基于分数阶微积分正则化的图像处理

全变分正则化方法已被广泛地应用于图像处理,利用此方法可以较好地去除噪声,并保持图像的边缘特征,但得到的优化解会产生"阶梯"效应.为了克服这一缺点,本文通过分数阶微积分正则化方法,建立了一个新的图像处理模型.为了克服此模型中非光滑项对求解带来的困难,本文研究了基于不动点方程的迫近梯度算法.最后,本文利用提出的模型与算法进行了图像去噪、图像去模糊与图像超分辨率实验,实验结果表明分数阶微积分正则化方法能较好的保留图像纹理等细节信息.     

图像处理中全变差正则化数据拟合问题算法回顾

全变差正则化数据拟合问题产生于许多图像处理任务,如图像去噪、去模糊、图像修复、磁共振成像、压缩图像感知等.近年来,求解此类问题的快速高效算法发展很快.以最小二乘、最小一乘等为例简要回顾求解此类问题的主要算法,并讨论一个全变差正则化非凸数据拟合模型在脉冲噪声图像去模糊问题中的应用.     

交替方向乘子法求解混合全变差模糊图像复原模型

针对全变差模型在模糊图像复原过程中易产生振铃效应的不足,提出了图像复原的混合全变差模型.混合模型在图像边缘轮廓区域趋向为标准全变差模型,能够有效地保留边缘轮廓信息;而在光滑区域能够逼近为高阶全变差模型,达到抑制振铃效应的目的.实验结果表明,提出的混合全变差模型在复原图像结构信息的同时能够有效地抑制振铃效应的产生,得到的复原图像在客观评价标准和主观视觉效果方面均有所提高.     

基于Canny算子边缘检测的小波阈值去噪方法

本文研究了信号处理中图像去噪的问题.利用小波变换理论提出了一种基于Canny算子边缘检测的小波阈值去噪方法,实验结果表明,该方法在有效去除噪声的同时能够更好地保留图像的边缘.     

基于改进的变分水平集C-V图像分割模型研究

为解决C-V模型中弱边缘或边缘模糊图像分割问题,提出了用边缘停止函数代替正则化Dirac函数的C-V图像分割模型.首先对正则化Heaviside函数和正则化Dirac函数中的参数进行了讨论,然后利用图像边缘信息将梯度算子引入正则化Driac函数中,对C-V模型进行改进,最后,用边缘停止函数代替C-V模型中的正则化Dirac函数.实验结果显示,提出的模型比C-V模型对图像的分割效果更好.     

基于PICCS的非局部TGV能谱CT重建算法

能谱CT将宽谱划分为窄谱,导致通道内光子数目明显减少,加大了噪声影响,故从噪声投影中重建出高质量图像是能谱CT的一个研究热点.传统全变分(total variational,TV)容易造成重建图像中出现块状伪影等问题,总广义全变分(total generalized variation,TGV)算法可以逼近任意阶函数,再结合非局部均值算法的思想,同时考虑到不同能谱通道下重建图像的相关性,将高质量全能谱重建图像作为先验图像指导能谱CT重建,提出了基于先验图像约束压缩感知(prior image constrained compressed sensing,PICCS)的非局部TGV重建算法.实验结果表明,所提算法在抑制噪声的同时能够有效复原图像细节及边缘信息,且收敛速度快.     

基于全变差空间正则化的纤维方向分布估计

提高白质纤维交叉重构能力是有效提高纤维跟踪技术的前提之一,目前大多纤维重构方法都是基于白质体素的独立重构,没有考虑到纤维的连续性特征,这就促使文章从全局范围考虑提高白质纤维重构能力.文章提出了一种基于全变差空间正则化的纤维方向分布估计方法,该方法首先利用字典基分布的球面反卷积策略拟合多壳采样信号,为了能够适用于单壳和多壳采样方案,文章重新定义了广义的纤维响应函数;进而在q空间中定义基函数系数的全变差正则化约束,旨在减少不必要的方向信息,降低因噪声引起的方向偏差,以获得纤维方向的空间局部一致性.实验分别在模拟数据和实际数据下进行,分别采用单壳和多壳数据验证了文章所提方法能够以更高效的性能实现纤维方向估计,相对于其他算法显著提高了纤维的连续性.     

一种基于脉冲噪声的新型迭代滤波算法

在局部极值噪声检测和迭代中值滤波的基础上,基于图像结构和脉冲噪声的特征分析,有效结合局部极值检测和幅度差阈值、梯度差阈值的检测方法,提出了一种基于噪声检测的迭代脉冲噪声滤除算法.并通过仿真实验和算法评价,验证了该算法不仅能够达到很好的去噪效果,而且在保留图像细节信息方面也取得了一定的成效.     

灰度图像复原的一种空间适应性向前向后扩散模型

该文考虑退化灰度图像复原问题. 首先, 作者利用时滞正则化方法定义退化图像去噪过程和去模糊过程之间的权重函数, 将激波过滤器边缘增强模型与水平集运动去噪模型相结合, 建立一种新的图像磨光增强偏微分方程. 然后, 证明该偏微分方程初值问题黏性弱解的存在唯一性. 最后, 给出该模型的部分数值算例.     

结合小波框架与TV的一个正则化方法

本文研究了图像恢复问题.利用结合小波框架与全变差方法 (TV)的多参数正则化方法,获得了比经典TV的ROF模型和小波框架更好的结果,推广了原本只使用这两种方法其中之一的模型.     

