L_1-L_2范数联合约束的鲁棒目标跟踪

针对稀疏原型跟踪方法中未考虑正交模板系数的密集性的问题,本文提出一种L1-L2范数联合约束的鲁棒目标跟踪。首先,该方法建立基于L1-L2范数联合约束的目标表示模型,对PCA基模板系数和琐碎模板系数分别进行L2范数和L1范数正则化约束,不仅提高了跟踪的准确性,而且保证了对目标遮挡的鲁棒性;其次,针对目标表示模型的优化问题,运用岭回归和软阈值收缩方法快速迭代求解PCA基模板系数和琐碎模板系数;最后以粒子滤波为框架,利用目标未被遮挡部分的重构误差和稀疏噪声项建立观测模型,并结合提出的L1-L2范数联合约束的算法实现目标跟踪。实验结果表明,与5个现有的跟踪算法相比,本文的跟踪算法具有更好的准确性和鲁棒性。

稳健李代数旋转平均用于GPS辅助无人机影像三维重建

针对最小二乘的旋转平均方法对粗差敏感,求解影像旋转参数不够精确的问题,提出了一种稳健的旋转平均方法。先利用李群和李代数之间的映射关系,将旋转矩阵的乘积运算简化为李代数中的减法运算,推导出旋转平均迭代解算的线性化方程;然后利用L1范数优化和迭代加权最小二乘相结合的方法求解全局一致旋转最优解;最后采用迭代策略剔除粗差,得到精确的旋转矩阵。实验结果表明,与传统最小二乘方法相比,提出方法的旋转参数求解精度更高,稳健性更好,用于三维重建可以得到更密集均匀的点云,重建完整性更好。旋转平均的精度优于0.15度,计算时间不超过0.31s,光束法平差后,重投影误差在1.3个像素以内。基本满足快速稳健三维重建的要求。

一种改进的压缩感知信号重构算法

针对支撑集未知且变化时的稀疏信号的重构问题,本文基于卡尔曼滤波思想,结合压缩感知算法,给出了一种改进的卡尔曼-压缩感知(Modified Kalman Filter Compressive Sensing,MKFCS)信号重构算法,该算法首先利用Kalman滤波获得信号残差的有效估计,然后根据残差变突情况,用改进的CS算法估计突变位置以确定信号的新的支撑集,最后用最小二乘方法重构信号,从而自适应的实现支撑集未知且变化的稀疏信号的重构。最后对所改进的通过重构精度、重构误差、稳健性等方面进行了仿真,仿真结果表明所提算法重构信号具有需要量测个数少、重构精度高、鲁棒性强等特点。

基于压缩感知的稀疏脉冲反射系数谱反演方法研究

基于压缩感知稀疏信号采样和重构理论提出了一种稀疏脉冲反射系数谱反演方法。在稀疏地层假设下,利用地震资料的部分谱信息,采用基追踪算法,反演地下地层在L1范数意义下的宽带稀疏脉冲反射系数。利用褶积宽频带的四参数Morlet子波,生成高分辨率地震剖面,提高地震资料对薄层的识别能力。一维理论模型试验结果证实了利用地震资料的部分谱信息可以准确地反演出稀疏脉冲反射系数序列。二维理论模型试验结果表明,得到的反演结果不仅能识别薄(互)层界面、透镜体边界和地层尖灭位置等薄层结构,还能保持原始地层模型的横向连续性特征,并且具有一定的抗噪性。最后,实际资料的应用结果显示,反演得到的高分辨率剖面不仅在整体地层格架上忠实于原始地震资料,而且能够分辨出原始地震记录中无法识别的薄层结构,使得地下地层的接触关系更加清晰,为地震地层学精细解释提供依据。

基于逆算子估计的AVO反演方法研究

传统反演算法以优化算法为主,而基于逆算子估计的AVO反演算法则利用了直接求逆的思路.算法的关键在于寻找存在逆函数的子域,进而可以在子域内直接求逆,这种解决反问题的思路不同于一般的优化类算法所采用的直接搜索解的方式,具有更高的效率.AVO反演利用了振幅随着偏移距的变化特征,反演的精度受到地震资料质量的影响,通过加入L1范数约束以及合理的初始模型有助于提高反演的稳定性以及准确度.模型测算和实际应用表明,基于逆算子估计的AVO反演方法具有较高的精确程度和可靠性.

