Oriented speckle reducing anisotropic diffusion.

Ultrasound imaging systems provide the clinician with noninvasive, low-cost, and real-time images that can help them in diagnosis, planning, and therapy. However, although the human eye is able to derive the meaningful information from these images, automatic processing is very difficult due to noise and artifacts present in the image. The speckle reducing anisotropic diffusion filter was recently proposed to adapt the anisotropic diffusion filter to the characteristics of the speckle noise present in the ultrasound images and to facilitate automatic processing of images. We analyze the properties of the numerical scheme associated with this filter, using a semi-explicit scheme. We then extend the filter to a matrix anisotropic diffusion, allowing different levels of filtering across the image contours and in the principal curvature directions. We also show a relation between the local directional variance of the image intensity and the local geometry of the image, which can justify the choice of the gradient and the principal curvature directions as a basis for the diffusion matrix. Finally, different filtering techniques are compared on a 2-D synthetic image with two different levels of multiplicative noise and on a 3-D synthetic image of a Y-junction, and the new filter is applied on a 3-D real ultrasound image of the liver.     

一种散斑模式的噪声统计模型与自适应滤波方法

本文介绍了一种实际散斑模式的数学模型和噪声统计模型,并提出了一种针对这种模型的自适应次优滤波方法。文中在分析了散斑模式及其噪声性质的基础上,利用其局部方向性特征,结合最优线性滤波器和非线性滤波器的特点,对线性最小均方误差滤波器进行了自适应逼近。实验结果表明,对散斑模式而言,本文的滤波方法与其它常用的图象滤波方法相比,具有更好的去噪和边缘保护性能,并且具有较好的滤波韧性。     

A STATISTICAL NOISE MODEL AND MATHEMATICAL MODEL OF SPECKLE PATTERN AND ADAPTIVE FILTERING APPROACH

A statistical noise model and a mathematical model for real speckle pattern are presented in this paper, and then, in view of the models, a new adaptive suboptimal image filtering approach is proposed. The proposed approach, with the local direction features of speckle pattern, combines the characteristics of optimal linear filter with non-linear filter and is an adaptive approximation to linear minimum mean square error filter. Experimental results show that the proposed approach has fairly good edge-preserved performance, compared with other present image filters, as well as much better filtering performance and robustness for speckle pattern.     

A new image smoothing method based on a simple model of spatialprocessing in the early stages of human vision

The difficulty of preserving edges is central to the problem of smoothing images. The main problem is that of distinguishing between meaningful contours and noise, so that the image can be smoothed without loss of details. Substantial efforts have been devoted to solving this difficult problem, and a plethora of filtering methods have been proposed in the literature. Non-linear filters have proved to be more efficient than their linear counterparts. Here, a new nonlinear filter for noise smoothing is introduced. This filter is based on the psychophysical phenomenon of human visual contrast sensitivity. Results on real images are presented to demonstrate the validity of our approach compared to other known filtering methods.     

Local noise weighted filtering for emphysema scoring of low-dose CT images

Computed tomography (CT) has become the new reference standard for quantification of emphysema. The most popular measure of emphysema derived from CT is the pixel index (PI), which expresses the fraction of the lung volume with abnormally low intensity values. As PI is calculated from a single, fixed threshold on intensity, this measure is strongly influenced by noise. This effect shows up clearly when comparing the PI score of a high-dose scan to the PI score of a low-dose (i.e., noisy) scan of the same subject. In this paper, the noise variance (NOVA) filter is presented: a general framework for (iterative) nonlinear filtering, which uses an estimate of the spatially dependent noise variance in an image. The NOVA filter iteratively estimates the local image noise and filters the image. For the specific purpose of emphysema quantification of low-dose CT images, a dedicated, noniterative NOVA filter is constructed by using prior knowledge of the data to obtain a good estimate of the spatially dependent noise in an image. The performance of the NOVA filter is assessed by comparing characteristics of pairs of high-dose and low-dose scans. The compared characteristics are the PI scores for different thresholds and the size distributions of emphysema bullae. After filtering, the PI scores of high-dose and low-dose images agree to within 2%-3% points. The reproducibility of the high-dose bullae size distribution is also strongly improved. NOVA filtering of a CT image of typically 400 x 512 x 512 voxels takes only a couple of minutes which makes it suitable for routine use in clinical practice.     

Partition-based vector filtering technique for suppression of noise in digital color images.

A partition-based adaptive vector filter is proposed for the restoration of corrupted digital color images. The novelty of the filter lies in its unique three-stage adaptive estimation. The local image structure is first estimated by a series of center-weighted reference filters. Then the distances between the observed central pixel and estimated references are utilized to classify the local inputs into one of preset structure partition cells. Finally, a weighted filtering operation, indexed by the partition cell, is applied to the estimated references in order to restore the central pixel value. The weighted filtering operation is optimized off-line for each partition cell to achieve the best tradeoff between noise suppression and structure preservation. Recursive filtering operation and recursive weight training are also investigated to further boost the restoration performance. The proposed filter has demonstrated satisfactory results in suppressing many distinct types of noise in natural color images. Noticeable performance gains are demonstrated over other prior-art methods in terms of standard objective measurements, the visual image quality and the computational complexity.     

