一种求解带有冲击噪声的图像去模糊去噪问题的变步长分裂Bregman算法

分裂Bregman算法是一种有效的求解L1正则化问题的算法,Chen等人结合线性化、变步长、非单调等技术,改进了固定步长的分裂Bregman算法,提出了变步长分裂Bregman算法(BOSVS),并将该算法用于求解带有高斯噪声的图像去模糊去噪问题,其数值实验结果令人满意.但是它不能求解带有冲击噪声的图像去模糊去噪问题,我们在BOSVS算法基础上,提出了一种新的变步长分裂Bregman算法,用于求解带有冲击噪声的图像去模糊去噪问题.该算法一方面保留了BOSVS算法的线性化、变步长、非单调等特点;另一方面通过在原模型目标函数上增加一个L1正则项,使得模型不仅可以处理高斯噪声,还可以处理冲击噪声,因而适用范围比BOSVS算法更为广泛.初步数值实验结果表明,新算法得到结果的质量明显优于FTVd,且计算时间、算法效率也较有竞争力.     

自适应全变分图像去噪模型及其快速求解*

在联合冲击滤波器和非线性各向异性扩散滤波器对含噪图像做预处理的基础上,利用边缘检测算子选取自适应参数,构建能同时兼顾图像平滑去噪与边缘保留的自适应全变分模型,并基于Bregman迭代正则化方法设计了其快速迭代求解算法.实验结果表明,自适应去噪模型及其求解算法在快速去除噪声的同时保留了图像的边缘轮廓和纹理等细节信息,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.     

基于分裂Bergman的图像去噪实现

本文设计了一种基于基于分裂Bregman迭代方法的全变差图像去噪算法,最终通过实验表明,该算法具有有效性强,实现效率高,并且通过全变差图像去噪方法,很好的保留图像的边缘。     

自适应广义全变差的图像泊松去噪算法

针对医学、天文图像中的泊松噪声,基于广义全变差的图像泊松去噪模型,结合交替迭代极小化方法,提出一种自适应广义全变差的图像去噪算法。该算法利用广义交叉验证技术,使得模型中的正则化参数在算法迭代过程中可以自动更新。数值实验结果验证了该算法的有效性与可行性。     

基于二阶广义全变差正则项的模糊图像恢复算法

针对图像去模糊问题, 采用二阶广义全变差作为修复图像的正则项构建恢复模型, 并针对重建模型的高阶与非光滑特性, 给出了基于分裂Bregman 迭代的快速算法. 实验结果表明, 该模型和数值算法能够较好地恢复被噪声和模糊污染的图像, 同时可以很好地保留图像的纹理和细节信息.     

基于复合正则化的荧光显微图像三维重建

针对荧光显微图像三维重建问题,采用广义全变差和剪切波变换作为重建图像的正则项,并构建重建模型,针对重建模型的高阶与非光滑特性,提出了基于变量分离理论和分裂Bregman迭代的快速重建算法,该算法不仅能够实现边缘保存,避免阶梯效应,还可以通过合理选择参数,获得很好的重建效果,在模拟图像栈和真实荧光显微图像栈的实验结果验证了该算法的有效性和可行性。     

结合波原子和全变差方法的图像去噪*

传统的硬阈值去噪会产生伪吉普斯现象,而波原子本身的周期化过程也会出现新的方向性纹理失真。采用全变差最小化方法来抑制这些失真,提出一种改进的波原子去噪算法。该算法不是直接将低于阈值的小系数置为零,而是对这些系数在全变差最小的意义上作修正迭代,得到最终的去噪图像。数值实验结果表明,波原子去噪保留边缘和纹理的效果优于小波和曲线波,改进算法去噪的视觉质量明显好于传统波原子去噪。最后还指出了进一步的研究方向。     

修正ROF模型的分裂Bregman算法

ROF去噪模型对高斯噪声有很好的去除效果,但并不适合处理泊松噪声.该模型会造成含泊松噪声图像的边界模糊.针对泊松噪声类型,文献上提出了修正ROF模型.分析了修正ROF模型解的存在性和唯一性.采用逐步线性化的方法处理该模型具有强烈非线性的保真项,克服了其求解上的困难,并应用分裂Bregman算法,使得该模型可以快速求解.数值实验结果表明,该算法较好地保留了图像亮度较弱部分的细节信息,对实际CT图像的去噪效果优于传统的ROF模型,且收敛速度快.     

