张量低秩约束下的多帧图像去模糊

矩阵低秩估计模型在图像处理任务中有着广泛地运用.针对图像去模糊,利用矩阵低秩先验能保留图像的重要边缘信息从而实现去模糊.而对于多帧图像去模糊,基于矩阵的低秩模型并未充分考虑多帧图像间的时序和空间关系.针对该问题,我们提出基于三维张量低秩先验的多帧视频图像盲去模糊模型.在模型中,首先将多帧连续图像按时序维堆叠成张量,显式...     

Weighted truncated nuclear norm regularization for low-rank quaternion matrix completion

In recent years, quaternion matrix completion (QMC) based on low-rank regularization has been gradually used in image processing. Unlike low-rank matrix completion (LRMC) which handles RGB images by recovering each color channel separately, QMC models retain the connection of three channels and process them as a whole. Most of the existing quaternion-based methods formulate low-rank QMC (LRQMC) as a quaternion nuclear norm (a convex relaxation of the rank) minimization problem. The main limitation of these approaches is that they minimize the singular values simultaneously such that cannot approximate low-rank attributes efficiently. To achieve a more accurate low-rank approximation, we introduce a quaternion truncated nuclear norm (QTNN) for LRQMC and utilize the alternating direction method of multipliers (ADMM) to get the optimization in this paper. Further, we propose weights to the residual error quaternion matrix during the update process for accelerating the convergence of the QTNN method with admissible performance. The weighted method utilizes a concise gradient descent strategy which has a theoretical guarantee in optimization. The effectiveness of our method is illustrated by experiments on real visual data sets.     

基于非局部相似块低秩的压缩感知图像重建算法

传统的压缩感知重建算法利用信号在某个特征空间下的稀疏性构建目标优化函数,但没有充分考虑信号的局部特性和结构化属性,影响了算法的重建性能和算法的适应性.本文考虑图像的非局部自相似性(NonlocalSelf-Similarity,NLSS),提出一种基于图像相似块低秩的压缩感知图像重建算法,将图像恢复问题转化为聚合的相似块矩阵秩最小问题.算法以最小压缩感知重建误差为约束构建优化模型,并采用加权核范数最小化算法(Weighed Nuclear Norm Minimization,WNNM)求解低秩优化问题,很好地挖掘了图像自身的信息和结构化稀疏特征,保护了图像的结构和纹理细节.多个测试图像、不同采样率下的实验证明了算法的有效性,特别是在低采率下对于纹理较为丰富的图像,提出的算法图像重建质量较明显的优于最新的同类算法.     

低秩遮挡图像去噪方法

为获得清晰的低秩图像,提出一种将低秩矩阵填充 (LRMC)与低秩矩阵恢 复(LRMR)联合的新模型,基于非精确增广拉格朗日乘子(IALM)法进行求解,运用LRMC去除遮 挡并填充缺失部 分,再利用LRMR去除噪声,得到完整的图像。以恢复时间、信噪比(SNR)、峰 值信噪比(PSNR)、差错率(err)等做评价标准,对3幅受噪声污染的图像的恢复结果表明, 本文提出的联合LRMC与LRMR的新模型,既能去除遮挡又能够填充图像的缺失部 分,能够达到理想的恢复效果。     

应用残差总变分和低秩表示的视频去噪算法

为了有效地去除视频当中的高斯噪声和脉冲噪声,提出了一种新的视频去噪算法。该算法通过相似图像块组内的残差值总变分及低秩表示来同时探索图像块内的局部相似性以及图像块之间的相似性。首先,采用块匹配的方式在含噪视频中寻找最相似图像块并组合成图像块组;其次将每个相似图像组表达为一个低秩矩阵及一个稀疏矩阵之和,并同时强调低秩矩阵内的残差总变分范数最小化;最后,通过求解最优化问题获得最终的低秩矩阵,即恢复出的图像块组数据。实验结果表明,本文的算法能够有效去除视频当中含有的高斯噪声和脉冲噪声。与同类算法相比,能够获得显著的峰值信噪比提升。      

