基于奇异值分解的图像去噪

提出了利用奇异值分解去除图像噪声的方法。从矩阵的角度出发,通过对图像矩阵进行奇异值分解,将包含图像信息的矩阵分解到一系列奇异值和奇异值矢量对应的子空间中,然后通过有效奇异值重构图像矩阵达到去噪目的。试验利用MATLAB通过对MRI(核磁共振)医学图像进行去噪处理,验证了奇异值分解的去噪效果,并且通过对多幅图像的试验结果进行分析,得到了去噪重构图像时所需有效奇异值数目的统计值。     

基于稀疏码收缩的图像去噪

数据的描述方法对提取数据特征至关重要,通常这种描述方法是基于数据的线性变换。传统的的傅立叶变换、离散余弦变换、主分量分析等线性变换方法都是基于全局变换的思想,无法反映图像在时频域的局部特征。独立分量分析是一种多维数据线性变换的方法,它从数据间的高阶统计特性出发,提取的图像数据特征基函数在空间频域中体现了方向性和局部性,能很好的自适应图像数据,并且其所得系数具有稀疏分布的特性。用它对无噪声图像数据进行学习,利用得到的稀疏码变换矩阵对噪声图像数据进行稀疏码变换,得到稀疏成分,并结合最大似然估计得到的软门限算子对该稀疏成分进行收缩,从而达到了去除图像噪声的目的。试验表明该方法在去噪效果和保存图像细节方面明显优于传统的维纳滤波方法。     

基于稀疏表达的图像去噪方法研究

提出一种基于混合字典的图像稀疏分解去噪方法。使用小波包函数和离散余弦函数构成混合字典,采用匹配追踪算法对图像进行稀疏分解,提取含噪图像中的稀疏成分,最后利用稀疏成分进行图像重构,达到去除图像中噪声的目的。实验中与单一字典稀疏分解去噪算法进行了对比,结果表明,所提出的混合字典稀疏去噪算法可有效提取图像中的稀疏结构,改善重构图像的主客观质量。     

基于稀疏表示的图像去噪和超分辨率重建

目前超分辨率的研究分成静态图像超分辨率和动态图像超分辨率两大类,静态图像超分辨率是指利用单张低分辨率图像内容来重建出高分辨率图像,本质上高分辨率图像的高频成分不能由原有低频成分算出,故如何补足高频成分以避免模糊现象是提升视觉质量的关键也是研究重点。图像去噪和超分辨率的目的是为了解决数字图像分辨率不足所提出的技术。这个技术主要是应用在某些只能得到单张低分辨率图像的场合,利用仅有的一张低分辨率图像来产生应用上所需的高分辨率图像。稀疏表示作为一种重要的数据编码与表达方式,不仅在人类的视觉认知机理上具有明确的理论依据,而且在信号表达与重建理论方面得到了严格的证明和推导。本文主要采用稀疏表示理论,对图像去噪和超分辨率重建的相关技术与算法进行研究。     

基于K-SVD字典稀疏分解的实木地板去噪方法

针对实木地板的图像获取过程中,所产生的噪声问题,引入了K-SVD字典的学习算法,提出了一种图像的有用信息稀疏分解去噪的方法,目的是有效的保留实木地板的有用纹理信息,并抑制其中掺杂的噪声。通过对图像稀疏分解后得到的值,来进行图像重构,就可以达到图像的去噪目的。首先,构造一个初始化的DCT字典,对图像分块处理;接着,在这个初始化字典的基础之上,进行纹理信息的稀疏分解,同时,对它们之间的残差值进行奇异值分解,更新字典;最后,利用得出的最优化字典,采用正交匹配重构算法,完成去噪图像的重建。实验表明,该算法得出的图像主观效果好,减少了去噪后的模糊程度及保留更多细节信息,在不同程度的噪声下,PSNR较高。     

基于差分进化算法的交通图像稀疏分解

提出了一种基于差分进化算法的交通图像稀疏分解方法,该方法采用非对称原子和收敛速度较快和寻优能力强的差分进化算法,来实现对交通图像的稀疏分解。仿真实验结果表明,该方法能对交通图像进行快速、有效地稀疏分解。     

