Efficient wavelet-based image denoising algorithm

Characterising the statistics of wavelet coefficients is a critical issue in image compression and denoising. Many powerful approaches have been investigated, but accurate modelling suffers from high computational complexity. In this work an efficient adaptive algorithm to capture the dependency of both inner and inter scale wavelet coefficients is proposed. Experimental results show that compared with other algorithms, in the case of higher noise variance, greater PSNR performance gain may be obtained     

Contourlet-based image denoising algorithm using directional windows

Contourlet is a new effective signal representation tool in many image applications. Proposed is a contourlet-based image denoising algorithm using directional windows which takes advantage of the captured directional information of the images. Experiments show that the proposed algorithm achieves better performance than other contourlet-based image denoising algorithms     

Non-convex hybrid total variation for image denoising

Image restoration problems, such as image denoising, are important steps in various image processing method, such as image segmentation and object recognition. Due to the edge preserving property of the convex total variation (TV), variational model with TV is commonly used in image restoration. However, staircase artifacts are frequently observed in restored smoothed region. To remove the staircase artifacts in smoothed region, convex higher-order TV (HOTV) regularization methods are introduced. But the valuable edge information of the image is also attenuated. In this paper, we propose non-convex hybrid TV regularization method to significantly reduce staircase artifacts while well preserving the valuable edge information of the image. To efficiently find a solution of the variation model with the proposed regularizer, we use the iterative reweighted method with the augmented Lagrangian based algorithm. The proposed model shows the best performance in terms of the signal-to-noise ratio (SNR) and the structure similarity index measure (SSIM) with comparable computational complexity.     

Spatially adaptive multiplicative noise image denoising technique

A new image denoising technique in the wavelet transform domain for multiplicative noise is presented. Unlike most existing techniques, this approach does not require prior modeling of either the image or the noise statistics. It uses the variance of the detail wavelet coefficients to decide whether to smooth or to preserve these coefficients. The approach takes advantage of wavelet transform property in generating three detail subimages each providing specific information with certain feature directivity. This allows the ability to combine information provided by different detail subimages to direct the filtering operation. The algorithm uses the hypothesis test based on the F-distribution to decide whether detail wavelet coefficients are due to image related features or they are due to noise. The effectiveness of the proposed technique is tested for orthogonal as well as biorthogonal mother wavelets in order to study the effect of the smoothing process under different wavelet types.     

Wavelet based image denoising: VQ-Bayesian technique

An image denoising algorithm for the wavelet-transform domain of an image is presented. In the proposed method, a Bayesian estimation procedure is used to restore the higher scale wavelet coefficients, while vector quantisation is used to realise a spatially adaptive Bayesian estimation procedure for the lower scales. The proposed algorithm provides an improved noise suppression performance as compared to that of the denoising algorithm of Mallat and Hwang (1992) and also that of Malfait and Roose (1997)     

基于图像局部方向特性的自适应全变分去噪模型

针对全变分模型(total variation,TV)以图像的梯度信息作为去噪的尺度参数,未考虑图像局部纹理的方向性的缺点,提出了一种基于图像局部方向特性的自适应全变分去噪模型(Adaptive directional total variation,ADTV),并推导出该模型的迭代数值求解过程。在该模型中,首先,计算出图像局部方向的角度矩阵。然后,构造与图像纹理方向一致的椭圆区域代替TV模型的圆形区域。最后,通过优化最小化算法迭代求解以获得去噪后图像。通过对比实验证明,本文提出的模型取得了更高的峰值信噪比,去噪过程中更好地增强了图像的细节信息。     

PDE-based image restoration: a hybrid model and color image denoising.

The paper is concerned with PDE-based image restoration. A new model is introduced by hybridizing a nonconvex variant of the total variation minimization (TVM) and the motion by mean curvature (MMC) in order to deal with the mixture of the impulse and Gaussian noises reliably. We suggest the essentially nondissipative (ENoD) difference schemes for the MMC component to eliminate the impulse noise with a minimum (ideally no) introduction of dissipation. The MMC-TVM hybrid model and the ENoD schemes are applied for both gray-scale and color images. For color image denoising, we consider the chromaticity-brightness decomposition with the chromaticity formulated in the angle domain. An incomplete Crank-Nicolson alternating direction implicit time-stepping procedure is adopted to solve those differential equations efficiently. Numerical experiments have shown that the new hybrid model and the numerical schemes can remove the mixture of the impulse and Gaussian noises, efficiently and reliably, preserving edges quite satisfactorily.     

