共查询到19条相似文献，搜索用时 46 毫秒
1.
在实际应用中,有一些信号是具有分片的结构的.本文我们提出一种分片正交匹配追踪算法(P_OMP)来求解分片稀疏恢复问题,旨在保护分片信号中的分片结构(或者小尺度非零元).P_OMP算法是基于CoSaMP和OMMP算法的思想上延伸出的一种针对分片稀疏问题的贪婪算法. P_OMP算法不仅仅具有OMP算法的优势,还能够在比CoSaMP方法更松弛的条件下得到同样的误差下降速率.进一步,P_OMP~算法在保护分片稀疏信号的尺度细节信息上表现的更好.数值实验表明相比于CoSaMP, OMP, OMMP和BP算法, P_OMP算法在分片稀疏恢复上更有效更稳定. 相似文献
2.
针对欠定系统中出现的稀疏信号恢复问题,提出了一种基于最小化近似零伪范数的处理方法,算法首先结合反正切函数构造出代价函数,再融合最速下降法和扩展牛顿迭代法逐步迭代寻优,并给出了算法的收敛性分析,数值仿真实验结果表明,与经典的稀疏信号恢复算法相比,方法有更好的计算速度和恢复精度. 相似文献
3.
众所周知,传统的信号压缩和重建遵循香农一耐奎斯特采样定律,即采样率必须至少为信号最高频率的两倍,才能保证在重建时不产生失真,这无疑将给信号采样,传输和存储过程带来越来越大的压力.随着科技的飞速发展,特别是近年来传感器技术获取数据能力提高,物联网等促使人类社会的数据规模遽增,大数据时代正式到来.大数据的规模效应给数据存储,传输,管理以及数据分析带来了极大的挑战.压缩采样应运而生.限制等距性(Restricted Isometry Property,RIP)在压缩传感中起着关键的作用.只有满足限制等距条件的压缩矩阵才能平稳恢复原始信号.RIP作为衡量矩阵是否能作为测量矩阵得到了认可,但是此理论的缺陷在于对任一矩阵,很难有通用,快速的算法来验证其是否满足RIP条件.很多学者尝试弱化RIP条件以找到测量矩阵构造的突破口.首先构造了新的限制等距条件δ_(1.5k)+θ_(k,1.5k)≤1,然后证明在这个条件下无噪声稀疏信号能被精确的恢复,并且噪声稀疏信号能被平稳的估计.最后,通过比较表明δ_(1.5k)+θ_(k,1.5k)≤1优于现存的条件. 相似文献
4.
对于一般的压缩感知模型,当模型中系数矩阵的每一项都是亚高斯随机变量并且稀疏矩阵满足限制等距性质时,在测量值满足最优条件m≥csln(e N/s)的情况下,模型的s稀疏解也可以通过?1最小化得到.文章中首先借助概率分布范数给出了三个重要的辅助定理,最后给出主要结论的证明并且通过一个简单的实验验证了最后的定理. 相似文献
5.
《数理统计与管理》2021,40(1):93-104
针对高维数据"维数灾难"问题,降维是最典型的处理方式之一。降维技术不仅可以减弱"维数灾难"的负面影响,而且能够剔除高维数据中的冗余特征,从而提升高维数据回归、分类等任务的效率。高维数据通常呈现出复杂或非线性结构,恰当的降维方法可以有效地将高维特征数据投影至低维空间,以实现原始数据的非线性特征提取。本文尝试使用无监督学习模型稀疏自编码网络对金融高维数据进行非线性特征提取,将提取到的特征作为有监督学习模型BP神经网络的输入以预测指数收益率。更进一步地,为了验证稀疏自编码算法在特征提取方面的优势与有效性,本文引入稀疏主成分模型进行对比分析。实证分析显示:本文所使用的稀疏自编码网络能够较好地提取非线性特征并进行预测,其预测精度优于以稀疏主成分为代表的线性降维方法。 相似文献
6.
本文通过引入支撑集捕获基数及MP广义逆,提出了一种用于稀疏恢复问题的矩阵广义逆硬阈值追踪算法,并在观测误差存在的情况下给出了算法在约束等距条件(RIP)下的收敛性.数值实验表明,算法不仅极大地减少了收敛所需迭代次数,且观测误差存在的情况下稀疏恢复是强健的. 相似文献
7.
8.
针对低秩稀疏矩阵恢复问题的一个非凸优化模型,本文提出了一种快速非单调交替极小化方法.主要思想是对低秩矩阵部分采用交替极小化方法,对稀疏矩阵部分采用非单调线搜索技术来分别进行迭代更新.非单调线搜索技术是将单步下降放宽为多步下降,从而提高了计算效率.文中还给出了新算法的收敛性分析.最后,通过数值实验的比较表明,矩阵恢复的非单调交替极小化方法比原单调类方法更有效. 相似文献
9.