低秩稀疏分解下多尺度积的运动目标检测方法

针对基于矩阵分解的运动目标检测方法易受自然场景中背景的小幅抖动和摄像头抖动等因素影响的问题,提出了一种利用多尺度积的低秩稀疏矩阵分解算法。算法假设,静态背景视频序列中,每帧图像背景可近似视为处于同一低秩子空间中,图像前景则可视为偏离低秩空间的残差部分。首先对图像序列进行滤波、仿射变换等预处理得到视频序列观测数据矩阵;然后对数据矩阵进行低秩稀疏分解得到序列图像的低秩背景部分和每帧图像的稀疏前景部分;最后对稀疏前景部分采用小波变换模极大值与多尺度积方法检测目标边缘,并进行形态学处理,得到准确的运动目标。实验结果表明,算法检测到的运动目标清晰、完整,能有效地处理光照变化、摄像头小幅度抖动、图像背景局部小幅度变化等情况下的运动目标检测。      

光照健壮人脸识别的低秩相对梯度直方图特征

为了进一步提升人脸梯度特征的光照健壮性,本文结合低秩分解能有效分离图像本质特征和噪声的特性,提出了一种光照健壮的低秩相对梯度直方图特征提取方法。首先,通过对人脸图像进行相对梯度运算获得了图像的相对梯度幅值图像和各像素的梯度方向信息。然后,为了去除相对梯度图像中由于非均匀光照而引入的光照边缘误差,利用低秩分解将相对梯度图像分解为低秩分量和稀疏噪声分量之和。最后,结合人脸图像的梯度方向信息对相对梯度图像的低秩分量进行离散化、滤波和局部二值模式编码形成了人脸的低秩相对梯度直方图特征。在经典的FE-RET子集以及具有代表性的YaleB和PIE光照子集上的实验显示：低秩相对梯度直方图特征的人脸识别性能显著优于相对梯度直方图特征、方向梯度幅值模式特征和图像低秩特征等方法的性能;在YaleB子集上,低秩相对梯度直方图特征的人脸识别精度比相对梯度直方图特征的人脸识别精度高至少4％。实验结果证明,低秩相对梯度直方图特征对光照变化,尤其是非均匀光照变化的人脸识别具有很强的健壮性。     

Gamma norm minimization based image denoising algorithm

Focusing on the issue of rather poor denoising performance of the traditional kernel norm minimization based method caused by the biased approximation of kernel norm to rank function,based on the low-rank theory,a gamma norm minimization based image denoising algorithm was developed.The noisy image was firstly divided into some overlapping patches via the proposed algorithm,and then several non-local image patches most similar to the current image patch were sought adaptively based on the structural similarity index to form the similar image patch matrix.Subsequently,the non-convex gamma norm could be exploited to obtain unbiased approximation of the matrix rank function such that the low-rank denoising model could be constructed.Finally,the obtained low-rank denoising optimization issue could be tackled on the basis of singular value decomposition,and therefore the denoised image patches could be re-constructed as a denoised image.Simulation results demonstrate that,compared to the existing state-of-the-art PID,NLM,BM3D,NNM,WNNM,DnCNN and FFDNet algorithms,the developed method can eliminate Gaussian noise more considerably and retrieve the original image details rather precisely.     

基于非局部双边随机投影低秩逼近图像去噪算法

该文提出一种基于非局部双边随机投影的低秩逼近图像去噪新方法。首先,对每个图像块通过非局部搜索寻找相似匹配块簇,然后对相似匹配块簇进行双边随机投影,用投影后的低秩结构恢复原图像。实验结果表明,所提方法比奇异值分解方法有较低的计算复杂度,比单边随机投影方法有较小的重构误差。特别是和3维块匹配方法相比,所提方法能保持相近的信噪比和较好的视觉质量。     

融合显著图和保真图的全参考图像质量评价

提出一种融合显著图(SM)和保真图(FM)的全参考图 像质量 评价算法,用于评价质降图像的失真度。利用亮度和色度的相似度提取质降图像相对于 参考图像的FM;对参考图像进行区域划分、全局显著性提取和纹理边缘补充得到SM,将SM与 质降图像的FM融合得到基 于感知的显著保真图(PSM),计算质降图像的客观评价得分。在标准数据库上的实验结果表 明,本文方法与主观评价能够很好保持一致,并对LIVE图像库中的5种失真图像均有很好的 表现。     

A unified framework for damaged image fusion and completion based on low-rank and sparse decomposition

