Relations Between Regularization and Diffusion Filtering

Regularization may be regarded as diffusion filtering with an implicit time discretization where one single step is used. Thus, iterated regularization with small regularization parameters approximates a diffusion process. The goal of this paper is to analyse relations between noniterated and iterated regularization and diffusion filtering in image processing. In the linear regularization framework, we show that with iterated Tikhonov regularization noise can be better handled than with noniterated. In the nonlinear framework, two filtering strategies are considered: the total variation regularization technique and the diffusion filter technique of Perona and Malik. It is shown that the Perona-Malik equation decreases the total variation during its evolution. While noniterated and iterated total variation regularization is well-posed, one cannot expect to find a minimizing sequence which converges to a minimizer of the corresponding energy functional for the Perona–Malik filter. To overcome this shortcoming, a novel regularization technique of the Perona–Malik process is presented that allows to construct a weakly lower semi-continuous energy functional. In analogy to recently derived results for a well-posed class of regularized Perona–Malik filters, we introduce Lyapunov functionals and convergence results for regularization methods. Experiments on real-world images illustrate that iterated linear regularization performs better than noniterated, while no significant differences between noniterated and iterated total variation regularization have been observed.     

基于正交小波变换的信号降噪算法研究

提出了一种基于正交小波变换的信号降噪方法,深入研究了小波变换中的信号分解与重构的Mallat算法,详细介绍了正交小波变换中阈值的选取,并进行了实验研究。实验结果表明,该方法可以取得较好的去噪效果。     

Multi-level denoising and enhancement method based on wavelet transform for mine monitoring

Based on low illumination and a large number of mixed noises contained in coal mine, denoising with one method usually cannot achieve good results, so a multi-level image denoising method based on wavelet correlation relevant inter-scale is presented. Firstly, we used directional median filter to effectively reduce impulse noise in the spatial domain, which is the main cause of noise in mine. Secondly, we used a Wiener filtration method to mainly reduce the Gaussian noise, and then finally used a multi-wavelet transform to minimize the remaining noise of low-light images in the transform domain. This multi-level image noise reduction method combines spatial and transform domain denoising to enhance benefits, and effectively reduce impulse noise and Gaussian noise in a coal mine, while retaining good detailed image characteristics of the underground for improving quality of images with mixing noise and effective low-light environment.     

Multiplicative noise removal combining a total variation regularizer and a nonconvex regularizer

A novel variational model for removing multiplicative noise is proposed in this paper. In the model, a novel regularization term is elaborately designed which is inherently equivalent to a combination of the classical total variation regularizer and a nonconvex regularizer. The proposed regularization term, on the one hand, can better remove the noise in homogeneous regions of a noisy image and, on the other hand, can preserve edge details of the image during the denoising process. In order to solve the model efficiently, we design an alternating iteration process in which two coupling minimization problems are solved. For each of the two minimization problems, the existence and uniqueness of their solutions are proved under some necessary assumptions. Numerical results are reported to demonstrate the effectiveness of the proposed regularization term for multiplicative noise removal.     

A Low‐Memory,Straightforward and Fast Bilateral Filter Through Subsampling in Spatial Domain

In this work we present a new algorithm for accelerating the colour bilateral filter based on a subsampling strategy working in the spatial domain. The base idea is to use a suitable subset of samples of the entire kernel in order to obtain a good estimation of the exact filter values. The main advantages of the proposed approach are that it has an excellent trade‐off between visual quality and speed‐up, a very low memory overhead is required and it is straightforward to implement on the GPU allowing real‐time filtering. We show different applications of the proposed filter, in particular efficient cross‐bilateral filtering, real‐time edge‐aware image editing and fast video denoising. We compare our method against the state of the art in terms of image quality, time performance and memory usage.     

二进小波与扩散滤波结合的光学相干层析图像降噪

斑点抑制各向异性扩散(SRAD)是一种重要的图像降噪方法。将二进小波与SRAD结合,提出一种光学相干层析图像的二进小波扩散滤波降噪方法。该方法利用二进小波分解得到的不同尺度间小波系数的相关性区分边缘和噪声,修改SRAD中扩散系数得到新的扩散系数计算公式。实验表明,新方法具有更好的降噪能力,降噪后得到的图像的信噪比和对比度噪声比率等量化衡量指标都优于经典SRAD方法。     

Research on Comparison and Evaluation Studies of Several Smoothing Denoising Method Based on γ-ray Spectrum Detector

The extraction of spectral parameters is very difficult because of the limited energy resolution for NaI(TI)[JP] gamma-ray detectors. For statistical fluctuation of radioactivity under complex environment, some smoothing filtering methods are proposed to solve the problem. These methods include adopting method of arithmetic moving average, center of gravity, least squares of polynomial, slide converter of discrete funcion convolution etc. The process of spectrum data is realized, and the results are assessed in H/FWHM(Peak High/Full Width at Half Maximum) and peak area based on the Matlab programming. The results indicate that different methods smoothed spectrum have respective superiority in different ergoregion, but the Gaussian function theory in discrete function convolution slide method is used to filter the complex γ-spectrum on Embedded system platform, and the statistical fluctuation of γ-spectrum is filtered well.     

基于泊松-高斯混合噪声的最大似然改进算法

传统的图像复原算法仅针对高斯噪声进行处理,没有考虑高斯及泊松混合噪声污染。为此,引入泊松-高斯混合分布的成像模型,对基于混合模型的最大似然算法进行有效近似,在此基础上提出基于泊松-高斯混合噪声的最大似然改进算法,避免对噪声敏感性和PSF初始估计的依赖。实验结果表明,与原有算法相比,改进算法复原效果明显,且稳健性较好。     

Image denoising using statistical model based on quaternion wavelet domain

Image denoising is the basic problem of image processing.Quaternion wavelet transform is a new kind of multiresolution analysis tools.Image via quaternion wavelet transform,wavelet coefficients both in intrascale and in interscale have certain correlations.First,according to the correlation of quaternion wavelet coefficients in interscale,non-Gaussian distribution model is used to model its correlations,and the coefficients are divided into important and unimportance coefficients.Then we use the non-Gaussian distribution model to model the important coefficients and its adjacent coefficients,and utilize the MAP method estimate original image wavelet coefficients from noisy coefficients,so as to achieve the purpose of denoising.Experimental results show that our algorithm outperforms the other classical algorithms in peak signal-to-noise ratio and visual quality.     

分数阶微积分在图像处理中的研究综述*

综述了关于分数阶微积分理论在数字图像底层处理中的应用研究,具体包括:分数阶微积分和分数阶偏微分方程的基本理论及分数阶傅里叶变换的基本性质;分数阶微分滤波器的构造及在图像增强中的应用研究;分数阶积分滤波器的构造及在图像去噪中的应用研究;分数阶偏微分方程在图像去噪中的应用研究。最后,总结了分数阶微积分理论在图像处理中已取得的研究成果,并结合已有的基于分数阶微积分理论的图像底层处理模型,展望了分数阶微积分理论在图像处理中的应用前景。