Seismic high-resolution processing method based on spectral simulation and total variation regularization constraints

There is little low-and-high frequency information on seismic data in seismic exploration,resulting in narrower bandwidth and lower seismic resolution.It considerably restricts the prediction accuracy of thin reservoirs and thin interbeds.This study proposes a novel method to constrain improving seismic resolution in the time and frequency domain.The expected wavelet spectrum is used in the frequency domain to broaden the seismic spectrum range and increase the octave.In the time domain,the Frobenius vector regularization of the Hessian matrix is used to constrain the horizontal continuity of the seismic data.It eff ectively protects the signal-to-noise ratio of seismic data while the longitudinal seismic resolution is improved.This method is applied to actual post-stack seismic data and pre-stack gathers dividedly.Without abolishing the phase characteristics of the original seismic data,the time resolution is signifi cantly improved,and the structural features are clearer.Compared with the traditional spectral simulation and deconvolution methods,the frequency distribution is more reasonable,and seismic data has higher resolution.

图像重建中total variation正则化项的有限元计算方法

为在迭代图像重建算法中获得更高质量的重建图像,推导出TV(Total Variation)正则化项关于重建图像的Fréchet导数,并给出该导数的有限元表示;利用两个数值实验,分别采用不同的网格尺寸和不同的形函数验证该有限元表示结果.数值实验结果表明:采用相同的k次单纯形元时,随着网格不断加密,计算结果的L1和L2误差均下降;采用相同的网格时,线性单纯形元函数计算结果明显优于分片常数有限元和二次单纯形元计算结果.

A Hybrid Regularization-Based Multi-Frame Super-Resolution Using Bayesian Framework

The prime purpose for the image reconstruction of a multi-frame super-resolution is to reconstruct a higher-resolution image through incorporating the knowledge obtained from a series of relevant low-resolution images,which is useful in numerousfields.Nevertheless,super-resolution image reconstruction methods are usually damaged by undesirable restorative artifacts,which include blurring distortion,noises,and stair-casing effects.Consequently,it is always challenging to achieve balancing between image smoothness and preservation of the edges inside the image.In this research work,we seek to increase the effectiveness of multi-frame super-resolution image reconstruction by increasing the visual information and improving the automated machine perception,which improves human analysis and interpretation processes.Accordingly,we propose a new approach to the image reconstruction of multi-frame super-resolution,so that it is created through the use of the regularization framework.In the proposed approach,the bilateral edge preserving and bilateral total variation regularizations are employed to approximate a high-resolution image generated from a sequence of corresponding images with low-resolution to protect significant features of an image,including sharp image edges and texture details while preventing artifacts.The experimental results of the synthesized image demonstrate that the new proposed approach has improved efficacy both visually and numerically more than other approaches.

Adaptive Parameter Selection for Total Variation Image Deconvolution

In this paper,we propose a discrepancy rule-based method to automatically choose the regularization parameters for total variation image restoration problems. The regularization parameters are adjusted dynamically in each iteration.Numerical results are shown to illustrate the performance of the proposed method.

An overview of image restoration based on variational regularization

Image restoration is a complicated process in which the original information can be recovered from the degraded image model caused by lots of factors.Mathematically,image restoration problems are ill-posed inverse prob-lems.In this paper image restoration models and algorithms based on variational regularization are surveyed.First,we review and analyze the typical models for denoising,deblurring and inpainting.Second,we construct a unified restoration model based on variational regularization and summarize the typical numerical methods for the model.At last,we point out eight diffcult problems which remain open in this field.

Iterative regularization method for image denoising with adaptive scale parameter

In order to decrease the sensitivity of the constant scale parameter, adaptively optimize the scale parameter in the iteration regularization model （IRM） and attain a desirable level of applicability for image denoising, a novel IRM with the adaptive scale parameter is proposed. First, the classic regularization item is modified and the equation of the adaptive scale parameter is deduced. Then, the initial value of the varying scale parameter is obtained by the trend of the number of iterations and the scale parameter sequence vectors. Finally, the novel iterative regularization method is used for image denoising. Numerical experiments show that compared with the IRM with the constant scale parameter, the proposed method with the varying scale parameter can not only reduce the number of iterations when the scale parameter becomes smaller, but also efficiently remove noise when the scale parameter becomes bigger and well preserve the details of images.

