基于DBSCAN-R的欠定盲源分离算法

doi:10.12305/j.issn.1001-506X.2026.05.02

摘要/Abstract

摘要：

针对欠定盲源分离问题中变换域稀疏性不足和混合矩阵估计精度不高的问题，对时延混合模型下的均匀线性阵列提出一种将基于密度的带噪空间聚类（density-based spatial clustering of applications with noise，DBSCAN）与随机一致性采样（random sample consensus，RanSaC）算法相结合的混合矩阵估计算法DBSCAN-R。利用变换矩阵优化变换域的稀疏度，进而以更精确的DBSCAN-R算法对混合矩阵进行估计。该算法首先引入变换矩阵改善稀疏特性，随后使用DBSCAN-R算法对具有线性聚类特征的数据进行聚类，并实现聚类质心修正，最后利用最小L₁范数方法实现源信号重构。实验结果表明，所提出的DBSCAN-R算法相较于传统DBSCAN算法的混合矩阵估计归一化均方误差平均降低了4.70 dB，具有鲁棒特性。

关键词: 欠定盲源分离, 均匀线性阵列, 密度空间聚类, 随机一致性采样, 鲁棒性

Abstract:

In response to the issues of insufficient sparsity in the transform domain and low accuracy in mixed matrix estimation in the problem of underdetermined blind source separation, a hybrid matrix estimation algorithm, density based spatial clustering of applications with noise （DBSCAN）-random sample consensus （RanSaC） algorithm （DBSCAN-R） is proposed for uniform linear arrays in time-delay mixed models. The sparse degree of the transform domain is optimized by using the transform matrix, and then the hybrid matrix is estimated by a more accurate DBSCAN-R algorithm. Firstly, the algorithm introduces a transformation matrix to improve sparsity. Secondly, uses the DBSCAN-R algorithm to cluster the data with linear clustering characteristics, and realizes the cluster center of mass correction. Finally, the minimum L₁ norm method is used to reconstruct the source signal. The experimental results show that the DBSCAN-R algorithm proposed reduces the normalized mean-square error of the hybrid matrix estimation by an average of 4.70 dB compared to the traditional DBSCAN algorithms, which has a robust characteristic.

Key words: underdetermined blind source separation, uniform linear array, density spatial clustering, random sample consensus （RanSaC）, robustness

中图分类号:

TN 911.7

季策, 王琳珊, 牟辉. 基于DBSCAN-R的欠定盲源分离算法[J]. 系统工程与电子技术, 2026, 48(5): 1465-1473.

Ce JI, Linshan WANG, Hui MOU. Underdetermined blind source separation algorithm based on DBSCAN-R[J]. Systems Engineering and Electronics, 2026, 48(5): 1465-1473.

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源信号	DBSCAN-R	DBSCAN	KM	Hierarchical+KM
$ {\hat s_1}(t) $	0.986 9	0.974 2	0.973 7	0.959 5
$ {\hat s_2}(t) $	0.891 9	0.870 3	0.873 2	0.851 9
$ {\hat s_3}(t) $	0.930 2	0.930 2	0.932 1	0.921 7

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