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.     

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。     

Spatially adaptive wavelet-based multiscale image restoration

In this paper, we present a new spatially adaptive approach to the restoration of noisy blurred images, which is particularly effective at producing sharp deconvolution while suppressing the noise in the flat regions of an image. This is accomplished through a multiscale Kalman smoothing filter applied to a prefiltered observed image in the discrete, separable, 2-D wavelet domain. The prefiltering step involves constrained least-squares filtering based on optimal choices for the regularization parameter. This leads to a reduction in the support of the required state vectors of the multiscale restoration filter in the wavelet domain and improvement in the computational efficiency of the multiscale filter. The proposed method has the benefit that the majority of the regularization, or noise suppression, of the restoration is accomplished by the efficient multiscale filtering of wavelet detail coefficients ordered on quadtrees. Not only does this lead to potential parallel implementation schemes, but it permits adaptivity to the local edge information in the image. In particular, this method changes filter parameters depending on scale, local signal-to-noise ratio (SNR), and orientation. Because the wavelet detail coefficients are a manifestation of the multiscale edge information in an image, this algorithm may be viewed as an "edge-adaptive" multiscale restoration approach.     

一种基于极值的自适应中值滤波算法

图像平滑处理中,如何在去除噪声的同时完整地保留图像边缘细节一直是非线性滤波算法研究的热点问题。提出了一种基于极值的自适应中值滤波算法,该算法根据图像中某点是否为邻域极值点将全部像素分为可疑噪声与信号两类。对可疑噪声点采用包括八个一维窗口和一个二维窗口在内的不同尺度和不同方向的九个子窗口,按照各个子窗口的均方差大小,自适应选择窗口进行中值滤波;对信号点不加处理,灰度值不变。测试结果表明,该算法的滤噪特性和细节保护能力优于多级中值滤波;执行速度较快,优于经典中值滤波。     

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.     

基于非线性加权均值的多方向广义形态滤波算法的Speckle噪声抑制

本文提出了一种新的用于散斑噪声抑制的非线性加权均值多方向广义形态滤波算法。对实际激光雷达图像处理结果表明:本文算法具备了小波阈值算法图像边缘保持好和局部统计滤波算法散斑噪声抑制能力强的优点,在算法复杂度降低的前提下具有了与F.Safa的改进算法(广义并行加权多方向形态滤波算法)相当的效果,即有效地抑制了散斑噪声,又保持了图像的几何结构。     

多尺度时变地震信号反褶积

本文针对石油地震勘探中地震信号的时变性，提出一个新的时变地震信号反褶积方法。在分析地层时变滤波特性的基础上，构造多尺度地震子波。分别用每一个尺度的地震子波作确定反褶积，并用基于信息熵准则构造的检测函数综合多尺度反褶积结果。实验表明本文提出的方法具有很好的效果。     

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.     

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.     

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。     

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。     

基于边缘吸引力场正则化的短程线主动轮廓模型

短程线主动轮廓模型是近几年提出的一种有效的多目标轮廓提取算法 .本文在详细分析其动力学过程的基础上 ,针对该模型中存在的局限性和不足 ,提出对边缘吸引力场进行正则化的方法 ,并采用多尺度模型 ,有效的改善了该模型不能对存在断裂轮廓的目标进行正确提取和凹边缘搜索能力弱的缺点 ,增强了抗噪声和虚假边缘干扰的能力 ,使该算法具有更好的鲁棒性和实用性 .     

Frequency-domain blind deconvolution based on mutual information rate

In this paper, a new blind single-input single-output (SISO) deconvolution method based on the minimization of the mutual information rate of the deconvolved output is proposed. The method works in the frequency domain and requires estimation of the signal probability density function. Thus, the algorithm uses higher order statistics (except for Gaussian source) and allows non-minimum-phase filter estimation. In practice, the criterion contains a regularization term for limiting noise amplification as in Wiener filtering. The score function estimation, which represents a key point of the algorithm, is detailed, and the most robust estimate is selected. Finally, experiments point to the relevance of the proposed algorithm: 1) any filter, minimum phase or not, can be estimated and 2) on actual data (underwater explosions, seismovolcanic phenomena), this deconvolution algorithm provides good results with a better tradeoff between deconvolution quality and noise amplification than existing methods.     

