基于振铃约束的全变差正则化图像去模糊算法

当前去模糊方法只利用图像单一的稀疏特性作为先验信息,忽略了伪边缘(如振铃瑕疵)对模糊核估计的影响,导致其去模糊性能不佳。本文充分利用复杂结构图像的先验信息,设计了振铃约束下的全变差正则化图像去模糊算法。首先,利用多分辨率图像金字塔策略建立多层图像模型,通过对比模糊图像和潜在清晰图像来获得振铃先验信息。其次,将振铃正则约束项融入全变差方法,构建多正则项去模糊模型,然后利用变量分离法将去模糊模型转化为多函数优化问题。最后,利用一阶原始对偶算法,根据低分辨率到高分辨率的顺序,对模糊核和原始图像完成计算,获取重构目标。实验结果表明：较当前图像去模糊技术而言,所提算法具备更为理性的去模糊效果,所复原的图像呈现出更高的峰值信噪比和结构相似度,可以更好地保持图像边缘与纹理信息。     

联合小波域和频域的图像去模糊算法

提出了一种在小波域和频域上联合恢复模糊图像的算法。首先在小波域上对模糊图像去噪,提出按照贝叶斯公式估计出小波系数的收缩因子,恢复出模糊图像的小波系数值。此后,按照正则化反卷积图像恢复算法,对去噪模糊图像进行恢复。该算法使得反卷积时的正则化算子选取为较小的值,从而恢复的图像既滤除了噪声,同时降低了边缘模糊等振铃效应。实验结果表明,选择拉普拉斯正则化算子,该算法恢复的图像质量优于频域正则化反卷积算法,此外在同等噪声水平下,不同图像的最优正则化参数处在较小的相同动态范围之内,避免了恢复算法中的反复经验试值寻求最优。     

基于深度多级小波变换的图像盲去模糊算法

近年来卷积神经网络广泛应用于单幅图像去模糊问题,卷积神经网络的感受野大小、网络深度等会影响图像去模糊算法性能.为了增大感受野以提高图像去模糊算法的性能,该文提出一种基于深度多级小波变换的图像盲去模糊算法.将小波变换嵌入编-解码结构中,在增大感受野的同时加强图像特征的稀疏性.为在小波域重构高质量图像,该文利用多尺度扩张稠密块提取图像的多尺度信息,同时引入特征融合块以自适应地融合编-解码之间的特征.此外,由于小波域和空间域对图像信息的表示存在差异,为融合这些不同的特征表示,该文利用空间域重建模块在空间域进一步提高重构图像的质量.实验结果表明该文方法在结构相似度(SSIM)和峰值信噪比(PSNR)上具有更好的性能,而且在真实模糊图像上具有更好的视觉效果.     

基于深度多级小波变换的图像盲去模糊算法

近年来卷积神经网络广泛应用于单幅图像去模糊问题,卷积神经网络的感受野大小、网络深度等会影响图像去模糊算法性能。为了增大感受野以提高图像去模糊算法的性能,该文提出一种基于深度多级小波变换的图像盲去模糊算法。将小波变换嵌入编-解码结构中,在增大感受野的同时加强图像特征的稀疏性。为在小波域重构高质量图像,该文利用多尺度扩张稠密块提取图像的多尺度信息,同时引入特征融合块以自适应地融合编-解码之间的特征。此外,由于小波域和空间域对图像信息的表示存在差异,为融合这些不同的特征表示,该文利用空间域重建模块在空间域进一步提高重构图像的质量。实验结果表明该文方法在结构相似度(SSIM)和峰值信噪比(PSNR)上具有更好的性能,而且在真实模糊图像上具有更好的视觉效果。     

基于小波域HMT模型的图像去噪研究

研究小波域隐式马尔可夫模型树(HMT),提出了一种基于小波域HMT模型抑制高斯白噪声的改进图像去噪算法.首先将噪声图像沿水平、垂直及对角方向进行平移变换;然后对平移后的图像进行小波变换,建立其对应的小波域HMT型,分别进行去噪处理.最后取所有去噪图像的均值作为最终的去噪图像.在仿真实验中,对不同程度污染下高斯白噪声的Lena图像分别采用该文算法、小波域硬阈值与软阈值去噪进行比较.结果表明,该文算法很好地保留了图像的细节和边缘信息;提高了图像的峰值信噪比;抑制了Gibbs效应;具有较好的去噪效果.通过实验仿真可以看出,这种方法较好地去除了白噪声;提高了图像的峰值信噪比;较好地保存了图像的边缘和细节信息;抑制了振铃现象.     

