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851.
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853.
The goal of this paper is to find a low‐rank approximation for a given nth tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP‐hard problem. In this paper, we formulate a sparse optimization problem via an l1‐regularization to find a low‐rank approximation of tensors. To solve this sparse optimization problem, we propose a rescaling algorithm of the proximal alternating minimization and study the theoretical convergence of this algorithm. Furthermore, we discuss the probabilistic consistency of the sparsity result and suggest a way to choose the regularization parameter for practical computation. In the simulation experiments, the performance of our algorithm supports that our method provides an efficient estimate on the number of rank‐one tensor components in a given tensor. Moreover, this algorithm is also applied to surveillance videos for low‐rank approximation. 相似文献
854.
855.
采用基于Morozov偏差原理的后验策略来选择最优正则参量,并采用此方法对单峰和多峰分布颗粒系的模拟电场自相关函数进行了反演,结果表明,对于单峰颗粒体系,当电场自相关函数的扰动误差小于0.05时,反演得到的峰值准确,当电场自相关函数的扰动误差大于0.05时,反演得到的峰值偏离所模拟的颗粒粒径.正则参量初始值在0.000 02~2范围内,在反演所得的峰值准确的基础上,正则参量初始值越小,反演得到的分布宽度越窄.收敛误差在0.000 05~50范围内,在保持反演结果稳定的基础上,收敛误差取值越大,反演得到的分布宽度越窄.对于多峰颗粒体系,当颗粒系中的颗粒粒径差别较小时,峰值向平均值偏移,当颗粒系中的颗粒粒径差别较大时,小颗粒粒径分布以噪音的形式出现. 相似文献
856.
Nguyen Buong 《Computational Mathematics and Mathematical Physics》2008,48(11):1927-1935
The purpose of this paper is to present a regularization variant of the extragradient method for finding a common element
of the solution sets for a variational inequality problem involving a -Lipschitz continuous monotone mapping A and for a finite family of λ
i
-inverse strongly-monotone operators {A
i
}
i = 1
N
from a closed convex subset K into the Hilbert space H.
This article was submitted by the author in English. 相似文献
857.
The prior knowledge of signal is the previous condition of image compressed sensing reconstruction. In order to improve the quality of the priors except for image sparsity, this paper proposes a new model of video image reconstruction. The texture is the important visual feature of video image as a result of its repeat, leading to image global geometrical structures. The nonlocal idea comes from image self-familiar and can represent image detail features from the geometrical point of view. Therefore, the texture geometrical feature of video image is researched, and we take advantage of dual-tree complex wavelet transform to portray the sparsity representation regularization of the texture. What is more, global constrained regularization is constructed with the help of the nonlocal idea. On the basis of the two regularizations above, a new reconstruction model of video image compressed sensing is proposed, which not only preserves the sparsity prior knowledge of image but also improves the quality of prior knowledge of image by promoting geometrical structure. Iterative shrinkage thresholding algorithm is adopted to solve the model leading to a both simple and quick iterative algorithm. Numerical experiments show that our method is efficient for video image recovery, especially preserving the global details of the original video image. 相似文献
858.
本文运用算子扰动理论研究了无穷维Hamilton算子的共轭算子,进而得到了无穷维Hamilton算子为辛自伴算子的若干充分条件. 相似文献
859.
Based on radial basis functions approximation, we develop in this paper a new com-putational algorithm for numerical differentiation.
Under an a priori and an a posteriori choice rules for the regularization parameter, we also give a proof on the convergence error estimate in reconstructing the
unknown partial derivatives from scattered noisy data in multi-dimension. Numerical examples verify that the proposed regularization
strategy with the a posteriori choice rule is effective and stable to solve the numerical differential problem.
*The work described in this paper was partially supported by a grant from CityU (Project No. 7001646) and partially supported
by the National Natural Science Foundation of China (No. 10571079). 相似文献
860.
声学温度场检测技术通过多路径声波传播时间数据,反演被测区域的温度分布。提供了一种高精度的三维复杂温度场的声学测量方法。首先从射线声学角度给出了三维非均匀温度场中声波传播路径的数学模型。在此基础上,将三维温度场的重建问题转化为声波传播路径的求解和温度场的反演问题,建立了基于多项式修正径向基函数(RBF-PR)和改进的Tikhonov正则化三维温度场重建算法。采用两种典型的炉膛三维温度场模型,在信噪比SNR=35 dB下进行了数值模拟,分析了声波传播路径在非均匀温度场中的弯曲特性、算法的重建质量和抗噪性,同时进行了实际炉膛内二维温度场的重建。结果表明了提出的考虑声线弯曲的温度场重建算法具有精度高,抗噪性强、适用性好的特点,为实现高精度的复杂温度场的声学测量提供了有效方法。 相似文献