基于可变指数及L1保真项的图像去噪算法

全变分(TV)模型采用了梯度的1范数作为正则化约束, 它能够沿着梯度方向较好地保护图像的边缘信息,但在图像较均匀区域,容易产生“阶梯”效应。利用梯度的可变指数函数作为正则化项,提出TV模型的改进模型, 该模型既保持TV模型保护图像边缘信息的优点,又可以明显地减少非边界区域“阶梯”效应的产生,同时把〖WTHX〗u-〖WTHX〗f的1范数作为数据保真项增强了模型修复图像破损部分的能力     

基于Lp伪范数和高阶OGS全变分的椒盐噪声去除

全变分(TV)模型广泛应用于椒盐噪声的去除。然而,TV 模型中存在着严重的阶梯效应。近年 来,由于低阶交叠组稀疏(LOGS)全变分能够很好地抑制阶梯效应,受到了越来越多的关注,但仍有改进空间。 实际上,其只考虑一阶图像梯度的先验信息,而忽略了高阶图像梯度的先验信息。为了进一步提高恢复图像的 质量,提出了一种结合 Lp 伪范数的高阶 OGS 全变分,在利用高阶梯度的 OGS 约束更好地描述图像梯度稀疏 先验的同时,还利用 Lp 伪范数的强稀疏诱导能力更好地描述椒盐噪声的稀疏性。该模型采用交替方向乘子法 求解,并将模型分解为若干个子问题求解。最后,通过实验验证了该模型的正确性,并结合峰值信噪比、结构 相似性度和梯度幅值相似性偏差对模型的恢复性能进行了评价。实验结果表明,该方法相比一些先进的去噪模 型具有很强的竞争力。     

基于非局部总广义变分的图像去噪

针对全变分(TV)模型在去除图像噪声时容易产生阶梯效应的缺点,将二阶总广义变分(TGV)作为正则项应用于全变分模型中可以有效地去除阶梯效应,并且还能够更好地保持图像边缘纹理结构;利用非局部均值滤波算法的思想来构造非局部微分算子,将非局部微分算子应用于总广义变分模型中,综合提出了一种基于非局部总广义变分的图像去噪新模型。新模型充分利用了图像的全局信息进行去噪。实验结果显示了该模型的有效性和优越性。     

基于分数阶全变分正则化的超分辨率图像重建

从退化的低分辨率图像重建得到高分辨率图像的本质是一病态逆问题,针对该问题,通过添加正则项进行处理。在使用传统的全变分(TV)的基础上,添加了分数阶全变分(FOTV)作为另一正则项来约束解空间。分数阶全变分正则项的使用可以更好地重建图像的细节纹理信息,弥补了全变分算子在平滑区域易出现阶梯效应的缺陷。利用交替方向乘子(ADMM)算法将问题划分为子问题,将全变分和分数阶全变分算子作为循环矩阵,通过傅里叶变换将其对角化,降低了计算的复杂程度。实验结果表明,与已有的方法相比,所提方法有效地避免了阶梯效应的产生,较好地保持了细节信息,并且具有更好的峰值信噪比(PSNR)和结构相似度(SSIM)。     

基于四阶偏微分方程的卡通—纹理图像分解方法

Luminita A.Vese和Stanley J.Osher的卡通-纹理分解模型能有效地将一幅含纹理的图像分解成卡通部分和纹理部分,但是在正则化过程中容易产生阶梯现象,使得图像分解不准确。针对此问题,在Vese-Osher分解模型的基础上,用四阶范数来代替二阶的TV范数,构造新的分解模型。实验结果表明,该模型克服了阶梯现象,使得图像分解更准确,卡通图像能保持较好的光滑性和较清晰的边缘,纹理图像更清晰、准确。     

基于L1范数的全变分正则化超分辨重构算法

针对结构化照明显微成像系统的超分辨图像重构算法存在边界振铃效应、噪声免疫性差的问题,提出了一种基于L1范数的全变分正则化超分辨图像重构算法（简称L1/TV重构算法）。从结构化显微成像模型入手,分析了传统算法的设计原理和局限性;论述了L1/TV重构算法的原理,采用L1范数对重构图像保真度进行约束,并利用全变分正则化有效克服了重构过程的病态性,保护了重构图像边缘。对比研究传统重构算法和L1/TV重构算法的性能。实验结果表明：L1/TV重构算法具有更强的抗噪声干扰能力,重构图像空间分辨率更高。     

