基于非负矩阵分解的盲源分离算法研究

发布时间：2018-04-19 20:19

本文选题：盲源分离 + 非负矩阵分解　；参考：《燕山大学》2016年硕士论文

【摘要】：在信号处理领域,盲源分离是研究的热点问题之一,不仅具有重要的理论研究价值,而且已经应用于科学科研的多个方面,有着广阔的应用前景。非负矩阵分解作为一种新兴的解决盲源分离问题的有效方法,也逐渐引起了研究学者们的高度重视。本文是在国内外研究基础上,对非负矩阵分解方法解决盲源分离问题的研究。首先,分析了盲源分离和非负矩阵分解的研究现状,对非负矩阵分解方法和盲源分离常用数学知识详细阐述。在此基础上,又介绍了梯度下降法、带约束的优化问题以及基本的非负矩阵分解算法。其次,针对超定混合模型下的盲源分离,研究了稀疏约束的非负矩阵分解方法。这种方法通过基础非负矩阵分解算法的目标函数增加稀疏约束,重新更新因子矩阵的迭代规则,能够实现超定盲源分离。进一步,对于正定盲源分离,引入了反馈非负矩阵分解算法,该算法比约束的二阶优化非负矩阵分解算法具有更好的性能,有效地解决了正定盲源分离问题,最后,运用联合非负矩阵分解方法解决欠定盲源分离问题。该方法的第一阶段用行列式和稀疏性约束的非负矩阵分解算法处理混合信号,并从中选择处分离效果最好的信号,直到混合信号矩阵不再是欠定矩阵,这就将欠定混合矩阵成功地转化为非欠定混合矩阵。第二阶段用约束二阶优化非负矩阵分解处理混合信号。最终实现了欠定混合模型下的盲源分离。
[Abstract]:In the field of signal processing, blind source separation (BSS) is one of the hot topics in research. It has not only important theoretical research value, but also has been applied in many aspects of scientific research, and has a broad application prospect. As a new effective method to solve the problem of blind source separation, nonnegative matrix factorization (NNM) has been paid more and more attention by researchers. On the basis of domestic and foreign research, this paper studies the method of nonnegative matrix decomposition to solve the blind source separation problem. Firstly, the research status of blind source separation and non-negative matrix decomposition is analyzed, and the common mathematical knowledge of non-negative matrix decomposition and blind source separation is described in detail. On this basis, gradient descent method, constrained optimization problem and basic nonnegative matrix factorization algorithm are also introduced. Secondly, the nonnegative matrix decomposition method with sparse constraints is studied for blind source separation under overdetermined mixed model. By adding sparse constraints to the objective function of the basic nonnegative matrix decomposition algorithm and updating the iterative rules of the factor matrix, the method can realize blind source separation. Furthermore, for positive definite blind source separation, a feedback nonnegative matrix decomposition algorithm is introduced, which has better performance than the constrained second-order optimization nonnegative matrix decomposition algorithm, and effectively solves the problem of positive definite blind source separation. The joint nonnegative matrix decomposition method is used to solve the problem of undetermined blind source separation. In the first stage of the method, the mixed signal is processed by determinant and sparse constraint nonnegative matrix decomposition algorithm, and the best signal is separated from it until the mixed signal matrix is no longer an underdetermined matrix. In this way, the underdetermined mixed matrix is successfully transformed into the undetermined mixed matrix. In the second stage, the mixed signal is processed by constrained second order optimization nonnegative matrix decomposition. Finally, blind source separation is realized under the underdetermined mixed model.
【学位授予单位】：燕山大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TN911.7

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