Image fusion can integrate the complementary information of multiple images. However, when the images to be fused are damaged, the existing fusion methods cannot recover the lost information. Matrix completion, on the other hand, can be used to recover the missing information of the image. Therefore, the step-by-step operation of image fusion and completion can fuse the damaged images, but it will cause artifact propagation. In view of this, we develop a unified framework for image fusion and completion. Within this framework, we first assume that the image is superimposed by low-rank and sparse components. To obtain the separation of different components to fuse and restore them separately, we propose a low-rank and sparse dictionary learning model. Specifically, we impose low-rank and sparse constraints on low-rank dictionary and sparse component respectively to improve the discrimination of learned dictionaries and introduce the condition constraints of low-rank and sparse components to promote the separation of different components. Furthermore, we integrate the low-rank characteristic of the image into the decomposition model. Based on this design, the lost information can be recovered with the decomposition of the image without using any additional algorithm. Finally, the maximum $l_1$-norm fusion scheme is adopted to merge the coding coefficients of different components. The proposed method can achieve image fusion and completion simultaneously in the unified framework. Experimental results show that this method can well preserve the brightness and details of images, and is superior to the compared methods according to the performance evaluation.     

基于低秩矩阵恢复的SAR图像相干斑抑制方法

针对合成孔径雷达(SAR)图像相干斑噪声的特点,提出了一种基于低秩矩阵恢复的SAR图像相干斑抑制算法。该算法首先对SAR图像进行对数变换,将SAR图像相干斑乘性噪声转化为加性噪声;然后对变换后图像等步长遍历提取图像子参考块,利用局部块匹配技术寻找子参考块的相似块组建相似子集,合并数据集中所有相似子集,构建近似低秩的矩阵;再通过低秩矩阵恢复算法将矩阵分解为低秩矩阵部分和稀疏矩阵部分;最后将低秩矩阵部分逆变换回图像块,基于图像块灰度值对图像的每个像素进行加权重构,生成相干斑抑制后的SAR图像。实验表明,文中所提出的算法能够有效抑制SAR图像中的相干斑噪声,同时很好地保留了边缘细节特征。     

基于联合低秩稀疏分解的红外与可见光图像融合

为进一步提高红外与可见光融合图像的细节信息和整体对比度,降低伪影和噪声,考虑了红外与可见光图像的相关性,提出了一种基于联合低秩稀疏分解的红外与可见光图像融合方法。首先,利用联合低秩稀疏分解方法将红外和可见光源图像分别分解成共同低秩分量、特有低秩分量和特有稀疏分量;其次,利用非下采样Shearlet变换方法对特有低秩分量进行融合;然后,采用区域能量融合策略实现特有稀疏分量融合;最后,共有低秩分量与融合后的特有低秩分量和特有稀疏分量相加得到最终融合图像。在Nato-camp、Bristol Eden Project和TNO公共测试数据集上进行的实验测试了所提算法性能。实验结果表明,与其他9种融合方法相比,所提方法能够有效地提取红外图像中的目标信息和保留可见光图像的背景信息,熵、互信息、标准差、视觉信息保真度、差异相关系数之和和 Qy 客观评价指标明显优于对比方法。      

基于低秩子空间恢复的联合稀疏表示人脸识别算法

 针对阴影、反光及遮挡等原因破坏图像低秩结构这一问题,提出基于低秩子空间恢复的联合稀疏表示识别算法.首先将每个个体的所有训练样本图像看作矩阵 D ,将矩阵 D 分解为低秩矩阵 A 和稀疏误差矩阵 E ,其中 A 表示某类个体的'干净’人脸,严格遵循子空间结构, E 表示由阴影、反光、遮挡等引起的误差项,这些误差项破坏了人脸图像的低秩结构.然后用低秩矩阵 A 和误差矩阵 E 构造训练字典,将测试样本表示为低秩矩阵 A 和误差矩阵 E 的联合稀疏线性组合,利用这两部分的稀疏逼近计算残差,进行分类判别.实验证明该稀疏表示识别算法有效,识别精度得到了有效提高.     

基于光谱加权低秩矩阵分解的高光谱影像去噪方法

高光谱遥感影像在获取和传输过程中会受到各种类型噪声的污染,不仅降低影像质量,也限制了其后续应用的精度。高光谱影像噪声类型复杂多样,且噪声在不同波段上的强度也并不相同。通过引入光谱域上的权重矩阵,文中提出了一种基于光谱加权低秩矩阵分解的高光谱遥感影像混合噪声去除方法,利用光谱权重矩阵均衡不同波段的噪声强度差异性。为进一步将噪声与纯净影像分离,利用加权核范数最小化来约束纯净高光谱影像的局部低秩结构,并利用交替方向乘子法对所提出的模型进行优化求解。通过对模拟与真实高光谱遥感数据的实验,验证了所提方法的有效性与优越性。     

Image-pair-based deblurring with spatially varying norms and noisy image updating

