基于剪切波的变分图像放大方法

针对图像放大的Chambolle 变分模型会出现阶梯效应的现象, 文中提出了一种基于Shearlet光滑分解空间的变分模型。利用有界变差空间和Shearlet分解空间的关系,特别是Shearlet分解空间的半范与加权Shearlet系数之间的等价关系,将所求的变分问题转化为基于Shearlet域的变分问题,其解归结于简单的Shearlet阈值。实验仿真表明,该方法放大后的图像有效地消除了阶梯块效应,保持了更多的细节,具有更高的峰值信噪比。     

3-D discrete shearlet transform and video processing

In this paper, we introduce a digital implementation of the 3-D shearlet transform and illustrate its application to problems of video denoising and enhancement. The shearlet representation is a multiscale pyramid of well-localized waveforms defined at various locations and orientations, which was introduced to overcome the limitations of traditional multiscale systems in dealing with multidimensional data. While the shearlet approach shares the general philosophy of curvelets and surfacelets, it is based on a very different mathematical framework, which is derived from the theory of affine systems and uses shearing matrices rather than rotations. This allows a natural transition from the continuous setting to the digital setting and a more flexible mathematical structure. The 3-D digital shearlet transform algorithm presented in this paper consists in a cascade of a multiscale decomposition and a directional filtering stage. The filters employed in this decomposition are implemented as finite-length filters, and this ensures that the transform is local and numerically efficient. To illustrate its performance, the 3-D discrete shearlet transform is applied to problems of video denoising and enhancement, and compared against other state-of-the-art multiscale techniques, including curvelets and surfacelets.     

采用剪切波变换的红外弱小目标背景抑制

提出了一种将剪切波变换与贝叶斯统计机理相结合的背景抑制新方法来解决红外搜索跟踪系统探测复杂空中和地面背景杂波中的弱小目标这一难题.根据红外图像中目标和背景杂波的不同分布特性,首先,采用剪切波变换对原始红外图像进行多尺度和多方向分解,获得原始图像的多尺度和方向细节特征,然后,通过应用高斯尺度混合模型进行处理,从而将红外图...     

Shearlet-Based Deconvolution

In this paper, a new type of deconvolution algorithm is proposed that is based on estimating the image from a shearlet decomposition. Shearlets provide a multidirectional and multiscale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. Constructions such as curvelets and contourlets share similar properties, yet their implementations are significantly different from that of shearlets. Taking advantage of unique properties of a new M-channel implementation of the shearlet transform, we develop an algorithm that allows for the approximation inversion operator to be controlled on a multiscale and multidirectional basis. A key improvement over closely related approaches such as ForWaRD is the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation (GCV). Various tests show that this method can perform significantly better than many competitive deconvolution algorithms.      

Shearlet变换和奇异值分解的图像隐藏方法

为了更好地平衡Shearlet域图像隐藏不可见性、鲁棒性和算法时间复杂度之间的关系,提出了一种基于Shearlet变换和奇异值分解的图像隐藏方法。利用Shearlet变换的能量聚集性、小波包分解低频子带抗攻击性强和矩阵奇异值良好的稳定性,载体图像先进行Shearlet分解,得到的低频子带再进行二级小波包分解。将秘密图像的重要信息位平面隐藏到小波包分解低频系数的奇异值矩阵中,次要信息嵌入Shearlet高频子带中。实验表明,该算法对高斯噪声、滤波和剪切等攻击都有较好的鲁棒性,同时,不可见性较好,时间复杂度较低。     

结合无下采样Shearlet模极大值和改进尺度积的有噪图像边缘检测

为从噪声污染的图像中提取出更为清晰、连续的边缘,进一步改善边缘检测效果,本文提出了一种基于无下采样Shearlet模极大值和改进尺度积的边缘检测方法。首先对含噪图像进行多尺度、多方向无下采样Shearlet变换（Non-subsampled Shearlet Transform, NSST）,得到图像在NSST域的高频系数;然后选取相邻的两个较大尺度的高频系数进行改进的尺度积运算,并经NSST模极大值处理得到边缘二值图像;最后使用区域连通方法去除二值图像中的孤立点,得到准确的边缘图像。大量实验结果表明,与小波模极大值、小波尺度积、基于无下采样Contourlet变换（Non-subsampled Contourlet Transform, NSCT）模极大值和尺度积、NSST模极大值等4种边缘检测方法相比,本文提出的方法具有更强的抗噪能力,且有效地避免了纹理的影响,检测出的边缘完整清晰,连续性好。      

Shearlet变换域自适应图像去噪算法

首先采用Haar小波滤波器,设计出一种数字Shearlet变换算法。然后对Shearlet系数间的相关性进行统计分析,提出了一种尺度相关的自适应阈值收缩图像去噪算法。最后选用峰值信噪比和视觉质量为评价标准,实验验证算法的去噪性能。结果表明,本文算法获得更高的峰值信噪比,更好地保留了图像的细节信息。     