Bregman交替迭代遥感图像复原方法

针对多种退化因素的遥感图像复原问题,提出一种基于Bregman迭代的遥感图像消除不规则采样、去模糊和去噪总变差复原方法。在此基础上,结合非局部正则化方法,提出一种自适应计算非局部均值滤波器参数的方法。求解时使用交替最小化方法将复杂的复原问题分割为两个容易求解的子问题。实验结果表明,本文方法比其他基于Bregman迭代的方法收敛速度快、复原效果好,且加入非局部正则化后具有更好的纹理细节信息保持能力。     

广义齐型Besov范数约束下的图像分解

为了将图像分解为分片光滑的结构部分和振荡部分,提出一种新的变分图像分解模型.该模型利用第二代曲波和局部余弦基分别表征含噪图像中的结构分量和纹理分量,并采用全变差半范约束分片光滑部分的结构性;同时利用 Meyer 所建议的广义齐型 Besov 范数对噪声分量进行约束;最后利用基追踪去噪算法对新模型进行迭代求解.理论分析和实验结果表明,该算法对噪声具有较强的鲁棒性,并使边缘和细小的纹理信息保持稳定.     

Operator Splittings,Bregman Methods and Frame Shrinkage in Image Processing

We examine the underlying structure of popular algorithms for variational methods used in image processing. We focus here on operator splittings and Bregman methods based on a unified approach via fixed point iterations and averaged operators. In particular, the recently proposed alternating split Bregman method can be interpreted from different points of view—as a Bregman, as an augmented Lagrangian and as a Douglas-Rachford splitting algorithm which is a classical operator splitting method. We also study similarities between this method and the forward-backward splitting method when applied to two frequently used models for image denoising which employ a Besov-norm and a total variation regularization term, respectively. In the first setting, we show that for a discretization based on Parseval frames the gradient descent reprojection and the alternating split Bregman algorithm are equivalent and turn out to be a frame shrinkage method. For the total variation regularizer, we also present a numerical comparison with multistep methods.     

A corner-weighted bounded Hessian model for image denoising

Image denoising is an essential step in the image processing task. The first-order variational model can remove noise while preserving edges, but it also generates the staircase effect. Although the bounded Hessian regulariser can reduce this side effect, it tends to blur object edges. In this paper, we propose a corner-weighted bounded Hessian model (CWBH) for image denoising, which has capability of removing noise without causing blurring object edges and artifacts. The bounded Hessian regularization at each pixel is controlled by a weight function which has an exponential form and depends on the corner response of the pixel. The split Bregman algorithm is adapted to decompose the proposed minimization problem into several subproblems which are solved directly using fast Fourier transform and the shrinkage operators. The proposed model is evaluated on synthetic and real noisy images for both spatially invariant and variant additive white Gaussian noise (AWGN). Extensive experiments demonstrate that our proposed model outperforms some state-of-the-art variational models for various types of noise and images. For uniform AWGN, CWBH surpasses other models on average by 0.014 for SSIM and by 0.77dB for PSNR; for spatially variant AWGN, these figures are 0.033 and 0.89dB, respectively.

     

基于小波包分解的整体变分去噪算法

由Rudin等人提出的整体变分（TV）模型被认为是目前最好的图像去噪模型之一。理论表明,TV模型对分块常量的图像去噪效果显著。对于纹理细节丰富的图像,通过引入小波包分解技术,对图像的纹理细节进行多层小波包分解,得到一系列近似分块常量的子图像,用TV模型对子图像分别进行处理,从而图像的纹理细节得到了更好的保留。相对于单独使用TV模型去噪,该方法得到的复原图像峰值信噪比（PSNR）提高了1 dB左右。同时由于采用改进的Bregman迭代方案求解TV模型,算法收敛时间得到了极大的减少。     

采用分裂Bregman的遥感影像亮度不均变分校正方法

目的：遥感影像成像过程由于受到传感器自身以及其他一些外部环境因素的影响,往往会呈现出整体的亮度不均,导致遥感影像解译和制图精度的降低。因此,需要对遥感影像进行亮度不均匀校正,提高影像的质量。方法：感知驱动的亮度不均变分校正方法,是一种新型的单幅遥感影像亮度不均校正方法,它受人眼视觉系统特性的启发,能够在有效校正影像整体亮度的同时增强局部对比度。本文用分裂Bregman迭代实现了对感知驱动亮度不均变分校正模型的最优化求解,在实现对影像整体亮度不均校正的同时,大幅提高了计算效率。结果：模拟实验和真实实验结果均表明采用分裂Bregman的亮度不均变分校正模型需要较少的计算时间,从效率上比采用最速下降法的校正模型提高了约6到7倍。结论：分裂Bregman方法能够有效求解感知驱动亮度不均变分模型,在保证校正结果整体亮度均匀,局部对比度增强的前提下,大大提高运算效率。     

