一种组稀疏高阶变分的图像复原模型

为了更好地利用图像的稀疏性以提高变分模型的图像复原性能,在自适应高阶变分模型中对图像的一阶梯度加以组稀疏限制,建立一种非凸的组稀疏高阶变分模型.为实现该非凸模型的优化求解,采用交替方向乘子法将模型的极小化问题分解成多变量的子问题,进而采用IRL1与MM算法分别求解高阶变分与组稀疏极小化问题,实现退化图像的复原处理.通过...     

结合稀疏表示与匹配梯度分布的图像复原

针对基于稀疏表示的传统图像复原方法无法准确恢 复图像小尺度细节的不足,提出了一种结合稀疏 表示与匹配梯度分布的图像复原方法。首先在稀疏表示图像复原模型的基础上,利用参数化 的超拉 普拉斯分布估计原始图像的梯度分布;然后,通过对图像的梯度分布进行全局约束,利用梯 度直方图匹配 操作匹配图像梯度分布,使复原图像的梯度分布尽可能接近原始图像。仿真实验结果表明 , 本文算法能够取得较优的复原效果, 并且能以较高精度复原图像的细节信息。     

基于投影的稀疏表示与非局部正则化图像复原方法

提出一种基于投影的稀疏表示与非局部正则化相结合的图像去模糊、去噪图像复原方法.该方法结合了自适应构造字典的稀疏表示与非局部总变差,提出的正则化模型分解为三个投影子问题进行求解以提高求解效率.实验结果表明,本文所提出的图像复原方法能够有效地保持原图像的纹理细节信息,对于不同程度的退化图像上均有较好的复原结果,在视觉效果和客观评价指标上均优于相比较的现有方法.     

基于多层小波变换的压缩感知图像快速复原算法研究

为了能够有效地改善低码率压缩图像的主客观质量,减少图像复原所需观测数据量,节约存储空间和计算量,提出了一种基于多层小波变换的压缩感知图像快速复原算法。该算法将压缩感知理论中的信号重构方法运用于图像复原领域,建立基于压缩感知的图像复原模型,通过少量低维投影空间的测量值并根据信号稀疏表示的先验知识对信号进行精确或高概率的复原。通过Matlab进行实验仿真,结果表明,该算法与传统的图像复原算法相比,通过相同的观测数据量可以获得更高的PSNR,复原效率也得到了提高。     

图像去模糊的l0范数最小化方法

针对经典的图像去模糊问题,提出了一种基于l0-范数约束的图像去模糊算法。该算法结合图像稀疏性的特点,利用l0-范数作为正则项约束,保证了恢复图像的稀疏性要求。为了有效的求解l0-范数优化问题,引入两个辅助变量,将原问题分解为两个子优化问题,并采用交替方向法进行快速求解。实验结果表明,对于不同程度的高斯模糊和运动模糊,该算法都能够得到有效的恢复结果。     

多形态稀疏性正则化的图像超分辨率算法

 如何设计更加高效并能保持图像几何和纹理结构的多幅图像超分辨模型和算法是目前该领域有待解决的难点问题.针对图像的几何、纹理结构形态,分别建立符合类内强稀疏而类间强不相干的几何结构和纹理分量稀疏表示子成份字典,形成图像的多形态稀疏表示模型,进而提出一种新的基于多形态稀疏性正则化的多帧图像超分辨凸变分模型,模型中的正则项刻画了理想图像在多成份字典下的稀疏性先验约束,保真项度量其在退化模型下与观测信号的一致性,采用交替迭代法对该多变量优化问题进行数值求解,每一子问题采用前向后向的算法分裂法进行快速求解.针对可见光与红外图像序列进行了数值仿真,实验结果验证了本文模型与数值算法的有效性.     

基于分裂Bregman方法的全变差图像去模糊

针对全变差图像去模糊问题,提出一种基于分裂Bregman方法的全变差图像去模糊算法,利用分裂Bregman方法来优化其求解问题模型.首先,利用辅助变量及其二次惩罚泛函把全变差去模糊优化问题转化为一个等价的无约束优化问题;其次,基于Bregman迭代将其分解为两个子优化问题采用交替最小化方法进行求解;最后,根据子问题结构特点,采用离散傅立叶变换及收缩技术实现子优化问题的快速计算.实验结果表明,在不同尺寸模糊核条件下本文算法能获得有效、稳定的图像复原结果,相比FTVd、IRN去模糊方法,本文算法复原效果更好,计算更加快速.     