基于模拟退火算法的稀疏表示图像去噪

使用稀疏表示的方法对图像去噪。对于稀疏表示最关键的是稀疏表示系数和自适应字典的确定,如何同时找到这两个最优的参数是研究的主要问题。通过模拟退火算法得到最优的自适应字典与相对应的稀疏系数。用求得的字典和稀疏系数进行逆运算得到去噪后的图像,完成图像去噪。与广泛使用的K-SVD算法对比,所提算法的峰值信噪比提高6.9%,在时间复杂度上改善了13.7%。     

利用FFT实现基于MP的信号稀疏分解

该文研究基于Matching Pursuit（MP）方法实现的信号稀疏分解算法，通过对信号稀疏分解中使用的过完备原子库结构特性的分析，提出了一种新的信号稀疏分解算法。该算法首先通过利用原子库的结构特性，很好地处理了稀疏分解过程中计算量和存储量之间的关系。在此基础上，把信号稀疏分解中计算量很大的内积运算转换成互相关运算，最后用FFT实现互相关运算，从而大大提高了信号稀疏分解的速度。算法的有效性为实验结果所证实。     

基于稀疏表示的Shearlet域SAR图像去噪

该文通过分析SAR图像的噪声成因以及其斑点噪声模型,结合图像的稀疏表示理论提出一种基于稀疏表示的Shearlet域SAR图像去噪算法。算法从整体上对SAR图像进行去噪：首先对SAR图像进行Shearlet变换,然后利用稀疏表示模型构造出去噪的最优化模型,在此基础上进行迭代去噪,然后重构SAR图像得到去噪后的图像。实验结果表明：该文所提出的算法不仅可以显著去除相干斑噪声,提高去噪图像的峰值信噪比(Peak Signal to Noise Ratio, PSNR),还明显地改善了图像的视觉效果,更好地保留了图像纹理信息。     

基于稀疏表示的红外图像去噪算法研究

红外图像具有动态范围窄、对比度低、易受噪声污染等缺点,传统红外图像去噪算法在去除噪声的同时也滤掉了图像细节。提出了一种基于稀疏表示的红外图像去噪新方法。该方法首先将原始红外图像进行聚类分析,再将每一聚类子图像分解成字典,由稀疏系数矩阵重构去噪后的红外图像。实验结果表明,该方法相比于传统红外图像去噪算法,能更好地保留图像的细节信息,视觉效果比较理想。     

Multi-stage image denoising based on correlation coefficient matching and sparse dictionary pruning

We present a novel image denoising method based on multiscale sparse representations. In tackling the conflicting problems of structure extraction and artifact suppression, we introduce a correlation coefficient matching criterion for sparse coding so as to extract more meaningful structures from the noisy image. On the other hand, we propose a dictionary pruning method to suppress noise. Based on the above techniques, an effective dictionary training method is developed. To further improve the denoising performance, we propose a multi-stage sparse coding framework where sparse representations are obtained in different scales to capture multiscale image features for effective denoising. The multi-stage coding scheme not only reduces the computational burden of previous multiscale denoising approaches, but more importantly, it also contributes to artifact suppression. Experimental results show that the proposed method achieves a state-of-the-art denoising performance in terms of both objective and subjective quality and provides significant improvements over other methods at high noise levels.     

Bayesian sparse hierarchical model for image denoising

Sparse models and their variants have been extensively investigated, and have achieved great success in image denoising. Compared with recently proposed deep-learning-based methods, sparse models have several advantages: (1) Sparse models do not require a large number of pairs of noisy images and the corresponding clean images for training. (2) The performance of sparse models is less reliant on the training data, and the learned model can be easily generalized to natural images across different noise domains. In sparse models, ${\ell }_0$ norm penalty makes the problem highly non-convex, which is difficult to be solved. Instead, ${\ell }_1$ norm penalty is commonly adopted for convex relaxation, which is considered as the Laplacian prior from the Bayesian perspective. However, many previous works have revealed that ${\ell }_1$ norm regularization causes a biased estimation for the sparse code, especially for high-dimensional data, e.g., images. In this paper, instead of using the ${\ell }_1$ norm penalty, we employ an improper prior in the sparse model and formulate a hierarchical sparse model for image denoising. Compared with other competitive methods, experiment results show that our proposed method achieves a better generalization for images with different characteristics across various domains, and achieves state-of-the-art performance for image denoising on several benchmark datasets.     