L1 norm optimal solution match processing in the wavelet domain

Greater attention has been paid to vintage-merge processing of seismic data and extracting more valuable information by the geophysicist. A match filter is used within many important areas such as splicing seismic data, matching seismic data with different ages and sources, 4-D seismic monitoring, and so on. The traditional match filtering method is subject to many restrictions and is usually difficult to overcome the impact of noise. Based on the traditional match filter, we propose the wavelet domain L1 norm optimal matching filter. In this paper, two different types of seismic data are decomposed to the wavelet domain, different detailed effective information is extracted for Ll-norm optimal matching, and ideal results are achieved. Based on the model test, we find that the L1 norm optimal matching filter attenuates the noise and the waveform, amplitude, and phase coherence of result signals are better than the conventional method. The field data test shows that, with our method, the seismic events in the filter results have better continuity which achieves the high precision seismic match requirements.

利用稀疏约束非平稳多项式回归去除地震噪声及拾取初至

非平稳多项式拟合是L2范数下的优化问题,尽管考虑了信号的时变特征,但是仍然假设残差呈随机分布,当地震数据中存在较强非随机噪声时,常规的基于L2范数的非平稳多项式拟合不再适用。为此,研究了稀疏约束非平稳多项式回归理论与方法。首先回顾了非平稳多项式回归的基本原理;针对复杂稀疏分布残差问题,在反问题正则化理论框架下,结合非平稳多项式回归和L1范数约束,采用整形正则化和L1范数联合约束策略,利用共轭梯度和投影算法联合求解多约束反问题,同时估计具有时变光滑特征的多项式回归系数和具有稀疏分布特征的回归残差,可克服稀疏分布强噪声对反演的影响,并给出了算法基本流程和参数分析。模拟和实际数据应用结果表明,稀疏约束非平稳多项式回归方法在地震噪声压制和初至拾取等方面具有较好的应用效果。

一种新的L_1度量Fisher线性判别分析研究

Fisher线性判别分析(Fisher Linear Discriminant Analysis,FLDA)是一种典型的监督型特征提取方法,旨在最大化Fisher准则,寻求最优投影矩阵。在标准Fisher准则中,涉及到的度量为L_2范数度量,此度量通常缺乏鲁棒性,对异常值点较敏感。为提高鲁棒性,引入了一种基于L_1范数度量的FLDA及其优化求解算法。实验结果表明:在很多情形下,相比于传统的L_2范数FLDA,L_1范数FLDA具有更好的分类精度和鲁棒性。

鲁棒原子范数降噪及其在线谱估计中的应用

针对测量数据中含有异常值的线谱估计问题,提出了一种对异常值鲁棒的原子范数降噪方法来提高线谱估计的性能。该方法构建了一个可以联合估计出异常值及原始信号的优化问题,并在代价函数中加入l1范数和原子范数惩罚项来分别对异常值的稀疏性和信号本身的特性进行约束。一旦获得了该优化问题的解,那么就可利用现有的算法对降噪后的信号进行线谱估计。仿真结果表明,在数据中存在异常值的情况下,所提的算法能够更准确地恢复原始信号,从而使降噪后的谱估计的精度和分辨率明显提高。

2-median location improvement problems under weighted l_1 norm and l_∞ norm on trees

This paper focuses on the 2-median location improvement problem on tree networks and the problem is to modify the weights of edges at the minimum cost such that the overall sum of the weighted distance of the vertices to the respective closest one of two prescribed vertices in the modified network is upper bounded by a given value.l1 norm and l∞norm are used to measure the total modification cost. These two problems have a strong practical application background and important theoretical research value. It is shown that such problems can be transformed into a series of sum-type and bottleneck-type continuous knapsack problems respectively.Based on the property of the optimal solution two O n2 algorithms for solving the two problems are proposed where n is the number of vertices on the tree.

