一种基于CGLS和LSQR的联合优化的匹配追踪算法

在压缩感知理论中,设计好的稀疏重构算法是一个比较重要,同时也是一个具有挑战性的问题.稀疏重构的基本目标是用较少的数据样本,通过解一个优化问题完成信号或者图像重构.关于稀疏重构过程,一个重要的研究方向是在数据受噪声干扰的情况下,如何高效快速地重建原信号.本文提出了基于共轭梯度最小二乘法（Conjugate gradient least squares,CGLS）和最小二乘QR分解（Least squares QR,LSQR）的联合优化的匹配追踪算法.该算法采用Alpha散度来测量CGLS和LSQR之间的离散度（差异度）,并通过离散度来选择最优的解序列.实验分析表明基于CGLS和LSQR的联合优化的匹配追踪算法在压缩采样的信号受噪声干扰情况下具有较好的恢复能力.     

基于压缩感知信号重建的自适应空间正交匹配追踪算法

传统的奈奎斯特采样定理规定采样频率最少是原信号频率的两倍,才能保证不失真的重构原始信号,而压缩感知理论指出只要信号具有稀疏性或可压缩性,就可以通过采集少量信号来精确重建原始信号.在研究和总结已有匹配算法的基础上,提出了一种新的自适应空间正交匹配追踪算法(Adaptive Space Orthogonal Matching Pursuit,ASOMP)用于稀疏信号的重建.该算法在选择原子匹配时采用逆向思路,引入正则化自适应和空间匹配的原则,加快了原子的匹配速度,提高了匹配的准确性,最终实现了原始信号的精确重建.最后与传统MP和OMP算法进行了仿真对比,结果表明该算法的重建质量和算法速度均优于传统MP和OMP算法.     

基于压缩感知的局部场电位信号重构算法研究

研究局部场电位信号(Local Field Potential,LFP)的重构问题.依据传统的采样定理对LFP信号进行采样,将会产生庞大的数据量,为LFP信号的传输、存储及处理带来巨大压力.为降低LFP信号的采样速率,减少有效的采样样本,提出压缩感知的局部场电位信号重构的新方法.利用LFP信号在变换域上的稀疏性,通过随机高斯测量矩阵将LFP信号重构模型转化为压缩感知理论中的稀疏向量重构模型.仿真结果表明,采样速率为奈奎斯特采样速率的一半即可准确重构LFP信号,且正交匹配追踪(OMP)重建算法要优于基追踪(BP)重建算法;当选用离散余弦矩阵(DCT)作为稀疏表示矩阵时,信号在正交匹配追踪和基追踪两种重构算法下都有很高的重构精度.     

基于能量的稀疏自适应匹配追踪算法

信号的重建算法在整个压缩感知领域中居于重要的地位。针对稀疏度未知的情况下的信号重建,在经典的稀疏自适应匹配追踪(SAMP)算法的基础上,提出一种基于能量的稀疏自适应匹配追踪(ESAMP)算法。根据测量向量与重建信号能量的比值自适应调整步长,确定步长的合理初始值,对二进制信号的重建算法进行进一步修正,提高了二进制信号的重建精度并实现了二进制信号的完整重建。仿真结果表明,在相同条件下该算法能够在提高重建速度的同时保证较高的重建精度,以更优越的综合性能恢复原始信号,并且使二进制信号的重建算法更具有实用性。     

部分哈达玛矩阵分段弱正交匹配追踪算法

为解决分段弱正交匹配追踪算法在测量过程中难以获得高精度重构信号的问题,首先对以高斯矩阵为测量矩阵的传统SWOMP算法进行了分析,指出问题的关键在于高斯矩阵列相干性过大会影响残差信号的匹配过程,从而导致部分信号丢失,使重构精度下降;然后,根据分析提出了一种基于部分哈达玛矩阵的分段弱正交匹配追踪(PH-SWOMP)算法,其中部分哈达玛矩阵根据偶数行抽取原则进行构造,可以显著降低测量矩阵的互相关性;最后,通过与传统SWOMP算法的图像重构对比仿真实验对PH-SWOMP算法性能进行了验证,其中传统SWOMP算法分别选取高斯矩阵、托普利兹矩阵等4种矩阵作为测量矩阵.仿真结果表明,在相同条件下,相比于传统SWOMP算法, PH-SWOMP算法信噪比最大提高了53.95%,相应的重构时间缩短了15.41%,具有更小的恢复残差以及更高的信号重构成功率.     