优化重加权L1范数的图像盲复原算法

在单幅运动模糊图像的盲复原问题中,图像中强边缘部分的利用成为模糊核估计的关键所在.为此,本文提出了一种优化重加权L1范数的图像盲复原算法.首先,建立了基于加权L1范数的模糊核盲估计模型,并引入了一种图像平滑模型对权重进行优化估计,从而减少计算权重时受细小结构以及噪声的影响,其次,设计了模糊核盲估计模型求解的迭代收缩阈值数值算法,最后采用了一种基于超拉普拉斯先验的快速图像非盲复原算法对模糊图像进行复原.仿真和实际数据实验结果验证了本文算法的有效性.     

基于非局部全变差模型的图像复原方法

面向图像复原问题,本文提出一种非局部的全变差图像复原方法。该方法将传统的全变差模型拓展为非局部变差模型,充分利用非局部子块对结构的保持作用,进一步提高复原图像的质量。此外,为了解决上述的非局部全变差模型,本文引入算子运算简化目标函数, 再利用迭代的Splitting算法对其进行交替求解,提高收敛精度。实验结果表明,本文算法在视觉效果和客观评价指标两方面均优于传统算法。     

图像复原的小波域稀疏模型方法

介绍了一种基于小波域稀疏模型的有效图像复原算法.首先采用Student-t分布模型刻画小波系数的边缘统计特征,该分布具有尖峰重尾的特性,能很好地拟合图像小波系数的分布情况.其次,基于Student-t模型,在最大后验估计框架下复原图像,等价于一个高维非凸目标函数的最小化问题,给出了一种有效的最小化算法,将非凸目标函数最小化问题转化为迭代二次目标函数最小化求解,而二次目标函数最小化可采用共轭梯度迭代法快速求解.实验结果表明:不论根据客观改善信噪比的大小还是主观视觉效果,该算法都能获取很好的复原效果,从而验证了该方法的有效性.     

基于小波变换与曲波变换的图像插值

提出了一种组合小波变换与曲波变换稀疏约束的图像插值算法。利用小波变换对图像纹理成份和曲波变换对图像卡通成份的稀疏表示特性,首先将图像插值问题转化成稀疏约束的图像重建问题,然后通过迭代投影对复原最优化问题进行求解,从而实现成份自适应的图像插值。实验结果表明,相比于现在有图像插值算法,本文算法可以显著地提高被插值图像的峰值信噪比(PSNR)和视觉质量。     

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.     

基于稀疏优化的图像压缩感知重建算法

在信号的稀疏表示方法中,传统的基于变换基的稀疏逼近不能自适应性地提取图像的纹理特征,而基于过完备字典的稀疏逼近算法复杂度过高.针对该问题,文章提出了一种基于小波变换稀疏字典优化的图像稀疏表示方法.该算法在图像小波变换的基础上构建图像过完备字典,利用同一场景图像的小波变换在纹理上具有内部和外部相似的属性,对过完备字典进行灰色关联度的分类,有效提高了图像表示的稀疏性.将该新算法应用于图像信号进行稀疏表示,以及基于压缩感知理论的图像采样和重建实验,结果表明新算法总体上提升了重建图像的峰值信噪比与结构相似度,并能有效缩短图像重建时间.     

基于图像稀疏表达的模拟退火图像复原

针对现有的图像复原方法振铃效应严重的问题,提 出了一种基于图像稀疏表达的模拟退火的图像复原方法来恢复模糊图像。首先根据模拟退火 算法的要求,建立价格函数并 通过图像的模糊因子确定参数;然后在价格函数中的约束项引入图像的稀疏性,以提高复原 图像的质量;接着给初始解一个随机扰动,产生扰动解,并根据扰动解所造成的价格函数 的变化判断是否接受该扰动解;最后,当价格函数小于某一预设值时所得到的解即为复原 图像。实验结果表明,复原后图像细节增加且振铃效应明显减少,相对于目前已有的复原方 法,峰值信噪比(PSNR)平均提高了2~3dB。恢复效果表明,本文方法具有较大的实用价值。     