IMAGE RESTORATION UNDER CAUCHY NOISE WITH SPARSE REPRESENTATION PRIOR AND TOTAL GENERALIZED VARIATION

This article introduces a novel variational model for restoring images degraded by Cauchy noise and/or blurring.The model integrates a nonconvex data-fidelity term with two regularization terms,a sparse representation prior over dictionary learning and total generalized variation(TGV)regularization.The sparse representation prior exploiting patch information enables the preservation of fine features and textural patterns,while adequately denoising in homogeneous regions and contributing natural visual quality.TGV regularization further assists in effectively denoising in smooth regions while retaining edges.By adopting the penalty method and an alternating minimization approach,we present an efficient iterative algorithm to solve the proposed model.Numerical results establish the superiority of the proposed model over other existing models in regard to visual quality and certain image quality assessments.     

A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising

The total variation model proposed by Rudin, Osher and Fatemi performs very well for removing noise while preserving edges. However, it favors a piecewise constant solution in BV space which often leads to the staircase effect, and small details such as textures are often filtered out with noise in the process of denoising. To preserve the textures and eliminate the staircase effect, we improve the total variation model in this paper. This is accomplished by the following steps: (1) we define a new space of functions of fractional-order bounded variation called the BV_α space by using the Grünwald–Letnikov definition of fractional-order derivative; (2) we model the structure of the image as a function belonging to the BV_α space, and the textures in different scales as functions belonging to different negative Sobolev spaces. Thus, we propose a class of fractional-order multi-scale variational models for image denoising. (3) We analyze some properties of the fraction-order total variation operator and its conjugate operator. By using these properties, we develop an alternation projection algorithm for the new model and propose an efficient condition of the convergence of the algorithm. The numerical results show that the fractional-order multi-scale variational model can improve the peak signal to noise ratio of image, preserve textures and eliminate the staircase effect efficiently in the process of denoising.     

Image restoration with a high-order total variation minimization method

In this paper, we propose a fast and efficient way to restore blurred and noisy images with a high-order total variation minimization technique. The proposed method is based on an alternating technique for image deblurring and denoising. It starts by finding an approximate image using a Tikhonov regularization method. This corresponds to a deblurring process with possible artifacts and noise remaining. In the denoising step, a high-order total variation algorithm is used to remove noise in the deblurred image. We see that the edges in the restored image can be preserved quite well and the staircase effect is reduced effectively in the proposed algorithm. We also discuss the convergence of the proposed regularization method. Some numerical results show that the proposed method gives restored images of higher quality than some existing total variation restoration methods such as the fast TV method and the modified TV method with the lagged diffusivity fixed-point iteration.     

Image denoising using the Gaussian curvature of the image surface

A number of high‐order variational models for image denoising have been proposed within the last few years. The main motivation behind these models is to fix problems such as the staircase effect and the loss of image contrast that the classical Rudin–Osher–Fatemi model [Leonid I. Rudin, Stanley Osher and Emad Fatemi, Nonlinear total variation based noise removal algorithms, Physica D 60 (1992), pp. 259–268] and others also based on the gradient of the image do have. In this work, we propose a new variational model for image denoising based on the Gaussian curvature of the image surface of a given image. We analytically study the proposed model to show why it preserves image contrast, recovers sharp edges, does not transform piecewise smooth functions into piecewise constant functions and is also able to preserve corners. In addition, we also provide two fast solvers for its numerical realization. Numerical experiments are shown to illustrate the good performance of the algorithms and test results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1066–1089, 2016     

Adaptive total variation regularization based scheme for Poisson noise removal

To better preserve the edge features, this paper investigates an adaptive total variation regularization based variational model for removing Poisson noise. This edge‐preserving scheme comprises a spatially adaptive diffusivity coefficient, which adjusts the diffusion strength automatically. Compared with the classical total variation based one, numerical simulations distinctly indicate the superiority of our proposed strategy in maintaining the small details while denoising Poissonian image. Copyright © 2012 John Wiley & Sons, Ltd.     

A variational formulation for physical noised image segmentation

Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others,these results show that our proposed model and algorithms are effective.     

Decomposition of images by the anisotropic Rudin‐Osher‐Fatemi model

The total‐variation‐based image denoising model of Rudin, Osher, and Fatemi can be generalized in a natural way to favor certain edge directions. We consider the resulting anisotropic energies and study properties of their minimizers. © 2004 Wiley Periodicals, Inc.     

利用对偶树复数小波与全变差模型实现图像去噪的新方法

本文首先研究了一种三层小波系数相关萎缩的概念与性质,利用对偶树复数小波与全变差模型相结合,提出了一种新的图像去噪方法。实验结果表明,与现有的图像去噪方法相比,本文方法无论是在视觉还是在均方误差等方面均有更好的效果。     

Anisotropic Total Variation Filtering

Total variation regularization and anisotropic filtering have been established as standard methods for image denoising because of their ability to detect and keep prominent edges in the data. Both methods, however, introduce artifacts: In the case of anisotropic filtering, the preservation of edges comes at the cost of the creation of additional structures out of noise; total variation regularization, on the other hand, suffers from the stair-casing effect, which leads to gradual contrast changes in homogeneous objects, especially near curved edges and corners. In order to circumvent these drawbacks, we propose to combine the two regularization techniques. To that end we replace the isotropic TV semi-norm by an anisotropic term that mirrors the directional structure of either the noisy original data or the smoothed image. We provide a detailed existence theory for our regularization method by using the concept of relaxation. The numerical examples concluding the paper show that the proposed introduction of an anisotropy to TV regularization indeed leads to improved denoising: the stair-casing effect is reduced while at the same time the creation of artifacts is suppressed.