Image Recovery via Diffusion Tensor and Time-Delay Regularization

We present a system of PDEs for image restoration, which consists of an anisotropic diffusion equation driven by a diffusion tensor, whose structure depends on the gradient of the image obtained from a coupled time-delay regularization equation, and governs the direction and the speed of the diffusion. The diffusion resulting from this model is isotropic inside a homogeneous region, anisotropic along its boundary, and is able to connect broken edges and enhance coherent structures. Experimental results are given to show its effectiveness in tracking edges and recovering images with high levels of noise. Moreover, the proposed model can be interpreted as a time continuous Hopfield neural network. This connection further illustrates how the proposed model enhances coherent structures. The existence, uniqueness, and stability for the solutions of the PDEs are proved.     

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.     

Edge extraction using zero-frequency resonator

This paper proposes an approach based on the zero-frequency resonator to extract the edge information of the images. The proposed approach is counterintuitive to the concept that edges correspond to high-frequency components of an image. The impulse-like characteristics of edges in an image distribute the energy uniformly over all frequencies of the spectrum including around the zero-frequency. This property is exploited in this paper by using the output of a zero-frequency resonator, for extracting the edge information. Spatial domain and Fourier domain methods are employed to realize the zero-frequency resonator for two-dimensional signals. The Laplacian of the Gaussian (LOG) and the proposed approach are similar in the sense that the former approach uses a Gaussian filter for smoothing operation, whereas a zero-frequency resonator is used in the proposed approach. The output of the resonator is processed using a Laplacian operator for the trend removal. In the resulting filtered image, the edge information is present at the zero-crossings, and the edges are extracted using sign correspondence principle to identify the zero-crossings corresponding to the edges. Results of edge extraction are illustrated for a few clear and noisy images.     

Filtering of medical ultrasonic images based on a modified anistropic diffusion equation

Speckle noise reduction is a key problem of the image analysis of medical UltraSound images. In this paper, two important improvements have been developed to a fast anisotropic diffusion algorithm for speckle noise reduction. The Gaussian filter is firstly used before gradient calculation, and then the adaptive algorithm of the factor k is proposed. Numerous experimental results show that the proposed model is superior to other methods in noise removal, fidelity and edge preservation. It is suitable for the preprocessing of a great number of medical UltraSound images, such as three dimen- sional reconstruction.     

Nonlinear multiscale wavelet diffusion for speckle suppression and edge enhancement in ultrasound images

This paper introduces a novel nonlinear multiscale wavelet diffusion method for ultrasound speckle suppression and edge enhancement. This method is designed to utilize the favorable denoising properties of two frequently used techniques: the sparsity and multiresolution properties of the wavelet, and the iterative edge enhancement feature of nonlinear diffusion. With fully exploited knowledge of speckle image models, the edges of images are detected using normalized wavelet modulus. Relying on this feature, both the envelope-detected speckle image and the log-compressed ultrasonic image can be directly processed by the algorithm without need for additional preprocessing. Speckle is suppressed by employing the iterative multiscale diffusion on the wavelet coefficients. With a tuning diffusion threshold strategy, the proposed method can improve the image quality for both visualization and auto-segmentation applications. We validate our method using synthetic speckle images and real ultrasonic images. Performance improvement over other despeckling filters is quantified in terms of noise suppression and edge preservation indices.     

基于各向异性扩散的SAR图像斑点噪声滤波算法

在SAR(Synthetic Aperture Radar)图像噪声抑制处理中,为了有效地保持图像边缘,作者在斑点噪声去除的各向异性扩散模型(SRAD模型)的基础上,提出了一个基于各向异性扩散的SAR图像斑点噪声滤波算法.该算法对应的扩散系数从理论上满足Charbonnier 等人提出的构造扩散系数准则,同时该算法能够通过对边缘直方图上累计百分比和相对信噪比阈值进行调节来得到一系列不同的滤波效果,从而满足不同的应用需求,如绘图、高分辨率或细节丰富的处理结果.实验结果表明,与传统的方法相比,该算法不论从噪声去除能力、边缘和纹理保持能力上,还是从视觉评价效果来看,都具有一定的优越性.     

Speckle reducing anisotropic diffusion

This paper provides the derivation of speckle reducing anisotropic diffusion (SRAD), a diffusion method tailored to ultrasonic and radar imaging applications. SRAD is the edge-sensitive diffusion for speckled images, in the same way that conventional anisotropic diffusion is the edge-sensitive diffusion for images corrupted with additive noise. We first show that the Lee and Frost filters can be cast as partial differential equations, and then we derive SRAD by allowing edge-sensitive anisotropic diffusion within this context. Just as the Lee (1980, 1981, 1986) and Frost (1982) filters utilize the coefficient of variation in adaptive filtering, SRAD exploits the instantaneous coefficient of variation, which is shown to be a function of the local gradient magnitude and Laplacian operators. We validate the new algorithm using both synthetic and real linear scan ultrasonic imagery of the carotid artery. We also demonstrate the algorithm performance with real SAR data. The performance measures obtained by means of computer simulation of carotid artery images are compared with three existing speckle reduction schemes. In the presence of speckle noise, speckle reducing anisotropic diffusion excels over the traditional speckle removal filters and over the conventional anisotropic diffusion method in terms of mean preservation, variance reduction, and edge localization.     