带总观测误差约束的模糊图像恢复

模糊图像恢复是数字图像处理领域的研究热点之一,总变差(Total Variation, TV)规整化可以很好的保持图像的细节,然而,传统的TV图像恢复模型需要考虑最优的正则化参数,由此,提出了一族包含不同规整化因子,带总观测误差约束的模糊图像恢复模型,并分为去模糊和去噪两步求解此模型。在去模糊过程中,利用共轭梯度法求出一个满足总观测误差约束的初始恢复图像;在去噪过程中,首先,以去模糊的结果作为初始估计;其次,针对 范数最小化问题,利用优化—最小化(Majoriziation-Minimization, MM)算法的思想,将原问题转化为一系列容易求解的优化子问题;最后,极小化优化子问题,得到最终的恢复图像。实验结果表明,该算法对模糊图像的恢复效果是显著地。      

Nonlocal Joint Regularizations Framework with Application to Image Denoising

Low-rank (LR) representation and the nonlocal model (NLM) are important techniques in the field of image restoration, offering significant improvements over many current recovery algorithms. Natural images contain global and local redundancy, and this can be utilized to enhance the restoration performance. Thus, we propose a novel optimization framework that incorporates the benefits of LR and NLM. First, NLM is employed to search for similar patches to reduce the global redundancy. An LR model is then exploited as the prior knowledge needed to constrain the low-rank property of the searched patches. We also use a 3D sparse model to constrain the local sparsity of these patches, thus preserving their underlying structure more effectively. To solve the minimization problem within our novel framework, we describe an iterative scenario that uses an alternating optimization method based on the improved split Bregman technique. Experimental results demonstrate that our proposed method outperforms several state-of-the-art algorithms.     

Sparse representation-based algorithm for joint SAR image formation and autofocus

Inaccuracies in the observation model of the synthetic aperture radar (SAR) due to inaccuracies of the velocity and position of the platform or atmospheric turbulence cause degradations in reconstructed images which necessitate the use of autofocus algorithms. In this paper we propose a novel signal processing algorithm for joint SAR image formation and autofocus in a synthesis dictionary based sparse representation framework. Proposed algorithm can be applied broadly to scenes that exhibit sparsity with respect to any dictionary. This is done by extending our previously developed sparse representation-based SAR imaging framework to joint SAR image formation and autofocus. To this end, the phase error vector is separated from the unknown phase of the complex-valued back-scattered field. Phase error vector is estimated using a MAP estimator and compensated through an iterative algorithm to produce focused images. We demonstrate the effectiveness of the proposed approach on synthetic and real imagery.     

Enhancing inverse halftoning via coupled dictionary training

Inverse halftoning is a challenging problem in image processing. Traditionally, this operation is known to introduce visible distortions into reconstructed images. This paper presents a learning-based method that performs a quality enhancement procedure on images reconstructed using inverse halftoning algorithms. The proposed method is implemented using a coupled dictionary learning algorithm, which is based on a patchwise sparse representation. Specifically, the training is performed using image pairs composed by images restored using an inverse halftoning algorithm and their corresponding originals. The learning model, which is based on a sparse representation of these images, is used to construct two dictionaries. One of these dictionaries represents the original images and the other dictionary represents the distorted images. Using these dictionaries, the method generates images with a smaller number of distortions than what is produced by regular inverse halftone algorithms. Experimental results show that images generated by the proposed method have a high quality, with less chromatic aberrations, blur, and white noise distortions.     

Solution of inverse problems in image processing by waveletexpansion

We describe a wavelet-based approach to linear inverse problems in image processing. In this approach, both the images and the linear operator to be inverted are represented by wavelet expansions, leading to a multiresolution sparse matrix representation of the inverse problem. The constraints for a regularized solution are enforced through wavelet expansion coefficients. A unique feature of the wavelet approach is a general and consistent scheme for representing an operator in different resolutions, an important problem in multigrid/multiresolution processing. This and the sparseness of the representation induce a multigrid algorithm. The proposed approach was tested on image restoration problems and produced good results.