图像差与加权核范数最小化的压缩图像融合

现有的图像融合算法存在非线性操作产生的噪声干扰和空间复杂度高等问题,使得融合图像易失真和丢失信息。一些学者提出的压缩感知图像融合算法能有效改善这一问题,但大多忽略了图像矩阵的低秩性,往往会降低融合质量。由此,将压缩感知融合技术与低秩矩阵逼近方法相结合,提出基于信息论图像差与自适应加权核范数最小化的图像融合算法。该算法由3个阶段组成。首先,将2幅源图像通过小波稀疏基稀疏化,并利用结构随机矩阵压缩采样,得到测量输出矩阵。然后,将测量输出矩阵进行分块,再利用图像差融合算法得到融合后的测量输出矩阵块。最后,利用自适应加权核范数最小化优化得到的块权重,通过正交匹配追踪法重建融合图像。实验结果表明了该算法的有效性和普适性,并且在多种评价指标上优于其他融合算法。     

基于压缩感知的EMT探伤和图像重建

为改善EMT逆问题的欠定性,提高探伤过程中裂纹图像重建质量,本文提出一种基于压缩感知原理的EMT探伤和图像重建方法.其本质是通过压缩感知弱化问题的求解条件,进而有效改善EMT逆问题的欠定性.本文采用压缩感知技术对EMT探伤信号进行处理,并引入了相应的图像重建算法.其中,信号处理包括选取恰当的稀疏变换基对原始信号进行稀疏表示,将稀疏处理后的原始信号进行投影;图像重建过程则采用了两种算法,分别是基于最小L1范数的迭代重加权最小二乘(IRLS)法和基于匹配追踪原理的压缩采样匹配追踪(CoSaMP)算法.仿真和实验结果均表明,IRLS图像重建算法和CoSaMP图像重建算法的图像重建质量都要好于传统的EMT图像重建算法,尤其是CoSaMP算法的图像重建质量更佳.     

基于压缩感知信号重建的自适应正交多匹配追踪算法*

近年来出现的压缩感知理论为信号处理的发展开辟了一条新的道路,不同于传统的奈奎斯特采样定理,它指出只要信号具有稀疏性或可压缩性,就可以通过少量随机采样点来恢复原始信号。在研究和总结传统匹配算法的基础上,提出了一种新的自适应正交多匹配追踪算法(adaptive orthogonal multi matching pursuit,AOMMP)用于稀疏信号的重建。该算法在选择原子匹配迭代时分两个阶段,引入自适应和多匹配的原则,加快了原子的匹配速度,提高了匹配的准确性,实现了原始信号的精确重建。最后与传统OMP算法     

压缩感知重构匹配类算法分析

压缩感知理论是一种利用信号的稀疏性或可压缩性而把采样与压缩融为一体的新理论体系,它成功地克服了传统理论中采样数据量大、资源浪费严重等问题。该理论的研究方向主要包括信号的稀疏表示、测量矩阵的设计和信号的重构算法。其中信号的重构算法是该理论中的关键部分,也是近年来研究的热点。本文主要对匹配追踪类重构算法作了详细介绍,并通过仿真实验结果对这些算法进行了对比和分析。     

一种改进的压缩采样匹配追踪算法研究

该文简单对信号稀疏重建的模型和测量矩阵的设计进行了介绍,主要介绍了几种稀疏重建算法,详细给出压缩采样匹配追踪算法及其改进算法的数学框架和基本思想,从原子选择策略和冗余向量的更新方式对算法进行了比较分析,最后通过模拟实验验证了MP,OMP,CoSaMP和IHTCoSaMP算法的重构效果,同时以MSE为性能指标评价了各种算法的重构质量,实验结果表明改进的压缩抽样匹配追踪算法的运算速度较快,重构质量较高。     