基于小波域改进HMT模型的图像恢复算法

针对图像恢复中的边缘模糊问题,提出了一种基于小波域改进隐马尔可夫树( IHMT) 模型的图像恢复算法。IHMT模型更多描述了相邻尺度小波系数的互相关性,能准确刻画自然图像小波系数的统计特性。本文从图像恢复的贝叶斯框架出发,将简化的IHMT模型作为图像小波域的先验模型,构造正则化约束进行图像恢复。采用近似等价的方法,将含有混合密度的恢复方程简化为单一密度求解。实验结果表明,该算法能有效再现图像的边缘信息,提高峰值信噪比。     

基于有理数多项式先验模型的图像盲去模糊

图像盲去模糊问题是当今图像处理领域的热点问题之一.基于混合高斯先验模型的变分贝叶斯去模糊算法可以有效地复原模糊图像,成为一种重要的图像去模糊算法.虽然混合高斯先验模型可以很好地逼近自然图像的梯度分布,但是该模型在图像梯度值较大处往往会产生过拟合导致去模糊后的图像产生振铃效应,严重影响了图像可读性.利用有理数多项式先验模型代替混合高斯模型逼近自然图像的梯度分布,克服算法的上述缺点.有理数多项式函数的分母多项式强制函数在梯度值较大值时平滑,所以有效地避免了过拟合现象的发生,从而使得模糊核估计得更准确,减少振铃效应.实验结果表明了算法的可行性和有效性.     

基于模糊算子的红外图像去模糊研究

针对镜头抖动,目标移动等因素引起的图像运动模糊问题,本文提出了一种基于模糊算子的红外图像去模糊算法,使用深度自编码网络对数据集中的模糊算子进行编码,通过编码后的模糊算子去逼近一个未知的模糊算子并搜索对应的清晰图像,从而实现真实场景下红外图像去模糊,弥补了现有基于深度学习的图像去模糊模型在跨域应用时对真实场景下运动模糊图像去模糊效果较差的不足。在红外图像上的实验结果表明,相比于其他去模糊算法,本文提出的去模糊算法取得了更高的性能指标,恢复出的图像有着清晰的边缘轮廓和局部细节,显著提升了红外图像的清晰度。     

基于最大后验估计的动态星图目标提取方法

深空探测时,由于星敏感器受到多种复合运动影响,使拍摄星图存在严重运动模糊,信噪比低。采用Sureshrink小波方法去噪,能够有效保留星图的边缘信息和灰度信息;根据星图梯度符合拉普拉斯分布的先验信息,提出一种基于最大后验概率估计方法的星图去模糊模型,并对动态模糊星图进行去模糊处理。仿真结果表明,高动态时,经过所提出的去模糊方法处理后的星图不会出现维纳滤波方法中的振铃影响,处理速度和提取质心精度优于Richardson-Lucy滤波,质心精度优于0.1个像素,满足动态星敏感器的处理精度和速度要求。     

基于边缘定向扩散方程的图像复原方法

讨论了光学图像中同时存在噪声与模糊时的复原问题。采用一种能根据边缘方向自适应选取扩散系数的各向异性扩散方程来约束复原后的图像的光滑性质,将其和图像复原模型一起使用,得到了一种图像复原的正则化模型,并利用Eluer方程将该模型转换成一种可以快速求解的各向异性非线性扩散模型。在光滑性约束项的构造上,构造了一种基于边缘定向扩散的各向异性张量型扩散方程,能有效地根据边缘的方向确定是增强边缘还是滤除噪声。相比图像复原的迭代正则化方法,新方法能在复原图像的同时有效地抑制噪声,并有效地减轻边缘处的振铃效应。数值计算结果表明,新方法在整幅图像的复原效果上明显强于迭代正则化方法,尤其在对背景噪声的抑制上效果更明显,峰值信噪比（PSNR）也比迭代正则化方法平均提高了约2dB。     