一种基于光滑L_1范数的地震数据插值方法

基于稀疏变换的地震数据插值可提供有效、可靠的波场,但为了适应不断增加的计算量和减少CPU计算时间,必须探寻更快速稳健的方法。本文提出一种基于曲波变换的快速梯度投影法并应用于地震数据重构。即构建一个光滑的L_1范数优化模型,并用梯度投影法求解该模型。由于曲波变换具有多尺度、多方向、各向异性等特性,可对曲线形状的同相轴进行稀疏表示,计算时利用曲波正交变换加快计算速度。数值实验结果表明,该方法显著快于目前主流的稀疏反演方法,实际数据的试算效果良好。

Distribution function estimates by Wasserstein metric and Bernstein approximation for C^(-1) functions

The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learning. Based on the classical Bernstein approximation, a scheme is presented. To get the error estimates of the scheme, the problem turns to estimating the L1 norm of the Bernstein approximation for monotone C-1 functions, which was rarely discussed in the classical approximation theory. Finally, we get a probability estimate by the statistical distance.

An improved Gaussian frequency domain sparse inversion method based on compressed sensing

The traditional compressed sensing method for improving resolution is realized in the frequency domain.This method is aff ected by noise,which limits the signal-to-noise ratio and resolution,resulting in poor inversion.To solve this problem,we improved the objective function that extends the frequency domain to the Gaussian frequency domain having denoising and smoothing characteristics.Moreover,the reconstruction of the sparse refl ection coeffi cient is implemented by the mixed L1_L2 norm algorithm,which converts the L0 norm problem into an L1 norm problem.Additionally,a fast threshold iterative algorithm is introduced to speed up convergence and the conjugate gradient algorithm is used to achieve debiasing for eliminating the threshold constraint and amplitude error.The model test indicates that the proposed method is superior to the conventional OMP and BPDN methods.It not only has better denoising and smoothing eff ects but also improves the recognition accuracy of thin interbeds.The actual data application also shows that the new method can eff ectively expand the seismic frequency band and improve seismic data resolution,so the method is conducive to the identifi cation of thin interbeds for beach-bar sand reservoirs.

L_1极小化问题的一种Gauss-Seidal算法

采用罚函数法与Gauss-Seidal算法相结合的思想研究求解L1极小化问题的数值算法:把L1正则化问题视为对L1极小化问题的一种罚函数,由于该函数是非光滑函数,采用光滑化函数对其进行光滑逼近;在此基础上,对此无约束光滑极小化问题采用Gauss-Seidal迭代法求其某种形式的非精确解;再通过合理调整罚参数和光滑化参数,使得算法产生点列收敛于L1极小化问题的解;最后,通过数值试验测试文中算法的效果,并从数值计算角度与已有算法进行比较,结果表明,文中算法具有很好的数值效果.

一种基于加速坐标下降的大规模图像分类算法研究

随着大规模图像分类数据集的出现,设计一种可扩展的、高效的多类分类算法成为目前一个重要的挑战。基于迹范数正则惩罚函数,提出一种新的大规模多类图像分类的可扩展学习算法。把具有挑战性的非光滑优化问题重构为一个带l1正则惩罚的无穷维优化问题,进而设计一个简单而有效的加速坐标下降算法。此外,展示了如何在量化的密集视觉特征的压缩域中进行高效的矩阵计算,该压缩域有100 000个例子,1 000多维特征和100多类图片。最后在图像网的子集"Fungeus"、"Ungulate"和"Vehicles"上的实验结果表明,所提出方法的性能明显优于目前最先进的16高斯Fisher向量方法。

A new approach on designing l_1 optimal regulator with minimum order for SISO linear systems

For a SlSO linear discrete-time system with a specified input signal, a novel method to realize optimal l1 regulation control is presented. Utilizing the technique of converting a polynomial equation to its corresponding matrix equation, a linear programming problem to get an optimal l1 norm of the system output error map is developed which includes the first term and the last term of the map sequence in the objective function and the right vector of its constraint matrix equation, respectively. The adjustability for the width of the constraint matrix makes the trade-off between the order of the optimal regulator and the value of the minimum objective norm become possible, especially for achieving the optimal regulator with minimum order. By norm scaling rules for the constraint matrix equation, the optimal solution can be scaled directly or be obtained by solving a linear programming problem with l1 norm objective.