一种高效的小波Contourlet变换阈值去噪算法

针对现有图像去噪算法去噪效率与信号保真度不高的现象,通过研究小波变换与Contourlet变换,将其有机的结合在一起从而实现优势互补,并提出一种高效的阈值去噪算法,通过建立最大值列表,引入适当的阈值将其系数进行分类,并使用优化后的软阈值去噪算法与边缘优化算法对其分类处理,实验表明,该算法能够有效的对含噪图像进行去噪的同时保留其边缘信息,具有高效性、保真度高的图像去噪特性,在图像去噪领域有较好的发展前景。     

几种图像去噪算法的应用分析

去噪处理是图像处理中较为重要的环节。从图像的噪声类型和去噪意义出发，讨论了均值滤波、中值滤波和小波变换三种常用的图像去噪方法，并对其去噪效果进行了对比分析，得出了三种方法各自的适用性特点。     

Dual-branch deep image prior for image denoising

In this work, we propose a two-stage denoising approach, which includes generation and fusion stages. Specifically, in the generation stage, we first split the expanding path of the UNet backbone of the standard DIP (deep image prior) network into two branches, converting it into a Y-shaped network (YNet). Then we adopt the initial denoised images obtained with DAGL (dynamic attentive graph learning) and Restormer methods together with the given noisy image as the target images. Finally, we utilize the standard DIP on-line training routine to generate two complementary basic images, whose image quality is quite improved, with the help of a novel automatic iteration termination mechanism. In the fusion stage, we first split the contracting path of the standard UNet network into two branches for receiving the two basic images generated in the previous stage, and obtain a fused image as the final denoised image in a fully unsupervised manner. Extensive experimental results confirm that our method has a significant improvement over the standard DIP or other unsupervised methods, and outperforms recently proposed supervised denoising models. The noticeable performance improvement is attributed to the proposed hybrid strategy, i.e., we first adopt the supervised denoising methods to process the common content of images substantially, then utilize the unsupervised method to fine-tune the specific details. In other words, we take full advantage of the high performance of the supervised methods and the flexibility of the unsupervised methods.     

基于混合滤波算法的数字图像去噪方法研究

双边滤波已广泛应用于数字图像处理领域,但在图像的高梯度区域,双边滤波会产生阶梯效应。双边滤波是局部模式滤波的一种特殊形式,提出了基于高斯滤波和双边滤波的混合图像去噪方法。利用高斯滤波器对噪声图像进行滤波,得到参考图像,将参考图像和噪声图像作为范围核函数的输入双边滤波器。参考图像提供图像的低频信息,噪声图像提供图像的高频信息。与传统双边滤波法比较,混合去噪方法能够有效地克服阶梯效应,滤波后的图像更平滑,纹理特征更接近原始图像,可获得更高的峰值信噪比。     

Nonlinear filtering for phase image denoising

The problem of phase image denoising through nonlinear (NL) filtering is addressed. There are various imaging systems in which the phase information is utilised to generate useful imaging data. However, the presence of noise makes difficult to obtain the appropriate phase image. The authors apply NL vector filtering techniques to denoise the complex data from which the phase image is extracted. A study was realised in which several NL filters were applied to a simulated complex image. The effects of filtering were determined through a Monte Carlo simulation in which the image was successively contaminated with six different noise models. The effectiveness of the filters was measured in terms of normalised mean square error, signal-to-noise ratio and the number of eliminated phase residues. Results indicate a significant noise reduction, especially when NL filters based on angular distances are applied to the noisy input.     

Tri-state median filter for image denoising

A novel nonlinear filter, called tri-state median (TSM) filter, is proposed for preserving image details while effectively suppressing impulse noise. We incorporate the standard median (SM) filter and the center weighted median (CWM) filter into a noise detection framework to determine whether a pixel is corrupted, before applying filtering unconditionally. Extensive simulation results demonstrate that the proposed filter consistently outperforms other median filters by balancing the tradeoff between noise reduction and detail preservation.     

The curvelet transform for image denoising

We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in the Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness of our interpolation, the visual performance is surprisingly good. Our ridgelet transform applies to the Radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain. Our curvelet transform uses our ridgelet transform as a component step, and implements curvelet subbands using a filter bank of a; trous wavelet filters. Our philosophy throughout is that transforms should be overcomplete, rather than critically sampled. We apply these digital transforms to the denoising of some standard images embedded in white noise. In the tests reported here, simple thresholding of the curvelet coefficients is very competitive with "state of the art" techniques based on wavelets, including thresholding of decimated or undecimated wavelet transforms and also including tree-based Bayesian posterior mean methods. Moreover, the curvelet reconstructions exhibit higher perceptual quality than wavelet-based reconstructions, offering visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems. The empirical results reported here are in encouraging agreement.     