An adaptive two phase blind image deconvolution algorithm for an iterative regularization model

This paper proposes a blind image deconvolution method which consists of two sequential phases, i.e., blur kernel estimation and image restoration. In the first phase, we adopt the L₀-norm of image gradients and total variation (TV) to regularize the latent image and blur kernel, respectively. Then we design an alternating optimization algorithm which jointly incorporates the estimation of intermediately restored image, blur kernel and regularization parameters into account. In the second phase, we propose to take the mixture of L₀-norm of image gradients and TV to regularize the latent image, and design an efficient non-blind deconvolution algorithm to achieve the restored image. Experimental results on both a benchmark image dataset and real-world blurred images show that the proposed method can effectively restore image details while suppress noise and ringing artifacts, the result is of high quality which is competitive with some state of the art methods.     

Non-convex hybrid total variation for image denoising

Image restoration problems, such as image denoising, are important steps in various image processing method, such as image segmentation and object recognition. Due to the edge preserving property of the convex total variation (TV), variational model with TV is commonly used in image restoration. However, staircase artifacts are frequently observed in restored smoothed region. To remove the staircase artifacts in smoothed region, convex higher-order TV (HOTV) regularization methods are introduced. But the valuable edge information of the image is also attenuated. In this paper, we propose non-convex hybrid TV regularization method to significantly reduce staircase artifacts while well preserving the valuable edge information of the image. To efficiently find a solution of the variation model with the proposed regularizer, we use the iterative reweighted method with the augmented Lagrangian based algorithm. The proposed model shows the best performance in terms of the signal-to-noise ratio (SNR) and the structure similarity index measure (SSIM) with comparable computational complexity.     

基于粒子群优化的正则化水下图像盲复原

水下图像恢复的难点在于缺少海水的点扩展函数的足够信息,而导致病态的问题.为了提高水下激光成像系统的成像质量,提出了用粒子群优化正则化参量的盲图像复原算法.该方法结合Tikhonov正则化和改进的全变分正则化的技术特点,使用一种交替迭代方法,分别估计点扩展函数和估计复原图像,同时用粒子群算法优化正则化参量.结果表明,该方法对水下图像复原具有较好的鲁棒性,算法收敛稳定.     

基于Poisson-Markov场的超分辨力图像复原算法

图像的超分辨力复原和信噪比的提高是图像复原追求的目标.Poisson-ML图像复原方法(PML)具有很强的超分辨力复原能力,但在复原过程中会产生振荡条纹且对带噪较大的图像不能取得理想的复原效果.在Poisson和Markov分布假设的基础上,提出基于Poisson-Markov场的超分辨力图像复原算法及其正则化参数的自适应选择方法(MPML).实验表明,MPML算法不但具有很好的超分辨力复原能力,而且能有效减少和去除复原图像中的振荡条纹,对于带噪较大的图像也能取得理想的复原效果,因此其图像复原质量明显好于PML算法.正则化参数能被自动优化地选择且与图像复原的迭代运算同步进行.     

一种改进的全变差盲图像复原方法

当点传播函数未知或不确知的情况下,从观察到的退化图像中复原原始图像的过程称为图像盲复原.传统的图像盲复原算法常采用最小均方误差作为复原效果的评判准则,但它很少考虑人类视觉心理,而图像最终都必须由人类的视觉系统来观测和解释.因此,本文提出一种新的基于人类视觉特性的图像盲复原算法:它采用交替最小化的结构,在模糊辨识阶段,采用全变差正则化算法;在复原阶段,采用基于Weber定律和全变差正则化相结合的算法.仿真实验表明,这种算法可在未知点扩展函数的情况下取得较好的复原效果.     

