Abstract
Underdetermined blind source separation (UBSS) is a hot and challenging problem in signal processing. In the traditional UBSS algorithm, the number of source signals is often assumed to be known, which is very inconvenient in practice. In addition, it is more difficult to obtain the accurate estimation of mixing matrix in the underdetermined case. However, this information has a great influence on the source separation results, which can easily lead to poor separation performance. In this paper, a novel UBSS algorithm is presented to carry out a combined source signal number estimation and source signal separation task. First, in the proposed algorithm, we design a gap-based detection method to detect the number of source signals by eigenvalue decomposition. Then, the estimation of the mixing matrix is processed using a higher-order cumulant-based method so that the uniqueness of the estimated mixing matrix is guaranteed. Furthermore, an improved l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm minimization algorithm is proposed to estimate the source signals. Meanwhile, the pre-conditioned conjugate gradient technology is employed to accelerate the convergence rate such that the computational load is reduced. Finally, a series of simulation experiments with synthetic heart sound data and image reconstruction results demonstrate that the proposed algorithm achieves better separating property than the state-of-the-art algorithms.
Highlights
Blind source separation (BSS) is to separate the unknown source signals from the mixture signals with no information about the mixing matrix, which has been applied in various fields, such as speech processing, image processing [1], [2]
We carefully consider the computational complexity of the proposed algorithm, one of the most timeconsuming calculations is the matrix-matrix multiplication H · (s∗)−1 ·H T, whose computational complexity is O(M 3), which is controlled by the number of sensors M
WORK In this paper, a novel algorithm has been presented based on higher-order statistics and sparse representation to solve the Underdetermined blind source separation (UBSS) problem
Summary
Blind source separation (BSS) is to separate the unknown source signals from the mixture signals with no information about the mixing matrix, which has been applied in various fields, such as speech processing, image processing [1], [2]. Most of BSS algorithms have been proposed by exploiting some assumptions about the source signals. The number of source signals is known, the source signals are mutually independent or assumed to be sparse. In practice, these assumptions are difficult to be satisfied. For the underdetermined case, i.e., the number of sensors is less than the number of source signals, which is a more challenging problem. For this reason, underdetermined BSS faces three challenging issues.
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