基于非负矩阵分解算法进行盲信号分离

独立分量分析(ICA)已被广泛运用于线性混合模型的盲源分离问题,但却有两个重要的限制:信源统计独立和信源非高斯分布。然而更有意义的线性混合模型是:观测信号是非负信源的非负线性混合,信源之间可以统计相关且可以为高斯分布。本文针对盲源分离问题,提出了一种运用新近国际上提出的一种非负矩阵分解算法(NMF算法)进行统计相关信源的盲源分离方法,该方法没有信源统计独立和信源非高斯分布的限制,只要信源之间没有一阶原点统计相关,则可很好实现对信源的分离。大量仿真及与传统ICA进行盲源分离的比较,验证了运用NMF进行包括统计相关信源和高斯分布信源的盲源分离的可行性和有效性。

Blind sources separation based on non-negative matrix factorization

Independent Component Analysis (ICA) is a widely applicable and effective approach in Blind Source Separation (BSS) with the limitation that the sources are independent to each other, while more commonly situation is blind source separation where sources are statistically dependent to each other. In this paper, a novel idea for blind source separation is presented that the blind independent source separation is essentially matrix factorization to factorize the observation matrix into a mixing matrix and a source matrix where the sources are independent to each other, while blind non-negative dependent source separation is essentially a matrix factorization to factorize the observation matrix into a non-negative mixing matrix and a non-negative source matrix where the sources can be dependent to each other. Non-negative Matrix Factorization (NMF) technique is applied to this non-negative dependent source separation and proved by computer simulations and by Partial Volume Correction (PVC) experiments for real microarray data that it is of great effectiveness when the sources are dependent to each other and/or Gaussian distributed.