Higher degree total variation (HDTV) regularization for image recovery

We introduce novel image regularization penalties to overcome the practical problems associated with the classical total variation (TV) scheme. Motivated by novel reinterpretations of the classical TV regularizer, we derive two families of functionals involving higher degree partial image derivatives; we term these families as isotropic and anisotropic higher degree TV (HDTV) penalties, respectively. The isotropic penalty is the L(1) - L(2) mixed norm of the directional image derivatives, while the anisotropic penalty is the separable L(1) norm of directional derivatives. These functionals inherit the desirable properties of standard TV schemes such as invariance to rotations and translations, preservation of discontinuities, and convexity. The use of mixed norms in isotropic penalties encourages the joint sparsity of the directional derivatives at each pixel, thus encouraging isotropic smoothing. In contrast, the fully separable norm in the anisotropic penalty ensures the preservation of discontinuities, while continuing to smooth along the linelike features; this scheme thus enhances the linelike image characteristics analogous to standard TV. We also introduce efficient majorize-minimize algorithms to solve the resulting optimization problems. The numerical comparison of the proposed scheme with classical TV penalty, current second-degree methods, and wavelet algorithms clearly demonstrate the performance improvement. Specifically, the proposed algorithms minimize the staircase and ringing artifacts that are common with TV and wavelet schemes, while better preserving the singularities. We also observe that anisotropic HDTV penalty provides consistently improved reconstructions compared with the isotropic HDTV penalty.     

二阶Hopfield型神经网络的稳定性 分析及收敛速度的估计

本文讨论二阶连续Hopfield型神经网络平衡点的全局稳定性问题,利用LMI方法和Lyapunov方法得到了网络平衡点全局渐近稳定和全局指数稳定的几个充分条件,并对其指数收敛速度进行了估计.     

Alternating minimization algorithm for speckle reduction with a shifting technique

Speckles (multiplicative noise) in synthetic aperture radar (SAR) make it difficult to interpret the observed image. Due to the edge-preserving feature of total variation (TV), variational models with TV regularization have attracted much interest in reducing speckles. Algorithms based on the augmented Lagrangian function have been proposed to efficiently solve speckle-reduction variational models with TV regularization. However, these algorithms require inner iterations or inverses involving the Laplacian operator at each iteration. In this paper, we adapt Tseng's alternating minimization algorithm with a shifting technique to efficiently remove the speckle without any inner iterations or inverses involving the Laplacian operator. The proposed method is very simple and highly parallelizable; therefore, it is very efficient to despeckle huge-size SAR images. Numerical results show that our proposed method outperforms the state-of-the-art algorithms for speckle-reduction variational models with a TV regularizer in terms of central-processing-unit time.     

Image decomposition via the combination of sparse representations and a variational approach.

The separation of image content into semantic parts plays a vital role in applications such as compression, enhancement, restoration, and more. In recent years, several pioneering works suggested such a separation be based on variational formulation and others using independent component analysis and sparsity. This paper presents a novel method for separating images into texture and piecewise smooth (cartoon) parts, exploiting both the variational and the sparsity mechanisms. The method combines the basis pursuit denoising (BPDN) algorithm and the total-variation (TV) regularization scheme. The basic idea presented in this paper is the use of two appropriate dictionaries, one for the representation of textures and the other for the natural scene parts assumed to be piecewise smooth. Both dictionaries are chosen such that they lead to sparse representations over one type of image-content (either texture or piecewise smooth). The use of the BPDN with the two amalgamed dictionaries leads to the desired separation, along with noise removal as a by-product. As the need to choose proper dictionaries is generally hard, a TV regularization is employed to better direct the separation process and reduce ringing artifacts. We present a highly efficient numerical scheme to solve the combined optimization problem posed by our model and to show several experimental results that validate the algorithm's performance.     

基于Hessian核范数正则化的快速图像复原算法

利用Hessian核范数进行图像复原是目前较好的高阶正则化方法,但是由于Hessian核范数正则项的高度非线性和不可微性,图像去模糊和去噪过程耦合度高,求解算法的复杂度高.本文利用变量分裂设计了一种具有闭解形式的交替迭代最小化快速图像复原算法,将图像去模糊、去噪分步进行,并给出算法的收敛性证明.实验结果表明,本文方法不仅在峰值信噪比方面优于原有的基于Hessian核范数图像复原的主优化(Majorization-Minimization,MM)方法,而且大大降低了算法的迭代次数和运行时间.