Image decomposition using adaptive regularization and div(BMO)

In order to avoid staircasing effect and preserve small scale texture information for the classical total variation regularization, a new minimization energy functional model for image decomposition is proposed. Firstly, an adaptive regularization based on the local feature of images is introduced to substitute total variational regularization. The oscillatory component containing texture and/or noise is modeled in generalized function space div （BMO）. And then, the existence and uniqueness of the minimizer for proposed model are proved. Finally, the gradient descent flow of the Euler-Lagrange equations for the new model is numerically implemented by using a finite difference method. Experiments show that the proposed model is very robust to noise, and the staircasing effect is avoided efficiently, while edges and textures are well remained.

Anisotropic fourth-order diffusion regularization for multiframe super-resolution reconstruction

A novel rcgularization-based approach is presented for super-resolution reconstruction in order to achieve good tradeoff between noise removal and edge preservation. The method is developed by using L1 norm as data fidelity term and anisotropic fourth-order diffusion model as a regularization item to constrain the smoothness of the reconstructed images. To evaluate and prove the performance of the proposed method, series of experiments and comparisons with some existing methods including bi-cubic interpolation method and bilateral total variation method are carried out. Numerical results on synthetic data show that the PSNR improvement of the proposed method is approximately 1.0906 dB on average compared to bilateral total variation method, and the results on real videos indicate that the proposed algorithm is also effective in terms of removing visual artifacts and preserving edges in restored images.

基于复合正则化的稀疏SAR成像方法研究

随着高分辨率对地观测要求的不断提高,合成孔径雷达(Synthetic Aperture Radar,SAR)的应用将越来越广泛。针对高分辨率SAR成像存在数据量大、存储难度高、计算时间长等问题,目前常用的解决方法是在SAR成像模型中引入压缩感知(Compressed Sensing,CS)的方法降低采样率和数据量。通常使用单一的正则化作为约束条件,可以抑制点目标旁瓣,实现点目标特征增强,但是观测场景中可能存在多种目标类型,因此使用单一正则化约束难以满足多种特征增强的要求。本文提出了一种基于复合正则化的稀疏高分辨SAR成像方法,通过压缩感知降低数据量,并使用多种正则化的线性组合作为约束条件,增强观测场景中不同类型目标的特征,实现复杂场景中高分辨率对地观测的要求。该方法在稀疏SAR成像模型中引入非凸正则化和全变分(Total Variation,TV)正则化作为约束条件,减小稀疏重构误差、增强区域目标的特征,降低噪声对成像结果的影响,提高成像质量;采用改进的交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)实现复合正则化约束的求解,减少计算时间、快速重构图像;使用方位距离解耦算子代替观测矩阵及其共轭转置,进一步降低计算复杂度。仿真和实测数据实验表明,本文所提算法可以对点目标和区域目标进行特征增强,减小计算复杂度,提高收敛性能,实现快速高分辨的图像重构。

一种基于稀疏重构的多视角MIMO雷达关联成像算法研究

为改善复杂目标的成像表现、提升雷达图像的视觉效果,提出一种基于稀疏重构的多视角多输入多输出(multiple input multiple output,MIMO)雷达关联成像方法,设计了多视角雷达散射面积(radar cross section,RCS)起伏的稀疏重构关联成像模型。所提算法能提高辐射场信号随机性,改善复杂目标雷达关联成像参考信号与回波之间相关性退化的情况,减小多视角RCS起伏对相关性的影响,提升多视角下的关联成像质量。最后,通过仿真验证了所提方法的有效性。

Lipschitz and Total-Variational Regularization for Blind Deconvolution

In[3],Chan and Wong proposed to use total variational regularization for both images and point spread functions in blind deconvolution.Their experimental results show that the detail of the restored images cannot be recovered.In this paper,we consider images in Lipschitz spaces,and propose to use Lipschitz regularization for images and total variational regularization for point spread functions in blind deconvolution.Our experimental results show that such combination of Lipschitz and total variational regularization methods can recover both images and point spread functions quite well.