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.     

Image recovery using the anisotropic diffusion equation

A new approach for image recovery using the anisotropic diffusion equation is developed which is based on the first derivative of the signal in time embedded in family of images with different scales. The diffusion coefficient is determined as a function of the gradient of the signal convolved with a symmetric exponential filter. A new discrete realization is developed for the simultaneous removal of noise and preservation of edges.     

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.     

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.     

An approach to suppress speckle noise and enhance edge

Anisotropic diffusion has good effect on reducing noise and preserving edge, but it may lose some details due to the blocky effect and can not suppress speckle effectively. The Laplacian factor is used to process the observed image which is considered as a piecewise planar image, so the Fourth Order Anisotropic Diffusion （FOAD） can avoid the blocky effect. The edge is preserved and enhanced by the Line Edge Detector （LED） based on stick technique and hypothesis test optimizing method. An approach called the Fourth Order Anisotropic Diffusion and Edge Enhancing （FOADEE）, where the LED is combined with the FOAD, is presented. For quantitative evaluation and comparison with the LED, the FOAD and the FOADEE, two parameters as measure of the noise suppression and edge preservation are introduced. It is proved that the novel method can not only suppress speckle prominently but also preserve even enhance edge and useful details effectively by applying it to the phantoms and tissue images.     

An edge-adapting Laplacian kernel for nonlinear diffusion filters

In this paper, first, a new Laplacian kernel is developed to integrate into it the anisotropic behavior to control the process of forward diffusion in horizontal and vertical directions. It is shown that, although the new kernel reduces the process of edge distortion, it nonetheless produces artifacts in the processed image. After examining the source of this problem, an analytical scheme is devised to obtain a spatially varying kernel that adapts itself to the diffusivity function. The proposed spatially varying Laplacian kernel is then used in various nonlinear diffusion filters starting from the classical Perona-Malik filter to the more recent ones. The effectiveness of the new kernel in terms of quantitative and qualitative measures is demonstrated by applying it to noisy images.     

一种基于偏微分方程的SAR图像去噪方法

传统的相干斑噪声抑制算法在多次迭代后通常会导致图像边缘的模糊,这一直是SAR图像去噪处理的难点和热点所在。该文分析了应用于图像处理的各向异性扩散方程(PDEs),在其基础上由最小化问题出发,引入棱边指示子对图像的边缘加以限制,得到新的去噪模型并降之应用于SAR图像的相干斑噪声去除。与传统的基于局部统计量和各向异性滤波器相比,新的算法在棱边保持和噪声去除能力均有提高。     

一种各向异性扩散图像去噪的方法

在用各向异性扩散的方法对图像去处噪声的过程中，有时要预先对图像进行平滑处理，再进行各向异性扩散，本文提出了一种对图像预先平滑的方法，并用实验验证了该方法的有效性。     

Edge preserving adaptive anisotropic diffusion filter approach for the suppression of impulse noise in images

This paper proposes a new anisotropic diffusion approach to remove the impulse noise and retain the fine details. The proposed approach contains two stages, the first stage detects the impulse noise, and the second stage removes the noisy pixel and retains the fine details of the original image. The Laplacian operator is used to fine-tune the image quality of the restored image in the anisotropic diffusion filter. The proposed approach is tested with PSNR, IEF, correlation factor, and NSER for different test images and the results are compared against existing algorithms. The simulation results show that the proposed approach gives better results than the existing denoising algorithms.     

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.     

基于非线性复扩散耦合冲激滤波器的图像放大算法研究简

为了提高放大算法的适应性,采用改进的非线性复扩散和自适应冲激滤波器,提出了一种图像放大方法。根据像素局部方差进行自适应改变扩散门限,扩散图像的虚部除以扩散时间以消除扩散时间的影响,特别是初期扩散近似线性扩散的特性,得到改进的复扩散模型耦合冲激滤波器进行无噪图像放大。对于噪声图像放大,根据像素局部方差进行自适应非线性复扩散,耦合局部方差约束的冲激滤波器增强模糊的图像边缘和细节。自适应非线性复扩散通过局部方差和图像二阶导数相结合分辨边缘和噪声,对噪声进行平滑的同时保持边缘,克服了复扩散不能分辨噪声和边缘的缺陷,同时保持复扩散保护斜坡结构,免除阶梯效应的优点。仿真实验验证了所提算法不仅对无噪图像有较好的放大效果,而且对一定范围的噪声图像也有较好的放大效果。     

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。      

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.