像滤波方法,同时提出了一个运算量少,且是归一化的对数变换,它将乘性的Speckle噪声转为加性噪声。在小波域内建立了局部统计特性SAR图像滤波算法,使用多分辨率的手段,因为在每个方向上的小波系数都具有相同的特征,可以很好地处理图像的一些特性,使得图像边缘被模糊的相对少些。实验结果表明,此方法比经典算法的效果要好。     

Adaptive two-pass rank order filter to remove impulse noise in highly corrupted images

In this paper, we present an adaptive two-pass rank order filter to remove impulse noise in highly corrupted images. When the noise ratio is high, rank order filters, such as the median filter for example, can produce unsatisfactory results. Better results can be obtained by applying the filter twice, which we call two-pass filtering. To further improve the performance, we develop an adaptive two-pass rank order filter. Between the passes of filtering, an adaptive process is used to detect irregularities in the spatial distribution of the estimated impulse noise. The adaptive process then selectively replaces some pixels changed by the first pass of filtering with their original observed pixel values. These pixels are then kept unchanged during the second filtering. In combination, the adaptive process and the second filter eliminate more impulse noise and restore some pixels that are mistakenly altered by the first filtering. As a final result, the reconstructed image maintains a higher degree of fidelity and has a smaller amount of noise. The idea of adaptive two-pass processing can be applied to many rank order filters, such as a center-weighted median filter (CWMF), adaptive CWMF, lower-upper-middle filter, and soft-decision rank-order-mean filter. Results from computer simulations are used to demonstrate the performance of this type of adaptation using a number of basic rank order filters.     

基于差分法的噪声检测和变分法的图像滤波算法

针对图像的椒盐噪声滤除算法中,在噪声检测阶段对噪声点的检测通常不够准确,在噪声恢复阶段,又缺乏对边缘信息的保护,文中提出了一种两步复原法,以用于复原被脉冲噪声破坏的模糊图像。算法将滤噪过程分为噪声检测和噪声恢复阶段。噪声检测过程中,在滑动窗口扩大当前的像素值和其他像素值之间的有序差异,来确定当前像素是否为噪声像素。而在噪声恢复过程中利用变分法,确保图像的边缘和细节。实验结果表明,文中所提检测、降噪方法在噪声密度较高的情况下,优于其他算法。     

一种基于数学形态学与小波域增强的滤波算法

为了有效滤除图像高斯噪声,将数学形态学与小波域增强相结合,提出了一种高斯噪声新型滤波算法.该算法首先将噪声图像进行二维小波分解,得到低频和高频子图像;然后保留低频子图像不变,对各高频子图像根据其噪声分布特点分别设计出多角度、多结构逐级形态学滤波器进行滤波处理,并进行小波分解系数重构;最后对经过形态学滤波后的图像进行2层小波分解,通过设计出一种新型小波增强函数对不同幅值的小波系数进行不同程度的收缩处理,在此基础上进行分解系数重构.将自适应中值滤波与数学形态学滤波与本文算法进行比较,实验证明本文滤波算法其去噪效果优于前两种算法.     

Propagated guided image filtering for edge-preserving smoothing

This paper proposes an edge-preserving smoothing filtering algorithm based on guided image filter (GF). GF is a well-known edge-preserving smoothing filter, but is ineffective in certain cases. The proposed GF enhancement provides a better solution for various noise levels associated with image degradation. In addition, halo artifacts, the main drawback of GF, are well suppressed using the proposed method. In our proposal, linear GF coefficients are updated sequentially in the spatial domain by using a new cost function, whose solution is a weighted average of the neighboring coefficients. The weights are determined differently depending on whether the pixels belong to the edge region, and become zero when a neighborhood pixel is located within a region separated from the center pixel. This propagation procedure is executed twice (from upper-left to lower-right, and vice versa) to obtain noise-free edges. Finally, the filtering output is computed using the updated coefficient values. The experimental results indicate that the proposed algorithm preserves edges better than the existing algorithms, while reducing halo artifacts even in highly noisy images. In addition, the algorithm is less sensitive to user parameters compared to GF and other modified GF algorithms.     

Adaptive image restoration using local statistics and directional gradient information

We present an adaptive restoration algorithm to effectively restore an image degraded by additive white Gaussian noise using local statistics and directional gradient information in the spatial domain. The proposed algorithm is a modified Lee algorithm considered to compensate its drawback that little noise is removed at edge regions even though the edges are well preserved. Experimental results show better performance than for conventional algorithms.     

自适应调节滤波强度的SAR图像非局部平均抑斑算法

为提升对SAR图像乘性相干斑的抑制水平与边缘保护性能,该文提出了一种可自适应调节滤波强度(AFS)的SAR图像非局部平均(NLM)抑斑新算法(AFS-NLM)。该算法利用Frost滤波图像计算的局部均值与方差来改善SAR图像场景参量的估计,形成了一种能更好刻画SAR图像同质区与边缘区的改进Kuan滤波系数。利用局部均值比与改进Kuan滤波系数分别作为新的相似性测量参量与自适应衰减因子,构建了一种更适应SAR图像乘性噪声特性的改进NLM滤波。利用偏平滑参数与偏边缘保护参数控制下的改进NLM滤波,分别替代经典Kuan滤波模型中的像素局部均值与自身灰度值作为加权项,并采用由改进Kuan滤波系数构建的自适应调节因子对二者进行加权平均,从而形成了一种可自适应调节滤波强度的加权滤波新模型。实验表明,该文算法与近期多种先进算法相比,具有更好的相干斑抑制与边缘保护性能。     

基于自适应滤波的单像素宽形态学边缘检测

为了进一步提高边缘检测算法的抗噪性和定位精度,提出了一种基于自适应滤波的单像素宽形态学边缘检测算法。首先,分别对图像进行中值滤波和加权均值滤波,并通过自适应调整中值滤波结果和加权均值滤波结果所占的权重抑制脉冲噪声和高斯噪声。然后根据不同取向的结构元素可以有效地检测出不同走向的边缘细节这一特性,定义了一种具有方向估计的形态学梯度,并利用其检测图像的边缘,最后沿梯度方向进行非极大值抑制以获取单像素宽边缘。实验结果表明,本文算法不仅能够准确地检测图像边缘,而且具有较好的抗噪性能,处理速度也较快。