基于自适应耦合局部数字全变分的超分辨重建

如何更好地保持重建图像的边缘信息是当今超分辨率重建技术的一个重要研究课题。针对基于全变分模型的超分辨率重建方法容易产生阶梯效应的不足,利用图像局部模糊熵信息,设计一个表征图像区域结构特征的局部自适应度量函数。利用该函数对全变分模型和超数字化全变分模型进行耦合,进而提出一种基于自适应耦合局部数字全变分模型的超分辨率重建方法。实验结果表明,该方法在保持图像几何边缘结构和消除平坦区域阶梯效应方面能力较强,重建效果较好。     

自适应步长非局部全变分约束迭代图像重建算法

针对计算机断层成像（CT）系统中,全变分（TV）迭代约束模型易于产生阶梯效应以及不能很好地保存图像中精细结构的问题,提出一种自适应步长的非局部全变分（NLTV）约束迭代重建算法。考虑到NLTV模型能较好保存和恢复图像细节以及纹理的特点,首先将CT模型当成在满足投影数据的保真项的解集中寻找满足特定正则项即NLTV最小化的解约束优化模型;然后,使用代数重建（ART）算法和分离布雷格曼（SB）来确保重建结果满足数据保真项和正则化项的约束;最后,以自适应最速下降-投影到凸集（ASD-POCS）算法作为基础迭代框架来重建图像。实验结果表明,在不含噪声的稀疏重建条件下,提出的算法使用30个角度的投影数据已经可以重建出理想的结果。在含噪稀疏数据重建实验中,该算法在30次迭代时已得到接近最终收敛的结果,且均方根误差（RMSE）是ASD-POCS算法的2.5倍。该重建算法能在稀疏投影数据下重建出精确的结果图像,同时改善了TV迭代模型的细节重建能力,且对噪声有一定的抑制作用。     

基于二阶总广义变差的欠采样图像重构方法

针对欠采样图像重构的凸优化问题,提出一种基于二阶总广义变差(TGV)范数最小化的算法。利用图像的二阶TGV半范作为正则约束项,自动地平衡一、二阶导数项,使得该算法可以更好地恢复图像边缘,有利于平滑噪声,避免阶梯效应。为了有效地计算该模型,通过正交投影和调整权重阈值对每一步迭代结果进行修正,最终获得更准确的重构结果。实验结果表明,与正交匹配追踪(OMP)模型和全变差(TV)模型比对,该算法重构的图像其峰值信噪比(PSNR)及结构相似度(SSIM)都有明显的提高,重构效果较好。     

一种基于图像边缘检测的全变分的去噪方法

提出了一种基于边缘检测的全变分图像去噪方法.在利用全变分去噪之前,先用Canny算子检测图像的边缘,对检测出的边缘区域和非边缘区域做标记;然后在边缘和非边缘区域设置不同的均衡系数,利用全变分模型对图像进行去噪.实验结果表明该算法能抑制以往全变分模型方法产生的阶梯效应,具有较好的图像恢复效果.     

Multiplicative noise removal via combining total variation and wavelet frame

Total variation (TV) regularization has been proved effective for cartoon images restoration however it produces staircase effects, and properly wavelet frames were confirmed to provide a more smoothing approximation to the original image. In this paper, a new model for multiplicative noise removal was proposed, which combines wavelet frame-based regularization and TV regularization. A modified proximal linearized alternating direction method is developed to solve the proposed model, considering that adding a new regularization term to the TV model would yield more parameters, which will result in computational difficulties. For the new model, the existence of solution and the convergence property of the proposed algorithm are proved. Numerical experiments have proved that the proposed model has a superior performance in terms of the peak signal-to-noise ratio and the relative error values for non-piecewise constant images when compared with some state-of-the-art multiplicative noise removal models.     

Low-rank tensor completion with fractional-Jacobian-extended tensor regularization for multi-component visual data inpainting

Several low-rank tensor completion methods have been integrated with total variation (TV) regularization to retain edge information and promote piecewise smoothness. In this paper, we first construct a fractional Jacobian matrix to nonlocally couple the structural correlations across components and propose a fractional-Jacobian-extended tensor regularization model, whose energy functional was designed proportional to the mixed norm of the fractional Jacobian matrix. Consistent regularization could thereby be performed on each component, avoiding band-by-band TV regularization and enabling effective handling of the contaminated fine-grained and complex details due to the introduction of a fractional differential. Since the proposed spatial regularization is linear convex, we further produced a novel fractional generalization of the classical primal-dual resolvent to develop its solver efficiently. We then combined the proposed tensor regularization model with low-rank constraints for tensor completion and addressed the problem by employing the augmented Lagrange multiplier method, which provides a splitting scheme. Several experiments were conducted to illustrate the performance of the proposed method for RGB and multispectral image restoration, especially its abilities to recover complex structures and the details of multi-component visual data effectively.     