焦雨领刘宇青 《数学建模及其应用》2020,(4):1-27
研究了基于最小二乘法的稀疏信号恢复问题.针对一类非凸稀疏性罚,包括l^0、bridge、capped-l^1、光滑剪切绝对差和极小极大凹罚,提出了一种新的原始对偶有效集算法.首先证明相关优化问题的全局极小值的存在性,然后利用相关阈值算子,推导出全局极小值的一个新的必要最优条件,必要最优条件的解是坐标极小值,在一定条件下,它们也是局部的极小值.引入对偶变量后,可同时使用原变量和对偶变量确定有效集.此外,这种关系适用于一种有效集类迭代算法,该算法在每一步中首先只更新有效集上的原始变量,然后显式地更新对偶变量.结合正则化参数的延拓性,证明了原始对偶有效集方法在一定正则化条件下全局收敛于潜在回归目标.大量的数值实验表明,与现有的稀疏恢复方法相比,该方法具有较高的效率和精度. 相似文献
10.
泊松回归模型作为广义线性回归模型之一,被广泛应用于计数型数据分析.随着计算机技术的迅速发展,获取和存储的变量越来越多,所建立模型越来越复杂.针对泊松回归模型的稀疏优化问题,本文考虑带有L0惩罚的泊松回归稀疏约束模型,应用二阶贪婪投影梯度牛顿(Greedy ProjectedGradient Newton,简称GPGN)算法估计参数.通过在合成数据集进行模拟研究说明算法的有效性,并将泊松回归应用于基于Wi-Fi信号预测楼层的建模分析,验证了GPGN算法在泊松回归稀疏约束优化问题中的优良表现. 相似文献
11.
《Expositiones Mathematicae》2022,40(4):1135-1158
In 1999, S. V. Konyagin and V. N. Temlyakov introduced the so-called Thresholding Greedy Algorithm. Since then, there have been many interesting and useful characterizations of greedy-type bases in Banach spaces. In this article, we study and extend several characterizations of greedy and almost greedy bases in the literature. Along the way, we give various examples to complement our main results. Furthermore, we propose a new version of the so-called Weak Thresholding Greedy Algorithm (WTGA) and show that the convergence of this new algorithm is equivalent to the convergence of the WTGA. 相似文献
12.
在基因的杂交试验中,传统的方法是在一个大的探针集中选择每条探针与成千上万条基因进行杂交,通过获得的杂交信号来区分所有的信息,这样不仅耗时长,而且从成本上考虑也是不划算的.建立了一个使得信息增量最大化的数学模型,依据该模型,可以从一个大的探针集中挑选出尽可能少的探针并达到区分所有信息的目的,节省了杂交试验的时间,也节省了成本,通过实例计算证明是有效的. 相似文献
13.
Compressed sensing has motivated the development of numerous sparse approximation algorithms designed to return a solution to an underdetermined system of linear equations where the solution has the fewest number of nonzeros possible, referred to as the sparsest solution. In the compressed sensing setting, greedy sparse approximation algorithms have been observed to be both able to recover the sparsest solution for similar problem sizes as other algorithms and to be computationally efficient; however, little theory is known for their average case behavior. We conduct a large‐scale empirical investigation into the behavior of three of the state of the art greedy algorithms: Normalized Iterative Hard Thresholding (NIHT), Hard Thresholding Pursuit (HTP), and CSMPSP. The investigation considers a variety of random classes of linear systems. The regions of the problem size in which each algorithm is able to reliably recover the sparsest solution is accurately determined, and throughout this region, additional performance characteristics are presented. Contrasting the recovery regions and the average computational time for each algorithm, we present algorithm selection maps, which indicate, for each problem size, which algorithm is able to reliably recover the sparsest vector in the least amount of time. Although no algorithm is observed to be uniformly superior, NIHT is observed to have an advantageous balance of large recovery region, absolute recovery time, and robustness of these properties to additive noise across a variety of problem classes. A principle difference between the NIHT and the more sophisticated HTP and CSMPSP is the balance of asymptotic convergence rate against computational cost prior to potential support set updates. The data suggest that NIHT is typically faster than HTP and CSMPSP because of greater flexibility in updating the support that limits unnecessary computation on incorrect support sets. The algorithm selection maps presented here are the first of their kind for compressed sensing. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
14.