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SVD的小波变换图像去噪方法

针对传统SVD图像去噪方法的不足,提出了一种基于SVD分解的小波分解图像去噪方法。通过对小波变换的系数矩阵进行奇异值分解,将其中的信号特征成分和噪声分解到不同的正交子空间中,在子空间中选取集成信号特征成分的奇异值矢量进行重构,从而提取出淹没在噪声中的信号成分。实验结果表明该文提出的方法适用于图像信号的提取,与传统的SVD去噪方法相比,它提取出的信号特征成分更完整,信噪比更高。     

Denoising by low-rank and sparse representations

Due to the ill-posed nature of image denoising problem, good image priors are of great importance for an effective restoration. Nonlocal self-similarity and sparsity are two popular and widely used image priors which have led to several state-of-the-art methods in natural image denoising. In this paper, we take advantage of these priors and propose a new denoising algorithm based on sparse and low-rank representation of image patches under a nonlocal framework. This framework consists of two complementary steps. In the first step, noise removal from groups of matched image patches is formulated as recovery of low-rank matrices from noisy data. This problem is then efficiently solved under asymptotic matrix reconstruction model based on recent results from random matrix theory which leads to a parameter-free optimal estimator. Nonlocal learned sparse representation is adopted in the second step to suppress artifacts introduced in the previous estimate. Experimental results, demonstrate the superior denoising performance of the proposed algorithm as compared with the state-of-the-art methods.     

基于多分辨奇异值分解的多聚焦图像融合

提出了一种多分辨奇异值分解（MSVD）的新框架,并把它应用于多聚焦图像融合中.首先,基于分块算法原理,利用奇异值分解获得具有不同分辨率的一幅近似和三幅细节图像.然后结合重构算法,给出了图像的融合框架.其次,对比基于离散小波变换（DWT）的融合算法,基于MSVD的融合效果更好,而且 MSVD的基向量只依赖于图像本身而不像小波需要固定的基.最后,采用客观性能指标对结果图像进行评价.实验结果表明,本文的方法不仅简单易行,而且图像表现出良好的视觉效果,清晰度和空间频率都有很大提高.     

轮廓波和非负稀疏编码收缩的毫米波图像恢复

针对毫米波图像存在的分辨率较低的问题,结合局部非负稀疏编码（non-negative sparse coding,NNSC）算法的自适应高阶统计特性以及轮廓波分解的方向性和能量变化特性,提出了一种新的基于轮廓波和NNSC收缩的毫米波图像恢复方法。NNSC算法是近年来发展起来的模拟人类视觉系统信息处理的有效方法。使用NNSC训练得到的特征基向量和最大似然估计（MLE）,能够自适应地确定收缩去噪阈值,并把该收缩技术应用到轮廓波变换域,则能够大大减少毫米波图像中的大量未知噪声,提高毫米波图像的恢复质量。采用无噪自然图像验证基于轮廓波和NNSC收缩的图像恢复方法,实验结果证实了所提出的算法的有效性和实用性,表明该方法能够有效地用于低分辨率图像的恢复。     

Color image quality assessment based on sparse representation and reconstruction residual

Image quality assessment (IQA) is a fundamental problem in image processing. While in practice almost all images are represented in the color format, most of the current IQA metrics are designed in gray-scale domain. Color influences the perception of image quality, especially in the case where images are subject to color distortions. With this consideration, this paper presents a novel color image quality index based on Sparse Representation and Reconstruction Residual (SRRR). An overcomplete color dictionary is first trained using natural color images. Then both reference and distorted images are represented using the color dictionary, based on which two feature maps are constructed to measure structure and color distortions in a holistic manner. With the consideration that the feature maps are insensitive to image contrast change, the reconstruction residuals are computed and used as a complementary feature. Additionally, luminance similarity is also incorporated to produce the overall quality score for color images. Experiments on public databases demonstrate that the proposed method achieves promising performance in evaluating traditional distortions, and it outperforms the existing metrics when used for quality evaluation of color-distorted images.