基于同态滤波与直方图均衡化的射线图像增强

针对同态滤波与直方图均衡化单独进行X射线图像增强时存在的不足,提出了在频域内将同态滤波与直方图均衡化结合使用的思想.首先,对X射线图像进行同态滤波的分频处理;再将得到的低频分量进行全局的直方图均衡化处理;最后,将高频分量跟低频分量进行线性融合.实验结果表明,经过该方法处理的X射线图像,边缘信息更加突出,且整体视觉效果更明亮清晰.通过分析均方根误差和信噪比数据,也证实了该方法能有效地增强X射线图像.     

An effective 2-stage method for removing impulse noise in images

In this paper, a robust 2-stage impulse noise removal system is proposed to remove impulse noise from extremely corrupted images. The contributions are in two-fold. First, a neuro-fuzzy based impulse noise detector (NFIDET) is introduced to identify the noisy pixels. NFIDET is a powerful noise detector that can handle image corruption even up to 90% with zero miss and false detection rate with a simple neuro-fuzzy structure. This is the best result among the other impulse noise detectors in the literature. Second, this paper presents a new approach for weight calculation of adaptive weighted mean filter by using robust statistical model. An adaptive robust weighted mean (ARWM) filter removes a detected noisy pixel by adaptively determining filtering window size and replacing a noisy pixel with the weighted mean of the noise-free pixels in its window. A Geman–McClure robust estimation function is used to estimate the weights of the pixels. Simulation results also show that the proposed robust filter substantially outperforms many other existing algorithms in terms of image restoration.     

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.     

基于提升小波变换的红外图像双重滤波算法

为了有效抑制红外图像中的随机噪声,采用一种基于提升小波变换的双重滤波算法来进行处理。该算法对含有噪声的红外图像实现第1次提升小波分解,然后对获得的低频和高频分解系数再次实现提升小波变换,舍弃由低频系数经过第2次提升小波变换后获得的低频系数以及由高频系数经过第2次提升小波变换后获得的高频系数。对剩余的高频系数和低频系数分别采用改进阈值函数模型以及改进非局部均值滤波算法进行处理,在此基础上实现小波系数重构。为了改善滤波后图像视觉效果,再引入直方图均衡化算法进行处理。通过理论分析和实验验证,获得了相关的标准测试图像和红外图像测试结果以及峰值信噪比和结构相似度测试数据。结果表明,该滤算法对于高质量地去除红外图像中的噪声是有帮助的。     

Fuzzy two-step filter for impulse noise reduction from color images.

A new framework for reducing impulse noise from digital color images is presented, in which a fuzzy detection phase is followed by an iterative fuzzy filtering technique. We call this filter the fuzzy two-step color filter. The fuzzy detection method is mainly based on the calculation of fuzzy gradient values and on fuzzy reasoning. This phase determines three separate membership functions that are passed to the filtering step. These membership functions will be used as a representation of the fuzzy set impulse noise (one function for each color component). Our proposed new fuzzy method is especially developed for reducing impulse noise from color images while preserving details and texture. Experiments show that the proposed filter can be used for efficient removal of impulse noise from color images without distorting the useful information in the image.     

Sharpening vector median filters

A sharpening vector median (VM) filter for simultaneous denoising and enhancing vector-valued signals is introduced. This filter uses the trimmed aggregated distance minimization concept and robust vector order statistics to enhance edges and image details while retaining the noise removal characteristics of the standard VM operator. The procedure accommodates various design, implementation and application objectives by enhancing the vector-valued signals depending on the local image statistics and/or the user's needs. The filter properties discussed in this paper are proven and suggest that the proposed solution is a robust vector processing operator. The performance and efficiency of the filter are analyzed and commented upon. Examples from its application to color image filtering and virtual restoration of artworks are provided.     