Reconstruction of multi-view compressed imaging using weighted total variation

This paper concentrates on the problem of image reconstruction from compressed sensing (CS) measurements in multi-view compressed imaging systems, where each view is acquired independently by CS technique. In order to take advantage of both the inter-view correlation and the spatial prior information in multi-view image sets, a weighted total variation (TV) regularized model, which combines the TV norm of a target view and the TV norm of the corresponding residual, is proposed. To efficiently solve the weighted TV regularization constrained problem, novel algorithms are presented for both the anisotropy TV and the isotropy TV cases. Given the multi-view CS measurements, a sliding window-based recovery framework is also developed to work with the weighted TV-based reconstruction algorithms and produce high-quality results. We show by experiments that the proposed methods greatly outperform the straight forward reconstruction which applies view by view image reconstruction independently, and also have significant advantages over other benchmark methods.     

Multiplicative noise removal via adaptive learned dictionaries and TV regularization

Multiplicative noise removal is a key issue in image processing problem. While a large amount of literature on this subject are total variation (TV)-based and wavelet-based methods, recently sparse representation of images has shown to be efficient approach for image restoration. TV regularization is efficient to restore cartoon images while dictionaries are well adapted to textures and some tricky structures. Following this idea, in this paper, we propose an approach that combines the advantages of sparse representation over dictionary learning and TV regularization method. The method is proposed to solve multiplicative noise removal problem by minimizing the energy functional, which is composed of the data-fidelity term, a sparse representation prior over adaptive learned dictionaries, and TV regularization term. The optimization problem can be efficiently solved by the split Bregman algorithm. Experimental results validate that the proposed model has a superior performance than many recent methods, in terms of peak signal-to-noise ratio, mean absolute-deviation error, mean structure similarity, and subjective visual quality.     

非凸总广义变差图像恢复模型

为有效地保护图像的几何结构,提出了一种非凸二阶总广义变差图像恢复模型。该模型引入了类似于[L0]范数的非凸稀疏正则约束,模型能更好地保护图像的结构特征。为有效地计算该模型,采用迭代重加权和原始-对偶算法。数值实验表明,相比于最近的二阶总广义变差方法,该方法获得了较好的实验结果。     

区间约束的全变差图像复原和自动参数估计

因为数字图像的像素仅能取得给定动态范围内的有限值,像素值的区间约束在图像复原中引起广泛关注. 该文研究了带有正则化参数自动估计的区间约束全变差图像复原问题. 通过变量分裂并引入多组辅助变量,区间约束的全变差最小化问题被分解为一系列更易求解的子问题. 随后,交替方向法被用以求解相关的子问题. 根据Morozov偏差准则,在每步迭代中,正则化参数以闭合形式实现自适应更新. 图像复原实验表明,当较高比例的图像像素值位于给定动态范围的边界时,所提方法可以获得更为精确的复原结果.     

Augmented Lagrangian Method for Total Variation Based Image Restoration and Segmentation Over Triangulated Surfaces

Recently total variation (TV) regularization has been proven very successful in image restoration and segmentation. In image restoration, TV based models offer a good edge preservation property. In image segmentation, TV (or vectorial TV) helps to obtain convex formulations of the problems and thus provides global minimizations. Due to these advantages, TV based models have been extended to image restoration and data segmentation on manifolds. However, TV based restoration and segmentation models are difficult to solve, due to the nonlinearity and non-differentiability of the TV term. Inspired by the success of operator splitting and the augmented Lagrangian method (ALM) in 2D planar image processing, we extend the method to TV and vectorial TV based image restoration and segmentation on triangulated surfaces, which are widely used in computer graphics and computer vision. In particular, we will focus on the following problems. First, several Hilbert spaces will be given to describe TV and vectorial TV based variational models in the discrete setting. Second, we present ALM applied to TV and vectorial TV image restoration on mesh surfaces, leading to efficient algorithms for both gray and color image restoration. Third, we discuss ALM for vectorial TV based multi-region image segmentation, which also works for both gray and color images. The proposed method benefits from fast solvers for sparse linear systems and closed form solutions to subproblems. Experiments on both gray and color images demonstrate the efficiency of our algorithms.     

一种改进的最小二乘正则化的图像复原方法

在常用的最小二乘正则化方法的基础上,提出了一种改进的图像复原方法。在运算中,首先用四阶偏微分方程方法对模糊图像进行噪声处理,得到一幅中间图像,然后对这个中间图像采用最小二乘正则化方法进行处理,便得到了最终的复原图像。实验表明,该方法不仅能克服问题的病态性,而且复原后的图像比最小二乘正则化方法复原后的图像整体视觉效果和峰值信噪比都有明显的提高。