Variational Image Restoration and Decomposition in Shearlet Smoothness Spaces

We present the shearlet-based variational model for image restoration and decomposition.The new model can be seen as generalizations of Daubechies-Teschke's model.By using regularization term in shearlets smoothness spaces,and writing the problem in a shearlet framework,we obtain elegant shearlet shrinkage schemes.Furthermore,the model allows us to incorporate general bounded linear blur operators into the problem.The experiments on denoising,deblurring and decomposition of images show that our algorithm is very efficient.     

变分框架下的多尺度图像恢复与重建

变分图像分解,通过极小化能量泛函将图像分解为不同的特征分量,可以被应用到图像的恢复和重建.提出了变分框架下的多尺度图像恢复和重建的思想.基于这种思想,首先提出了一个单参数的（BV,G,E）三元变分分解模型,并且理论分析了参数与不同特征分量的尺度的关系.然后将此模型的参数选为一个二进制序列,得到多尺度的（BV,G,E）变分分解.该多尺度变分分解可以将图像分解为一序列图像结构、纹理和噪声.证明了此多尺度分解的收敛性并且基于对偶理论和交替迭代算法给出了其数值求解方法.最后将提出的多尺度的（BV,G,E）变分分解应用到图像恢复和重建,实验结果证实了理论分析的正确性,显示了将此模型进行图像多尺度恢复和重建的有效性,和与一些其他分解模型相比较的优越性.     

脑电逆问题的延时相关阵子空间分解算法

 根据头表观测电位反演脑电源的空间信息是脑电研究中的一个重要问题.本文提出了脑电逆问题的延时相关阵子空间分解算法.通过在三层同心球头模型上,与现行延时为零的相关阵子空间分解算法的对比研究表明,该方法能更好的压制空间相干噪音,显示了一定的应用前景.     

多尺度卡尔曼滤波探测气体浓度

针对差分吸收激光雷达系统,研究了对原始测量信号和气体浓度模型采用多尺度分解 与卡尔曼滤波相结合的方法,实现了在强噪声的情况下对气体浓度进行探测。应用MonteCarlo仿真实验验证了该算法的有效性,仿真表明:该算法的性能优于仅在原始尺度上进行卡尔曼滤波的性能,也优于小波变换软阈值去噪的性能。     

Fusion of multiparametric SAR images based on SW-nonsubsampled contourlet and PCNN

In this paper, a new fusion rule based on a pulse coupled neural network (PCNN) and the clarity of images is proposed for multi-band synthetic aperture radar (SAR) image fusion. By using a stationary wavelet-based nonsubsampled contourlet transform (SW-NSCT), we can calculate a flexible multiscale, multidirectional, anisotropy and shift-invariant representation of registered SAR images. A weighted fusion rule is performed on the low frequency subbands to calculate the fused lowpass band. For the fusion of high frequency directional subband images, a PCNN model is constructed, where the linking strength of each neuron is determined by the clarity of the decomposed subband images. The fusion approach exploits the advantages of both SW-NSCT in multiscale geometric representations and that of PCNN in the determination of fusion rules; as predicted, the obtained fusion image can preserve much more information regarding textures and edges of the images, compared to its counterparts. Some experiments are performed by comparing the new algorithm with other existing fusion rules and methods. The experimental results show that the proposed fusion approach is effective and can provide better performance in fusing multi-band SAR images than some current methods.     

基于多尺度Wiener滤波器的分形噪声滤波

针对淹没在1/f噪声中的有用信号恢复问题,本文提出了一套基于双正交小波变换与Wiener滤波的多尺度滤波算法,并设计出多尺度Wiener滤波器.首先,利用双正交小波变换将带有1/f噪声的信号分解成多尺度的子带信号,通过小波变换对1/f噪声的白化作用,消除了1/f噪声的非平稳性、自相似性和长程相关性.其次,在小波域内,利用Wiener滤波,实现了噪声和有用信号的分离,估计出了各子带中的有用信号.最后,利用双正交小波的精确重构性,较好地恢复出淹没在1/f噪声中的有用信号.仿真实验表明,该滤波器能有效的抑制分形噪声,显著地提高信噪比.