基于超拉普拉斯正则化的冲击波超压层析重建

超压层析成像是利用传感器采集到的冲击波信号来反演测试区域的超压分布,是典型的不完全数据重建问题,为了提高求解精度,本文提出了一种基于高斯牛顿迭代联合超拉普拉斯正则化的冲击波超压层析重建方法。由于实际采集到的冲击波信号通常与干扰信号混叠在一起,会影响超压值的测量精度,本文首先采用改进的小波阈值算法对冲击波信号进行去噪处理;其次利用超拉普拉斯先验对图像边缘和二维层析模型进行正则约束;然后采用高斯牛顿迭代算法和交替方向乘子算法,解决大型病态稀疏矩阵的求解问题。实际实验结果表明本文的正则化方法与传统的全变分正则化和广义全变分正则化相比,重建精度可保持在15%左右,在实际场景中具有一定的应用价值。

自适应模糊正则化椒盐噪声去除模型

为有效抑制椒盐噪声对图像信息的影响,根据椒盐噪声随机破坏图像中像素值的显著特征,本文提出一种耦合噪声检测的自适应模糊正则化噪声去除模型。一方面,基于L_(1)范数建立数据保真项,实现对图像统计分布进行有效拟合。另一方面,通过对图像中像素相似性的有效量化实现图像中噪声的检测,并将此耦合至正则项中,使得模型可依据像素点实际受噪声的污染对其施加惩罚程度,最终实现椒盐噪声的自适应模糊去除。本文采用交替方向乘子法(Alternating direction method of multipliers,ADMM)进行模型的数值结果实现,并运用峰值信噪比(Peak signal-to-noise ratio,PSNR)及结构相似性(Structural similarity,SSIM)对实验结果进行评定。实验结果表明,本文提出的模型在PSNR及SSIM方面得到显著提升,其中对于灰度图像的去噪实验PSNR最高可提高1.3dB,SSIM最高可提高0.2。

基于MC_RTV正则化的高分辨SAR特征增强算法

针对合成孔径雷达(synthetic aperture radar,SAR)稀疏成像中目标反射率易低估、目标结构特征难以精确提取的问题,提出一种基于非凸和相对全变分(relative total variation,RTV)正则化的稀疏SAR成像算法。该算法利用非凸惩罚抑制偏差效应、RTV自适应保护图像结构,在交替方向乘子法(alternating direction method of multipliers,ADMM)分布式优化框架下,实现多个正则项的协同优化增强。为更好地提高成像效率和降低内存占用量,利用匹配滤波(match filter,MF)算子构造测量矩阵进行近似观测,并对重建的SAR图像质量进行定量评价。仿真与实测数据处理结果表明,所提方法可有效抑制噪声杂波,在保证空间分辨率的情况下有效提高目标重建精度和辐射分辨率。

基于自适应加权非凸正则化和全变分的稀疏SAR成像

针对传统压缩感知(Compressive Sensing, CS)重构算法成像精度低及抗噪性能差等问题,提出了一种基于自适应加权极小极大凹罚函数和全变分的稀疏合成孔径雷达(Synthetic Aperture Imaging Radar, SAR)成像重建方法。首先,将加权思想同非凸函数簇中的极小极大凹罚函数结合,以进一步促进解的稀疏性;然后,与全变分判罚函数线性组合构成复合正则化器,以进一步提高抗噪性能;最后,采用交替方向乘子法求解该成像模型,并在求解过程中使用方位-距离解耦算子替换测量矩阵及其厄米特转置以减少存储空间。仿真与实测数据处理结果表明,所提方法相比于其他算法有更好的聚焦性能和重建精度。

基于分数群稀疏混合范式和空间正则化的高光谱解混

高光谱稀疏解混合方法旨在寻找光谱库的最佳子集以对场景中的混合像元进行建模。大多数稀疏解混合方法使用美国地质调查局光谱库,易造成与所研究的高光谱数据失配。利用顶点分量分析和概率输出支持向量机,设计了一种结合空间和光谱信息的基于图像的端元光谱库提取方法。由于提取的端元光谱库具有群结构,即多个端元光谱代表一类材料,因此估计的丰度也具有群体结构。提出了基于分数群稀疏混合范式和空间正则化的解混算法,用来解决丰度估计优化问题。分数混合范式诱导丰度群内和群间稀疏性,全变分(Total variation,TV)空间正则化诱导丰度群空间平滑。在模拟数据集和真实数据集上的实验结果表明,与传统稀疏解混合方法相比,该方法可以显著提高解混性能。