Well-posed anisotropic diffusion for image denoising

A nonlinear iterative smoothing filter based on a second-order partial differential equation is introduced. It smooths out the image according to an anisotropic diffusion process. The approach is based on a smooth approximation of the total variation (TV) functional which overcomes the non-differentiability of the TV functional at the origin. In particular, the authors perform linear smoothing over smooth areas but selective smoothing over candidate edges. By relating the smoothing parameter to the time step, they arrive at a CFL condition which guarantees the causality of the discrete scheme. This allows the adoption of higher time discretisation steps, while ensuring the absence of artefacts deriving from the non-smooth behaviour of the TV functional at the origin. In particular, it is shown that the proposed approach avoids the typical staircase effects in smooth areas which occur in the standard time-marching TV scheme     

Adaptive wavelet threshold for image denoising

Threshold selection is the critical issue in image denoising via wavelet shrinkage. Many powerful approaches have been investigated, but few have been to make the threshold values adaptive to the changing statistics of images and meanwhile maintain the efficiency of the algorithm. In this work an efficient adaptive algorithm to capture the dependency of inter-scale wavelet coefficients is proposed. Experiments show that higher peak signal-to-noise ratio can be obtained as compared to other threshold-denoising algorithms.     

利用近场Gordon积分近似的矩量法-物理光学混合方法

针对电大金属目标的电磁计算, 提出了一种新的矩量法-物理光学(Method of Moment-Physical Optics, MoM-PO)混合方法, 以解决传统的MoM-PO混合法中PO区域和MoM区域耦合项的计算时间过长问题.用Gordon积分计算目标的PO区域对MoM区域的作用, 并加入近场近似处理.该方法避免了传统的MoM-PO混合法中耦合项积分方程的计算, 加大PO区域的剖分面元的大小, 能够有效地降低矩阵规模和未知数个数, 因而降低了内存, 减少了计算时间.数值算例结果表明, 近场Gordon积分近似的MoM-PO混合方法能够有效地减少耦合项的计算时间, 并能达到理想的精度.     

Efficient image denoising method based on a new adaptive wavelet packet thresholding function

This paper proposes a statistically optimum adaptive wavelet packet (WP) thresholding function for image denoising based on the generalized Gaussian distribution. It applies computationally efficient multilevel WP decomposition to noisy images to obtain the best tree or optimal wavelet basis, utilizing Shannon entropy. It selects an adaptive threshold value which is level and subband dependent based on analyzing the statistical parameters of subband coefficients. In the utilized thresholding function, which is based on a maximum a posteriori estimate, the modified version of dominant coefficients was estimated by optimal linear interpolation between each coefficient and the mean value of the corresponding subband. Experimental results, on several test images under different noise intensity conditions, show that the proposed algorithm, called OLI-Shrink, yields better peak signal noise ratio and superior visual image quality-measured by universal image quality index-compared to standard denoising methods, especially in the presence of high noise intensity. It also outperforms some of the best state-of-the-art wavelet-based denoising techniques.     

一种新的图像去噪混合滤波方法

为了去除图像中混入的脉冲噪声和高斯噪声,提出了一种基于自适应中值滤波和模糊加权均值滤波的混合滤波方法.该方法首先进行噪声检测把受高斯型噪声污染的像素和受脉冲型噪声污染的像素区别开来,然后对受高斯噪声污染的像素采用模糊加权均值滤波算法,而对受脉冲噪声污染的像素则采用改进的中值滤波算法进行去噪.仿真结果证明,该方法更具有实用性和有效性.     

Fractional-order anisotropic diffusion for image denoising.

This paper introduces a new class of fractional-order anisotropic diffusion equations for noise removal. These equations are Euler-Lagrange equations of a cost functional which is an increasing function of the absolute value of the fractional derivative of the image intensity function, so the proposed equations can be seen as generalizations of second-order and fourth-order anisotropic diffusion equations. We use the discrete Fourier transform to implement the numerical algorithm and give an iterative scheme in the frequency domain. It is one important aspect of the algorithm that it considers the input image as a periodic image. To overcome this problem, we use a folded algorithm by extending the image symmetrically about its borders. Finally, we list various numerical results on denoising real images. Experiments show that the proposed fractional-order anisotropic diffusion equations yield good visual effects and better signal-to-noise ratio.