为快速准确重构含有未知初始条件的无约束结构外激励,提出了一种基于稀疏Bayes学习算法的荷载重构方法.结合函数拟合的思想建立控制方程,以噪声服从Gauss分布为先验,在Bayes模型中使用快速算法,稀疏重构未知荷载.为合理表达分段拟合中的初始条件,提出了改进的分段拟合手段,以上一分段末状态响应作为可能初始条件,并辅以低阶振型作为初始位移和初始速度的补充.算例以简化运载火箭模型为研究对象,考虑不同等级噪声和不同初始条件表达形式的影响,验证方法的精度和效率. 相似文献
15.
In this paper, we propose a Quasi-Orthogonal Matching Pursuit (QOMP) algorithm for constructing a sparse approximation of functions in terms of expansion by orthonormal polynomials. For the two kinds of sampled data, data with noises and without noises, we apply the mutual coherence of measurement matrix to establish the convergence of the QOMP algorithm which can reconstruct $s$-sparse Legendre polynomials, Chebyshev polynomials and trigonometric polynomials in $s$ step iterations. The results are also extended to general bounded orthogonal system including tensor product of these three univariate orthogonal polynomials. Finally, numerical experiments will be presented to verify the effectiveness of the QOMP method. 相似文献
16.
V. N. Temlyakov 《Advances in Computational Mathematics》2007,26(4):431-449
We study convergence and rate of convergence of expansions of elements in a Banach space X into series with regard to a given dictionary
. For convenience we assume that
is symmetric:
implies
. The primary goal of this paper is to study representations of an element f∈X by a series
In building such a representation we should construct two sequences: {g
j
(f)}
j=1∞
and {c
j
(f)}
j=1∞
. In this paper the construction of {g
j
(f)}
j=1∞
will be based on ideas used in greedy-type nonlinear approximation. This explains the use of the term greedy expansion. We use a norming functional
of a residual f
m−1
obtained after m−1 steps of an expansion procedure to select the mth element
from the dictionary. This approach has been used in previous papers on greedy approximation. The greedy expansions in Hilbert
spaces are well studied. The corresponding convergence theorems and estimates for the rate of convergence are known. Much
less is known about greedy expansions in Banach spaces. The first substantial result on greedy expansions in Banach spaces
has been obtained recently by Ganichev and Kalton. They proved a convergence result for the L
p
, 1<p<∞, spaces. In this paper we find a simple way of selecting coefficients c
m
(f) that provides convergence of the corresponding greedy expansions in any uniformly smooth Banach space. Moreover, we obtain
estimates for the rate of convergence of such greedy expansions for
– the closure (in X) of the convex hull of
.
This research was supported by the National Science Foundation Grant DMS 0200187 and by ONR Grant N00014-91-J1343. 相似文献
17.
Aveiro method is a sparse representation method in reproducing kernel Hilbert spaces, which gives orthogonal projections in linear combinations of reproducing kernels over uniqueness sets. It, however, suffers from determination of uniqueness sets in the underlying reproducing kernel Hilbert space. In fact, in general spaces, uniqueness sets are not easy to be identified, let alone the convergence speed aspect with Aveiro method. To avoid those difficulties, we propose an new Aveiro method based on a dictionary and the matching pursuit idea. What we do, in fact, are more: The new Aveiro method will be in relation to the recently proposed, the so‐called pre‐orthogonal greedy algorithm involving completion of a given dictionary. The new method is called Aveiro method under complete dictionary. The complete dictionary consists of all directional derivatives of the underlying reproducing kernels. We show that, under the boundary vanishing condition bring available for the classical Hardy and Paley‐Wiener spaces, the complete dictionary enables an efficient expansion of any given element in the Hilbert space. The proposed method reveals new and advanced aspects in both the Aveiro method and the greedy algorithm. 相似文献
18.
The Tridiagonal Transportation Problem deals with shipments of goods from n origins to n destination aalong 3n - 2 routes that correspond to the diagonal and off diagonal cells. This paper presents an equivalent Linear Programming Problem with only 2n - 1 decision variables. A greedy algorithm is developed by making simple changes to the right hand side of the L.P. Several extensions are also discussed. 相似文献
19.
We present a generalization of Temlyakov's weak greedy algorithm, and give a sufficient condition for norm convergence of the algorithm for an arbitrary dictionary in a Hilbert space. We provide two counter-examples to show that the condition cannot be relaxed for general dictionaries. For a class of dictionaries with more structure, we give a more relaxed necessary and sufficient condition for convergence of the algorithm. We also provide a detailed discussion of how a real-world implementation of the weak greedy algorithm, where one has to take into account floating point arithmetic and other types of finite precision errors, can be modeled by the new algorithm. 相似文献