基于变分多尺度的红外与可见光图像融合

为解决变换域融合法对强噪声抑制能力差的问题,提出一种基于变分多尺度分解的红外与可见光图像融合方法.首先对待融合图像分别进行变分多尺度分解,获得纹理分量和结构分量.采用引导滤波的方法进行待融合图像的纹理分量融合,在结构分量融合上提出一种以相位一致性、清晰度、亮度综合信息来权衡融合权重的方法,最后将两幅图像融合后的纹理分量和结构分量相加获取最终融合图像.实验结果从主观观察和客观指标看,本文方法在清晰度和细节信息上比离散小波变换（discrete wavelet transform）法、非下采样轮廓波变换（non-subsampled contourlet transform）法、稀疏表示（sparse representation）法、剪切波变换（shearlet transform）法都要高.     

shearlet变换和区域特性相结合的图像融合

为了提高多模医学图像或多聚焦图像的融合性能,结合shearlet变换能够捕捉图像细节信息的性质,提出了一种基于shearlet变换的图像融合算法。首先,用shearlet变换将已精确配准的两幅原始图像分解,得到低频子带系数和不同尺度不同方向的高频子带系数。低频子带系数使用改进的加权融合算法,用平均梯度来计算加权参量,以此来改善融合图像轮廓模糊度高的问题,高频子带系数采用区域方差和区域能量相结合的融合规则,以得到丰富的细节信息。最后,进行shearlet逆变换得到融合图像。结果表明,此算法在主观视觉效果和客观评价指标上优于其它融合算法。     

基于RDU-PCNN和NSST的红外和可见图像融合算法

针对可见光和红外图像的融合容易出现块状噪声 、边缘有振铃现象等不足,提出了一种基于区 域双通道脉冲耦合神经网络(RDU-PCNN)和非下采样剪切波变换(NSST)的红外和见光图像融 合算法。首先 对待融合的可见光和红外图像进行NSST分解得到低频系数和高频方向系数,低频系数采用R DU-PCNN的 规则融合,高频方向系数采用离散余弦变换(DCT)的融合规则,对融合后的系数进行逆NSST ,从而得到融合后 的图像。仿真结果表明,与其他5种目前流行或者较为先进的算法相比,本文的算法在视觉 和客观评价指标上优于其他算法。     

No-reference image quality assessment using statistical characterization in the shearlet domain

Image and video quality measurements are crucial for many applications, such as acquisition, compression, transmission, enhancement, and reproduction. Nowadays, no-reference (NR) image quality assessment (IQA) methods have drawn extensive attention because it does not rely on any information of original images. However, most of the conventional NR-IQA methods are designed only for one or a set of predefined specific image distortion types, which are unlikely to generalize for evaluating image/video distorted with other types of distortions. In order to estimate a wide range of image distortions, in this paper, we present an efficient general-purpose NR-IQA algorithm which is based on a new multiscale directional transform (shearlet transform) with a strong ability to localize distributed discontinuities. This is mainly based on distorted natural image that leads to significant variation in the spread discontinuities in all directions. Thus, the statistical property of the distorted image is significantly different from that of natural images in fine scale shearlet coefficients, which are referred to as ‘distorted parts’. However, some ‘natural parts’ are reserved in coarse scale shearlet coefficients. The algorithm relies on utilizing the natural parts to predict the natural behavior of distorted parts. The predicted parts act as ‘reference’ and the difference between the reference and distorted parts is used as an indicator to predict the image quality. In order to achieve this goal, we modify the general sparse autoencoder to serve as a predictor to get the predicted parts from natural parts. By translating the NR-IQA problem into classification problem, the predicted parts and distorted parts are utilized to form features and the differences between them are identified by softmax classifier. The resulting algorithm, which we name SHeArlet based No-reference Image quality Assessment (SHANIA), is tested on several database (LIVE, Multiply Distorted LIVE and TID2008) and shown to be suitable for many common distortions, consistent with subjective assessment and comparable to full-reference IQA methods and state-of-the-art general purpose NR-IQA algorithms.     

基于非下采样剪切波变换和QR分解的鲁棒零水印算法

针对数字图像的版权保护问题,提出了一种基于非下采样剪切波变换(NSST,non-subsam-pled shearlet transform)和QR分解的零水印算法。首先,采用NSST对宿主图像进行分解;然后利用Logistic混沌系统从分解后的低频逼近分量中随机抽取出一幅子图,并将其分割成互不重叠的子块;最后对每一个子块进行QR分解,通过判断各个子块R矩阵中第1行元素向量的l1范数和所有子块R矩阵第1行元素向量l1范数的均值之间的大小关系构造零水印。实验结果表明,本文算法对添加噪声、滤波、JPEG压缩和剪切具有很强的鲁棒性,同时还能抵抗一定程度的旋转、缩放和平移(RST)几何攻击。     