扩展声源全变分规则化二维稀疏DOA估计方法

针对空间扩展声源的稀疏波达方向(DOA)估计问题,提出一种全变分规则化的二维DOA估计方法(简记为2DTV-CES)。首先利用扩展声源的空间分布成组性和声源相关性特征建立扩展声源模型;然后,通过构建二维广义阵列流形及其过完备表述,实现声源的稀疏表示;通过定义二维全变分,构建二维全变分正则项,实现对于声源结构特征的几何约束,促进解的分段常数轮廓的形成;最后结合全变分正则项与一般LASSO构建二维全变分稀疏DOA估计模型,由凸优化求解。理论分析表明,与传统二维DOA估计方法相比,所提方法避免了去相关处理、角度配对的步骤。仿真实验验证了方法的有效性,在涉及扩展源的DOA估计中,2DTV-CES方法性能明显优于一般LASSO方法和改进的ESPRIT方法,检测概率超过95%,实现了对扩展声源的二维波达方向的高精度快速估计。

自适应正则化稀疏表示的遥感图像SR重建

基于稀疏表示的单幅图像超分辨率(Super-Resolution, SR)重建近年来引起了广泛的关注,并取得了较好的效果.然而,低分辨率(Low Resolution, LR)遥感图像容易受到噪声及模糊的影响,从而导致SR重建结果会出现高频细节丢失的现象.针对这一问题,本文提出一种基于自适应正则化稀疏表示的遥感图像SR重建方法.该方法首先根据提出的步进式图像放大的方法将LR图像放大得到高分辨率(High Resolution, HR)图像的初始估计;然后,构建稀疏表示的SR重建模型,通过评估初始估计HR图像的噪声水平来自适应选择不同的正则项,即梯度直方图正则项或可控方向滤波全变分正则项,对重建图像进行约束;最后,利用迭代收缩算法对提出的模型进行求解得到稀疏编码系数,将学习的字典与稀疏编码系数相乘得到最终的HR图像.实验结果表明,本文提出的SR重建算法获得的结果无论是主观视觉效果还是客观定量评价,都优于一些主流的遥感图像SR重建方法.

基于L_(1−2)时空域总变分正则项的红外弱小目标检测算法

针对红外图像序列中复杂背景干扰下容易出现的高虚警问题,提出一种基于L_(1-2)时空域总变分正则项的红外弱小目标检测算法。首先,将红外图像序列转化为时空域红外张量块,该步骤可利用张量的高维数据结构优势关联图像序列中的时空域信息。然后,利用加权Schattenp范数和L_(1-2)时空域总变分正则项对低秩背景成分进行重构,以保留背景中起伏剧烈的边缘和角点,提高稀疏目标的重构精度。最后,将目标张量恢复为图像序列,利用自适应阈值分割方法得到最终的目标图像。与另外5种检测算法进行对比实验,结果显示,该方法的虚警率较Maxemeidan算法、Tophat算法、LIRDNet算法、DNANet算法以及WSNMSTIPT算法平均分别下降了71.4%、71.1%、68.5%、74.3%和20.47%;而在检测实时性方面,该算法耗时为Maxemeidan算法、DNANet算法以及WSNMSTIPT算法的42.4%、82.9%和28.7%。实验结果验证了该方法在检测性能上的优越性,表明该算法能够显著提高复杂背景干扰下的目标检测精度和效率。

Total Variation Based Parameter-Free Model for Impulse Noise Removal

We propose a new two-phase method for reconstruction of blurred im-ages corrupted by impulse noise.In the first phase,we use a noise detector to iden-tify the pixels that are contaminated by noise,and then,in the second phase,we reconstruct the noisy pixels by solving an equality constrained total variation mini-mization problem that preserves the exact values of the noise-free pixels.For images that are only corrupted by impulse noise(i.e.,not blurred)we apply the semismooth Newton’s method to a reduced problem,and if the images are also blurred,we solve the equality constrained reconstruction problem using a first-order primal-dual algo-rithm.The proposed model improves the computational efficiency(in the denoising case)and has the advantage of being regularization parameter-free.Our numerical results suggest that the method is competitive in terms of its restoration capabilities with respect to the other two-phase methods.