Abstract
In recent years, the problem of underdetermined blind source separation (UBSS) has become a research hotspot due to its practical potential. This paper presents a novel method to solve the problem of UBSS, which mainly includes the following three steps: Single source points (SSPs) are first screened out using the principal component analysis (PCA) approach, which is based on the statistical features of signal time-frequency (TF) points. Second, a mixing matrix estimation method is proposed that combines Ordering Points To Identify the Clustering Structure (OPTICS) with an improved potential function to directly detect the number of source signals, remove noise points, and accurately calculate the mixing matrix vector; it is independent of the input parameters and offers great accuracy and robustness. Finally, an improved subspace projection method is used for source signal recovery, and the upper limit for the number of active sources at each mixed signal is increased from m−1 to m. The unmixing process of the proposed algorithm is symmetrical to the actual signal mixing process, allowing it to accurately estimate the mixing matrix and perform well in noisy environments. When compared to previous methods, the source signal recovery accuracy is improved. The method’s effectiveness is demonstrated by both theoretical and experimental results.
Highlights
As the speech signal can often remain stable in a short time interval, the subinterval can be used as an independent unit, and principal component analysis (PCA) can be used for Single source points (SSPs) screening
As there is a problem of column vector ordering uncertainty in the mixing matrix estimation result, first, the order of the column vector is adjusted according to the principle of the smallest angle between the obtained result and the actual mixing matrix column vector
In order to obtain better sparsity, the signal is transformed from the time domain to the TF domain, and the SSPs are screened using the PCA method, which is based on the statistical features of TF points
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The potential function method [23] is one of the earliest methods proposed in UBSS research, and it has strong robustness under the condition of strong noise or insufficient data samples, but it has its limitations It can only be used in two-dimensional observation signals, and the number of source signals needs to be known. The application of combined clustering algorithm shows a growing trend This is due to the fact that the combined approach can accurately estimate the column vector of the mixing matrix while determining the number of source signals, overcoming the limitations of a single clustering methods.
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