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Blind source separation (BSS) involves recovering unobserved source signals from several mixed observations, typically obtained at the output of a set of sensors. Each sensor receives a different combination of the source signals. The adjective “blind” emphasizes the fact that: first, the source signals are not observed; and next, no information is available about the mixture. The assumption is often held physically that the source signals are mutually independent. Recently, BSS in signal processing has received considerable attention from researchers, due to its numerous promising applications in the areas of biomedical signal processing, digital communications and speech signal, sonar, image processing, and monitoring (Cichocki & Unbehauen, 1996), (Tangdiongga et al, 2001), (Yilmaz & Rickard, 2004), (Herault & Juten, 1986). A number of blind separation algorithms have been proposed based on different separation models. These algorithms play increasingly important roles in many applications. Since the pioneering work of Jutten and Herault (Herault & Juten, 1986), a variety of algorithms have been proposed for BSS. In general, the existing algorithms can be divided into five major categories: neural network-based algorithms (Cichocki & Unbehauen, 1996), (Zhang & Kassam, 2004), density model-based algorithms (Amari et al, 1997), (Lee et al, 1999a), algebraic algorithms (Belouchrani et al, 1997), (Li & Wang, 2002), information-theoretic algorithms (Pajunen, 1998), (Pham & Vrins, 2005) and space-based algorithms (Yilmaz & Rickard, 2004), (Lee et al, 1999b). A source signal with sparse representation means that at most one value of the signal isn’t zero at an instant, making the vector of sensor signals (mixtures) equivalent to some mixing vector. Therefore, the sparse-based BSS problem could be solved by searching for mixing vectors; moreover, recovering source signals. Like the mixtures with sparse representation, each base vectors of the unknown mixing matrix will be displayed on a 2-D plane coordinate as a directional line when two sensors are used. The sparse representation is first introduced in underdetermined BSS by Lee et al. (Lee et al, 1999b). After its introduction, several related methods have been proposed continuously for solving underdetermined BSS

Noise reduction has a lot attention no matter in practical applications or a signal processing research field. Recently, a novel denoisy method which removes noise from received signals by threshold operation on wavelet coefficients was developed and its efficiency has been confirmed. However, its definition of parameters is not general-purpose enough to deal with variant cases. In order to seek high quality to denoisy, this study introduces a frequency analysis tool, empirical mode decomposition (EMD), to separate received signal into several elements which are termed intrinsic mode functions (IMF). And then, according to the order from high frequency to low frequency, IMFs could be separated into finite pair consisting of estimated noise and estimated original signal. Each estimated pair is calculated the correlation measurement which involves second-order correlation and high-order correlation since original signal and noise are mutually independent. A smallest measure value implies an optimal pair approximating to the real. In simulations, four benchmarks and three noise level are tested; moreover, two state of the art algorithms are compared with the proposed method. Finally, the excellent robustness and efficiency of proposed method are demonstrated by simulation results.

For the research field of adaptive de-noisy, the technique which determinates an adequate threshold in wavelet domain of signal is novel and feasible. The most of threshold determination are developed from universal method proposed by Donoho. Unfortunately, these methods are just performed in some wavelet level and involve several incorrectly estimated factors; therefore, they can't result the best performance and can't work well in general cases. By the reason, this paper replaces the universal threshold determination by an intelligent determination, genetic algorithm (GA). Because original signals and noise are mutually independent, an objective function of GA is created to evaluate the second order correlation and high order correlation. Moreover, GA searching is applied in progressively wavelet levels to explore the most suitable wavelet decomposition and the optimal threshold. In order to confirm the validity and efficiency of the proposed algorithm, several simulations which include four benchmarks with variant noise degrees are designed. Moreover, the performance of proposed algorithm will have compared with that of other existing algorithms.