结合NSST和快速非局部均值滤波的刀具图像去噪

为消除基于图像处理的刀具磨损检测中的图像噪声,提出了结合非下采样Shearlet变换(Non-subsampled Shearlet Transform, NSST)和快速非局部均值(Fast Non-local Means, FNLM)滤波的图像去噪方法。首先,利用基于决策的非对称剪切中值(Decision Based Un-symmetric Trimmed Median, DBUTM)方法滤除图像中的椒盐噪声;然后,对图像进行NSST多尺度分解,得到一个低频子带和一系列高频子带;最后,分别使用FNLM滤波和各向异性扩散模型调整低频和高频子带系数,并由调整后的各子带系数重构出噪声滤除后的图像。实验结果表明,与基于小波的阈值收缩方法、基于Contourlet的全变差模型结合各向异性扩散方法、基于NSST和标准非局部均值滤波方法相比,本文方法在主观视觉去噪效果、峰值信噪比、结构相似度以及处理速度等4个方面性能更优。      

基于双域分解的图像增强算法

为解决图像增强中对比度提高与噪声抑制的矛盾,本文提出了一种基于双域分解的图像增强算法,同步实现图像对比度提高与噪声抑制.文中详述了空域分解、分层图像空域增强与变换域降噪、分层图像合成三个主要环节的原理、方法.首先,高斯滤波器将图像分解为基础层和细节层,实现对比度提高与噪声抑制的解耦合;其次,带校正功能的单尺度Retinex和硬阈值收缩的非下采样剪切波降噪算法同步实现基础层的增强和细节层的降噪;最后,分层图像合成、灰度数值延展和微分算子强化,实现合成图像的灰度延展与细节加强,确保增强图像的颜色均匀、细节突出.实验表明,本文算法提高图像对比度和抑制噪声的性能优于其他九种算法.     

A Shearlet Approach to Edge Analysis and Detection

It is well known that the wavelet transform provides a very effective framework for analysis of multiscale edges. In this paper, we propose a novel approach based on the shearlet transform: a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges. Indeed, unlike traditional wavelets, shearlets are theoretically optimal in representing images with edges and, in particular, have the ability to fully capture directional and other geometrical features. Numerical examples demonstrate that the shearlet approach is highly effective at detecting both the location and orientation of edges, and outperforms methods based on wavelets as well as other standard methods. Furthermore, the shearlet approach is useful to design simple and effective algorithms for the detection of corners and junctions.     

基于非下采样剪切波变换的红外与可见光图像融合

由于传统稀疏表示(SR)冗余字典单一,脉冲耦合 神经网络(PCNN)模型参数设置复杂,为了解决上述问题,提 出了基于非下采样剪切波变换(NSST)的红外与可见光图像融合算法。该算法首先通过NSST将 源图像分解成低频子 带和高频子带。然后,使用自适应稀疏表示(ASR)模型进行NSST域低频部分稀疏系数的融合 ;同时,采用参数自适 应脉冲耦合神经网络(PA-PCNN)模型融合相应的高频部分。最后,对融合后的低频和高频波 段进行NSST反变换,重 建得到融合结果图。实验结果表明:该算法解决了传统SR模型的“块效应”问题,克服了PC NN模型中自由参数的设置难点,在主观视觉和客观评价上均优于现有算法。     

基于剪切波域改进Gamma校正的医学图像增强算法

为了解决医学图像在采集和传输过程中引入噪 声和干扰导致图像质量恶化从而严重影响医学诊断的问题,提出 一种基于剪切波(shearlet)域改进Gamma校正的图像增强方法。首先,通过剪切波变换,把 图像分解成高频 部分和低频部分;其次,用改进的Gamma校正处理剪切波分解后的低频部分以调整图像的整 体对比 度,采用改进的自适应阈值函数对高频部分进行去噪;最后,把剪切波反变换的重构图 像进行模糊对比 增强,以突出图像的细节信息。实验结果表明,本文算法的峰值信噪比(PSNR )、结构相似度(SSIM)和 绝对均值差(MAE)优于其他对比算法,尤其是PSNR的提升更加明显。这些 客观指标说明,本 文算法不仅能有效地抑制噪声,而且能明显改善增强对比度。从主观方面观察,本文算法与 其他算法相比,能获得更好的视觉效果。     

基于剪切波域改进Gamma校正的医学图像增强算法

通过傅里叶光学理论和透镜成像理论对轴棱锥线 聚焦与凸透镜点聚焦两种成像系统进行分析, 并探讨了它们对成像系统焦深的影响。利用ZEMAX光学设计软件,仿真模拟出系统在不同轴 向距离的截面 光强分布图。以蓝光LED为光源,对这两种成像系统进行实验验证,拍摄不同轴向距离处的 截面光强分布 图。结果表明,轴棱锥所具有的线聚焦特性,能将光线连续地会聚到沿轴线不同位置上,图 像的清晰度高, 且在最大无衍射距离内无需调焦,具有更大的焦深;理论分析、仿真模拟与实验结果相吻合 。     

基于最大范数的低秩稀疏分解模型

为了更好地解决高维数据矩阵低秩稀疏分解问题,该文提出以Max-范数凸化秩函数的Max极小化模型,并给出该模型的相应算法。在对新模型计算复杂性分析的基础上,该文进一步提出了Max约束模型,改进模型不仅在分解问题中效果良好,且相应的投影梯度算法具有更强的时效性。实验结果表明,该文提出的两组模型对于低秩稀疏分解问题均行之有效。