A content-based recommendation algorithm for learning resources

Automatic multimedia learning resources recommendation has become an increasingly relevant problem: it allows students to discover new learning resources that match their tastes, and enables the e-learning system to target the learning resources to the right students. In this paper, we propose a content-based recommendation algorithm based on convolutional neural network (CNN). The CNN can be used to predict the latent factors from the text information of the multimedia resources. To train the CNN, its input and output should first be solved. For its input, the language model is used. For its output, we propose the latent factor model, which is regularized by L₁-norm. Furthermore, the split Bregman iteration method is introduced to solve the model. The major novelty of the proposed recommendation algorithm is that the text information is used directly to make the content-based recommendation without tagging. Experimental results on public databases in terms of quantitative assessment show significant improvements over conventional methods. In addition, the split Bregman iteration method which is introduced to solve the model can greatly improve the training efficiency.     

Bregmanized Domain Decomposition for Image Restoration

Computational problems of large-scale data are gaining attention recently due to better hardware and hence, higher dimensionality of images and data sets acquired in applications. In the last couple of years non-smooth minimization problems such as total variation minimization became increasingly important for the solution of these tasks. While being favorable due to the improved enhancement of images compared to smooth imaging approaches, non-smooth minimization problems typically scale badly with the dimension of the data. Hence, for large imaging problems solved by total variation minimization domain decomposition algorithms have been proposed, aiming to split one large problem into N>1 smaller problems which can be solved on parallel CPUs. The N subproblems constitute constrained minimization problems, where the constraint enforces the support of the minimizer to be the respective subdomain. In this paper we discuss a fast computational algorithm to solve domain decomposition for total variation minimization. In particular, we accelerate the computation of the subproblems by nested Bregman iterations. We propose a Bregmanized Operator Splitting–Split Bregman (BOS-SB) algorithm, which enforces the restriction onto the respective subdomain by a Bregman iteration that is subsequently solved by a Split Bregman strategy. The computational performance of this new approach is discussed for its application to image inpainting and image deblurring. It turns out that the proposed new solution technique is up to three times faster than the iterative algorithm currently used in domain decomposition methods for total variation minimization.     

采用分裂Bregman的遥感影像亮度不均变分校正

目的 遥感影像成像过程由于受到传感器自身以及其他一些外部环境因素的影响,往往会呈现出整体的亮度不均,导致遥感影像解译和制图精度的降低。因此,需要对遥感影像进行亮度不均匀校正,提高影像的质量。方法 感知驱动的亮度不均变分校正方法,是一种新型的单幅遥感影像亮度不均校正方法,它受人眼视觉系统特性的启发,能够在有效校正影像整体亮度的同时增强局部对比度。本文用分裂Bregman迭代实现了对感知驱动亮度不均变分校正模型的最优化求解,在实现对影像整体亮度不均校正的同时,大幅提高了计算效率。结果 模拟实验和真实实验结果均表明,采用分裂Bregman的亮度不均变分校正模型需要较少的计算时间,从效率上比采用最速下降法的校正模型提高了约67倍。结论 分裂Bregman方法能够有效求解感知驱动亮度不均变分模型,在保证校正结果整体亮度均匀,局部对比度增强的前提下,大大提高运算效率。     

一种基于局部符号差能量的非局部分割模型

针对灰度非均匀的图像,提出一种基于局部符号差能量的非局部图像分割模型。该模型包含基于局部符号差能量的数据驱动项和非局部全变分正则项,具有局部可分离性和全局一致性的特点。由于本文模型是凸的,因此在数值实现上可以采用split-Bregman迭代算法,具有较快的运算速度。同经典的基于局部区域的主动轮廓分割模型相比,该方法具有以下优点:(1)该模型受初始化的影响很小;(2)采用split-Bregman迭代算法,运算速度更快;(3)能够对具有细密纹理和具有弱边缘目标的图像进行正确分割。实验结果表明,该模型对灰度非均匀图像能够进行较准确的分割,相比其他模型具有更好的鲁棒性。