A new nonconvex approach for image restoration with Gamma noise

In this paper, a new total generalized variational(TGV) model for restoring images with multiplicative noise is proposed, which contains a nonconvex fidelity term and a TGV term. We use a difference of convex functions algorithm (DCA) to deal with the proposed model. For multiplicative noise removal, there exist many models and algorithms, most of which focus on convex approximation so that numerical algorithms with guaranteed convergence can be designed. Unlike these algorithms, we use the DCA algorithm to remove multiplicative noise. By numerical experiments, it is shown that the proposed approach leads to a better solution compared with the gradient projection algorithm for solving the classic multiplicative noise removal models. We prove that the sequence generated by the DCA algorithm converges to a stationary point, which satisfies the first order optimality condition. Finally, we demonstrate the performance of our whole scheme by numerical examples. A comparison with other methods is provided as well. Numerical results demonstrate that the proposed algorithm significantly outperforms some previous methods for multiplicative Gamma noise removal.     

Achieving a More Robust Neural Network Model for Control of a MR Damper by Signal Sensitivity Analysis

Most neural network models can work accurately on their trained samples, but when encountering noise, there could be significant errors if the trained neural network is not robust enough to resist the noise. Sensitivity to perturbation in the control signal due to noise is very important for the prediction of an output signal. The goal of this paper is to provide a methodology of signal sensitivity analysis in order to enable the selection of an ideal Multi-Layer Perception (MLP) neural network model from a group of MLP models with different parameters, i.e. to get a highly accurate and robust model for control problems. This paper proposes a signal sensitivity which depends upon the variance of the output error due to noise in the input signals of a single output MLP with differentiable activation functions. On the assumption that noise arises from additive/multiplicative perturbations, the signal sensitivity of the MLP model can be easily calculated, and a method of lowering the sensitivity of the MLP model is proposed. A control system of a magnetorheological (MR) fluid damper, which is a relatively new type of device that shows the future promise for the control of vibration, is modelled by MLP. A large number of simulations on the MR damper’s MLP model show that a much better model is selected using the proposed method.     

Multiplicative noise removal via combining total variation and wavelet frame

Total variation (TV) regularization has been proved effective for cartoon images restoration however it produces staircase effects, and properly wavelet frames were confirmed to provide a more smoothing approximation to the original image. In this paper, a new model for multiplicative noise removal was proposed, which combines wavelet frame-based regularization and TV regularization. A modified proximal linearized alternating direction method is developed to solve the proposed model, considering that adding a new regularization term to the TV model would yield more parameters, which will result in computational difficulties. For the new model, the existence of solution and the convergence property of the proposed algorithm are proved. Numerical experiments have proved that the proposed model has a superior performance in terms of the peak signal-to-noise ratio and the relative error values for non-piecewise constant images when compared with some state-of-the-art multiplicative noise removal models.     

非加性噪声情形下卡尔曼滤波器的推广

在数字信号处理中,得到的信号总是或多或少伴随着噪声。如何去除噪声,恢复真实的信号,是信号处理面临的首要问题。一般情形下我们都假定噪声是加性的,即噪声是不依赖于信号的,此时,卡尔曼滤波器是一种非常简便的降噪方法,它是一个最优化自回归数据处理算法,是用前一个估计值和最近一个观察数据来估计信号的当前值,是用状态方程和递推的方法进行估计的,而且它在均方误差意义下是最优的。本文将噪声推广到一般的乘性噪声的情形,利用卡尔曼滤波的基本思想,同样可以得到均方误差意义下的最优滤波,最后通过一个模拟的例子验证了该方法的有效性。     

侧扫声呐图像的3维块匹配降斑方法

斑点噪声是影响侧扫声呐图像质量的主要因素,降斑处理对侧扫声呐图像的判别与分析非常重要。针对侧扫声呐图像自身特性和斑点噪声分布特点,提出一种基于3维块匹配(BM3D)的降斑方法。根据海底散射模型,得到侧扫声呐图像斑点噪声的瑞利分布模型,然后通过高斯光滑函数幂变换将瑞利分布的噪声转化为高斯分布,通过对数变换将乘性噪声转变为加性噪声,再进行自适应的BM3D滤波,最后采用逆变换得到降斑图像。实验结果表明,该方法在降噪、边缘和纹理保持等方面均优于空间域、小波域、Curvelet域的一些降斑方法。     