一种基于图像结构保持降低SAR图像斑点噪声的非局部均值滤波

本文提出一种针对合成孔径雷达（SAR）图像保持结构的斑点去除（SPSR）非局部均值滤波算法,它基于图像的非局部自相似性。该SPSR算法的独特之处在于对相似结构中像素的辨识度强,因此可在散斑滤除的过程中避免图像模糊。为缓解散斑噪声对相似性测量的影响,两级过滤方案引入其中。滤波的第一阶段旨在得到一个结构相似性更精确的相似值,然后依据相似度大小对这区域实施强度不一的扩散滤波。与传统滤波器相比,该算法大大提高了散斑滤除的性能,同时,图像的结构保持更完好。     

Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography

A comparison between two nonlinear diffusion methods for denoising OCT images is performed. Specifically, we compare and contrast the performance of the traditional nonlinear Perona-Malik filter with a complex diffusion filter that has been recently introduced by Gilboa et al.. The complex diffusion approach based on the generalization of the nonlinear scale space to the complex domain by combining the diffusion and the free Schridinger equation is evaluated on synthetic images and also on representative OCT images at various noise levels. The performance improvement over the traditional nonlinear Perona-Malik filter is quantified in terms of noise suppression, image structural preservation and visual quality. An average signal-to-noise ratio (SNR) improvement of about 2.5 times and an average contrast to noise ratio (CNR) improvement of 49% was obtained while mean structure similarity (MSSIM) was practically not degraded after denoising. The nonlinear complex diffusion filtering can be applied with success to many OCT imaging applications. In summary, the numerical values of the image quality metrics along with the qualitative analysis results indicated the good feature preservation performance of the complex diffusion process, as desired for better diagnosis in medical imaging processing.     

Statistical properties of local extrema in two-dimensional Gaussianrandom fields

This paper is concerned with the statistical properties of the local extrema and local maxima of two-dimensional (2D) Gaussian random fields (GRFs). A GRF may be represented by a linear filtering operation on a white noise field; the spatial properties of the GRF are then determined by the shape of the filter kernel function. New expressions are derived for the mean spatial density of local extrema and for the distribution of local extrema in a 2-D random field. The work is motivated by the problem of detecting known structures in images using 2D matched filters. The new results enable accurate performance predictions to be made of the reliability of such filters in the presence of noise. Case studies are presented for several well-known 2-D filter kernel functions     

A multidimensional nonlinear edge-preserving filter for magneticresonance image restoration

The paper presents a multidimensional nonlinear edge-preserving filter for restoration and enhancement of magnetic resonance images (MRI). The filter uses both interframe (parametric or temporal) and intraframe (spatial) information to filter the additive noise from an MRI scene sequence. It combines the approximate maximum likelihood (equivalently, least squares) estimate of the interframe pixels, using MRI signal models, with a trimmed spatial smoothing algorithm, using a Euclidean distance discriminator to preserve partial volume and edge information. (Partial volume information is generated from voxels containing a mixture of different tissues.) Since the filter's structure is parallel, its implementation on a parallel processing computer is straightforward. Details of the filter implementation for a sequence of four multiple spin-echo images is explained, and the effects of filter parameters (neighborhood size and threshold value) on the computation time and performance of the filter is discussed. The filter is applied to MRI simulation and brain studies, serving as a preprocessing procedure for the eigenimage filter. (The eigenimage filter generates a composite image in which a feature of interest is segmented from the surrounding interfering features.) It outperforms conventional pre and post-processing filters, including spatial smoothing, low-pass filtering with a Gaussian kernel, median filtering, and combined vector median with average filtering.     

A study of the generalized morphological filter

A new class of morphological filters is proposed for image enhancement. The filter, known as the generalized morphological filter (GMF), uses multiple structuring elements and combines linear and morphological operations. The GMF can be designed to suppress various types of noise yet preserve geometrical structure in an image. A study of several aspects of the performance of the filter is presented. The study includes geometrical feature preservation, noise suppression, structuring element selection, and the root signal structure. For the sake of comparison, averaging and median filters are also used in the experiments and corresponding figures of merit of the performance of the filter. The empirical study shows that the generalized morphological filter possesses effective noise suppression with reduced geometrical feature blurring.This work was supported by the National Science Foundation, under Grant No. CDR-8803017 to the Engineering Research Center for Intelligent Manufacturing Systems.     

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.     

一种基于同态滤波的红外图像增强新方法

针对红外图像分辨率低,对比度低,噪声大等不足,提出了一种基于同态滤波的红外图像增强新方法。这种方法首先用自适应中值滤波对红外图像进行去噪,保证噪声不被增强;然后利用同态滤波的原理,对图像细节进行增强。为了克服同态滤波结果所存在缺陷,最后联合使用限制对比度自适应直方图均衡进一步调整图像的动态范围。实验结果验证本文方法对红外图像的分辨率和对比度增强有很好的效果。     

Diffusion PDEs on vector-valued images

In this article, we propose a local and geometric point of view of vector image filtering using diffusion PDEs. It allows us to analyze proposed methods of vector data regularization, as well as propose a new vector PDE, well adapted for image restoration. This equation, whose key feature is the use of a local vector geometry, combines the advantages of diffusion PDEs for noise removing but also uses vector shock filters to enhance blurred edges. The extension to norm constrained vector fields can be the start for other well-known constrained problems, as optical flow computation, orientation analysis, and tensor image restoration.