矩阵完成
计算机科学
基质(化学分析)
低秩近似
矩阵范数
算法
缩小
秩(图论)
数学优化
透视图(图形)
数学
人工智能
几何学
组合数学
量子力学
物理
张量(固有定义)
特征向量
复合材料
高斯分布
材料科学
作者
Yi Yang,Jianwei Ma,Stanley Osher
出处
期刊:Inverse Problems and Imaging
[American Institute of Mathematical Sciences]
日期:2013-01-01
卷期号:7 (4): 1379-1392
被引量:85
标识
DOI:10.3934/ipi.2013.7.1379
摘要
In seismic processing, one goal is to recover missing traces when the data is sparsely and incompletely sampled. We present a method which treats this reconstruction problem from a novel perspective. By utilizing its connection with the general matrix completion (MC) problem, we build an approximately low-rank matrix, which can be reconstructed through solving a proper nuclear norm minimization problem. Two efficient algorithms, accelerated proximal gradient method (APG) and low-rank matrix fitting (LMaFit) are discussed in this paper. The seismic data can then be recovered by the conversion of the completed matrix into the original signal space. Numerical experiments show the efficiency and high performance of data recovery for our model compared with other models.
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