稀疏表示中稀疏系数的 l-1 范数的特性分析

doi:10.3969/j.issn.1001-506X.2019.12.04

系统工程与电子技术 ›› 2019, Vol. 41 ›› Issue (12): 2692-2696.doi: 10.3969/j.issn.1001-506X.2019.12.04

稀疏表示中稀疏系数的 l-1 范数的特性分析

宗静静1,2, 邱天爽1

1.大连理工大学电子信息与电气工程学部, 辽宁大连 116024;
2. 大连交通大学电气信息工程学院, 辽宁大连 116028

出版日期:2019-11-25 发布日期:2019-11-25

Characteristic analysis for the l-1 norm of sparse coefficients in sparse representation

ZONG Jingjing1,2, QIU Tianshuang1

1. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China; 2. School of Electrical and Information Engineering, Dalian Jiaotong University, Dalian 116028, China

Online:2019-11-25 Published:2019-11-25

摘要/Abstract

摘要：

稀疏表示模型被广泛应用于计算机视觉和模式识别领域,该数学模型中参数稀疏系数的 l-1 范数作为图像块的活跃度度量(activity level measurement,ALM)特征被成功应用于稀疏表示图像融合领域,但该参数的物理意义至今没有明确的解释。以此问题为出发点,首先,从广义的角度出发,将图像块的稀疏系数向量的 l-1 范数定义为奇异度;其次,在理论上定性说明了该定义的合理性;第三,通过实验,以图形化方式侧面展示了该参数的物理意义。理论与实验分析结果表明:信号向量的稀疏系数可看作该向量在字典基函数下的投影坐标,稀疏系数的 l-1 范数可用来描述信号的奇异性特征。

关键词: 稀疏表示, 图像融合, 稀疏系数的, l-1范数, 奇异度

Abstract:

The sparse representation model is widely used in the field of computer vision and pattern recognition. The l-1 norm of sparse coefficients in this model is successfully applied in the field of sparse representation-based image fusion as an activity level measurement (ALM) feature of image patches, but the physical meaning of this parameter is not clearly explained so far. Starting from this issue, firstly, from a generalized viewpoint, the l-1 norm of the sparse coefficient vector of an image patch is defined as the singularity; secondly, the rationality of the definition is qualitatively explained in theory; thirdly, the physical meaning of the parameter is shown in a graphical way through experiments. Theoretical and experimental analysis results show that the sparse coefficient of the signal vector can be regarded as the projection coordinate of the signal under the dictionary basis function, and the l-1 norm of the sparse coefficient can be used to describe the singularity characteristics of a signal.

Key words: sparse representation, image fusion, l-1 norm of sparse coefficient, singularity

宗静静, 邱天爽. 稀疏表示中稀疏系数的 l-1 范数的特性分析[J]. 系统工程与电子技术, 2019, 41(12): 2692-2696.

ZONG Jingjing, QIU Tianshuang. Characteristic analysis for the l-1 norm of sparse coefficients in sparse representation[J]. Systems Engineering and Electronics, 2019, 41(12): 2692-2696.

稀疏表示中稀疏系数的 l-1 范数的特性分析

Characteristic analysis for the l-1 norm of sparse coefficients in sparse representation

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 0

编辑推荐

Metrics

本文评价