基于稀疏重构框架下剪切波的SAR图像去噪

SAR图像很容易被乘性噪声多污染,进而影响SAR图像后序的分析与处理。本文中提出了一种基于剪切波稀疏编码的SAR图像移除乘性噪声的新模型。首先通过压缩感知理论建立SAR图像去噪模型;其次通过剪切波变换获得剪切波系数,每个尺度的系数视为一个单元;对于每个单元,通过剪切波域的贝叶斯估计对稀疏系数进行迭代估计。重现的单元最后结合起来构造去噪后的图像。SAR图像去噪效果显示了该算法有良好的表现性,对噪声具有鲁棒性;本文提出的算法不仅有较好的去噪效果,而且还保存了更多的边界信息。     

四元数扩维无迹卡尔曼滤波算法及其在大失准角快速传递对准中的应用

针对快速传递对准中量测失准角为大角度的情况,在非线性欧拉角误差模型基础上,推导了一种基于乘性四元数的等效快速传递对准模型.为解决四元数在无迹卡尔曼滤波（UKF）算法中的应用问题,提出了一种基于四元数的状态扩维无迹卡尔曼滤波（Q--AUKF）算法.该算法将系统噪声增广到状态向量中,解决了乘性四元数噪声无法进行向量意义下四则运算的问题.针对四元数加权均值规范化的限制,采用平均四元数算法保证其正交规范化要求.最后将其应用到快速传递对准中的仿真实验结果表明,在量测误差角为大角度的情况下,该算法具有更高的估计精度与收敛速度.     

State estimation for multi‐channel stochastic singular systems with multiplicative noise

The state estimation problem for multi‐channel singular systems with multiplicative noise is considered based on singular value decomposition. First, two equivalent reduced order subsystems are obtained via the decomposition. Then, in order to solve the estimation problem, the subsystems are rewritten into a new form. It is noted that the measurement noise here becomes colored noise, which contains the dynamic noise, measurement noise, and multiplicative noise of the original system. In this situation, existing filtering methods cannot be directly applied, so a modified filtering method is given. The recursive algorithm for the state estimation is obtained by the filtering method. In addition, the estimation of dynamic noise is derived via the algorithm. A simulation example is given to show the effectiveness of the proposed algorithm. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

一种基于组件树的SAR图像分割算法

合成孔径雷达(SAR)图像中存在严重的相干斑干扰,使得SAR的图像解译过程较为困难。为此,提出一种基于组件树的SAR图像分割算法。对SAR图像建立组件树,给出基于全局特征的自适应非局部判定准则,使用该准则对组件树中的相似组件进行合并,保留组件树中最重要的组件,以完成图像滤波,获取分割后的目标。实验结果表明,该算法能获得准确的分割结果,保持目标的细节信息。     

A new variational model for removal of combined additive and multiplicative noise and a fast algorithm for its numerical approximation

Variational image restoration models for both additive and multiplicative noise (MN) removal are rarely encountered in the literature. This paper proposes a new variational model and a fast algorithm for its numerical approximation to remove independent additive and MN from digital images. Two previous works by L. Rudin, S. Osher, and E. Fatemi [Nonlinear total variation based noise removal algorithms, Phys. D 60 (1992), pp. 259–268] and Z. Jin and X. Yang [Analysis of a new variational model for multiplicative noise removal, J. Math. Anal. Appl. 362 (2010), pp. 415–426] are used to develop the new model. As a result, developing a fast numerical algorithm is difficult because the associated Euler–Lagrange equation is highly nonlinear and standard unilevel iterative methods are not appropriate. To this end, we develop an efficient nonlinear multigrid approach via a robust fixed-point smoother. Numerical tests using both synthetic and realistic images not only confirm that our new model delivers quality results but also that the proposed numerical algorithm allows a very fast numerical realization of the model.