Location of Tibetan earthquakes──a nonlinear approach by a simplex optimized technique

An advanced earthquake location technique presented by Prugger and Gendzwill (1988) was introduced in this paper. Its characteristics are: 1) adopting the difference between the mean value by observed arrival times and the mean value by calculated travel times as the original reference time of event to calculate the traveltime residuals, thus resulting in the 'true' minimum of travel-time residuals; 2) choosing the L1 norm statistic of the residuals that is more suitable to earthquake location; 3) using a simplex optimized algorithm to search for the minimum residual value directly and iteratively, thus it does not require derivative calculations and avoids matrix inversions, it can be used for any velocity structures and different network systems and can solve out hypocentral parameters (λ, ,h) rapidly and exactly; 4) original time is further derived alone, so the trade-off between focal depth and original time is avoided. All these prominent features make us obtain more accurate Tibetan earthquake locations in the rare network condition by using this method. In this paper, we examined these schemes for our mobile and permanent networks in Tibet with artificial data sets,then using these methods, we determined the hypocentral parameters of partial events observed in the field work period of this project from July 1991 to September 1991 and the seven problematic earthquakes during 1989 - 1990. The hypocentral location errors may be estimated to be less than 3. 6 km approximately. The events with focal depth more than 40 km seem to be distributed in parallel to Qinghai-Sichuan-Yunnan arc structural zone.

Blind Deblurring Based on L_0 Norm from Salient Edges

Motion deblurring is a basic problem in the field of image processing and analysis. This paper proposes a new method of single image blind deblurring which can be significant to kernel estimation and non-blind deconvolution. Experiments show that the details of the image destroy the structure of the kernel, especially when the blur kernel is large. So we extract the image structure with salient edges by the method based on RTV. In addition, the traditional method for motion blur kernel estimation based on sparse priors is conducive to gain a sparse blur kernel. But these priors do not ensure the continuity of blur kernel and sometimes induce noisy estimated results. Therefore we propose the kernel refinement method based on L0 to overcome the above shortcomings. In terms of non-blind deconvolution we adopt the L1/L2 regularization term. Compared with the traditional method, the method based on L1/L2 norm has better adaptability to image structure, and the constructed energy functional can better describe the sharp image. For this model, an effective algorithm is presented based on alternating minimization algorithm.

Sparse approximate solution of fitting surface to scattered points by MLASSO model

The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the principal shift invariant(PSI) space and the l_1 norm minimization. In order to obtain different sparsity of the approximation solution, the problem is represented as a multilevel LASSO(MLASSO)model with different regularization parameters. The MLASSO model can be solved efficiently by the alternating direction method of multipliers. Numerical experiments indicate that compared to the AGLASSO model and the basic MBA algorithm, the MLASSO model can provide an acceptable compromise between the minimization of the data mismatch term and the sparsity of the solution. Moreover, the solution by the MLASSO model can reflect the regions of the underlying surface where high gradients occur.

Variational reconstruction using subdivision surfaces with continuous sharpness control

We present a variational method for subdivision surface reconstruction from a noisy dense mesh. A new set of subdivision rules with continuous sharpness control is introduced into Loop subdivision for better modeling subdivision surface features such as semi-sharp creases, creases, and corners. The key idea is to assign a sharpness value to each edge of the control mesh to continuously control the surface features.Based on the new subdivision rules, a variational model with L_1 norm is formulated to find the control mesh and the corresponding sharpness values of the subdivision surface that best fits the input mesh. An iterative solver based on the augmented Lagrangian method and particle swarm optimization is used to solve the resulting non-linear, non-differentiable optimization problem. Our experimental results show that our method can handle meshes well with sharp/semi-sharp features and noise.