This paper presents a deblurring method that effectively restores fine textures and details, such as a tree’s leaves or regular patterns, and suppresses noises in flat regions using consecutively captured blurry and noisy images. To accomplish this, we used a method that combines noisy image updating with one iteration and fast deconvolution with spatially varying norms in a modified alternating minimization scheme. The captured noisy image is first denoised with a nonlocal means (NL-means) denoising method, and then fused with a deconvolved version of the captured blurred image on the frequency domain, to provide an initially restored image with less noise. Through a feedback loop, the captured noisy image is directly substituted with the initially restored image for one more NL-means denoising, which results in an upgraded noisy image with clearer outlines and less noise. Next, an alpha map that stores spatially varying norm values, which indicate local gradient priors in a maximum-a-posterior (MAP) estimation, is created based on texture likelihoods found by applying a texture detector to the initially restored image. The alpha map is used in a modified alternating minimization scheme with the pair of upgraded noisy images and a corresponding point spread function (PSF) to improve texture representation and suppress noises and ringing artifacts. Our results show that the proposed method effectively restores details and textures and alleviates noises in flat regions.     

Image completion with approximate convex hull tensor decomposition

Many image completion methods are based on a low-rank approximation of the underlying image using matrix or tensor decomposition models. In this study, we assume that the image to be completed is represented by a multi-way array and can be approximated by a conical hull of subtensors in the observation space. If an observed tensor is near-separable along at least one mode, the extreme rays, represented by the selected subtensors, can be found by analyzing the corresponding convex hull. Following this assumption, we propose a geometric algorithm to address a low-rank image completion problem. The extreme rays are extracted with a segmented convex-hull algorithm that is suitable for performing noise-resistant non-negative tensor factorization. The coefficients of a conical combination of such rays are estimated using Douglas–Rachford splitting combined with the rank-two update least-squares algorithm. The proposed algorithm was applied to incomplete RGB images and a hyperspectral 3D array with a large number of randomly missing entries. Experiments confirm its good performance with respect to other well-known image completion methods.     

Significance of image representation for face verification

In this paper we discuss the significance of representation of images for face verification. We consider three different representations, namely, edge gradient, edge orientation and potential field derived from the edge gradient. These representations are examined in the context of face verification using a specific type of correlation filter, called the minimum average correlation energy (MACE) filter. The different representations are derived using one-dimensional (1-D) processing of image. The 1-D processing provides multiple partial evidences for a given face image, one evidence for each direction of the 1-D processing. Separate MACE filters are used for deriving each partial evidence. We propose a method to combine the partial evidences obtained for each representation using an auto-associative neural network (AANN) model, to arrive at a decision for face verification. Results show that the performance of the system using potential field representation is better than that using the edge gradient representation or the edge orientation representation. Also, the potential field representation derived from the edge gradient is observed to be less sensitive to variation in illumination compared to the gray level representation of images.     

High resolution 3D imaging in MIMO radar with sparse array

High resolution three-dimensional (3D) imaging method using MIMO radar with sparse array is studied in this paper. A method based on compressive sensing (CS) is firstly given. However, the CS-based method has the off-grid problem which will reduce the estimation accuracy of scatterers’ position on the target. Moreover, a high dimensional measurement matrix is required in the CS-based method, which will lead to a heavy storage and computation burden. To solve the two problems of CS, a new method based on matrix completion is proposed in this paper. After reshaping the sparse 3D echo into a low-rank structured matrix, the full 3D echo can be recovered by solving a nuclear norm minimization problem. Then the accurate position of scatterers can be estimated by applying multi-dimensional harmonic retrieval methods to the full 3D echo. Finally, the high resolution 3D image of targets is reconstructed. The effectiveness of the method is validated by the results of comparative simulations.     

有监督低秩子空间恢复的正则鲁棒稀疏表示人脸识别算法

针对训练样本和测试样本均存在光照及遮挡时,破坏图像低秩结构问题,本文提出基于监督低秩子空间恢复的正则鲁棒稀疏表示人脸识别算法。首先,将所有训练样本构造成矩阵D,对矩阵D进行监督低秩矩阵分解,分解为低秩类相关结构A,低秩类内差异结构B和稀疏误差结构E;然后用主成分分析方法找到类相关结构A低秩子空间的变换矩阵;再通过变换矩阵将训练样本和测试样本投影到低秩子空间;最后,在低秩子空间中,通过正则鲁棒稀疏编码进行加权分类识别。在AR和Extended Yale B公开人脸数据库上的实验结果验证本文算法的有效性及鲁棒性。