A wavelet-based forward BSS algorithm for acoustic noise reduction and speech enhancement Khadidja Ghribi a , Mohamed Djendi b,⇑ , Daoued Berkani a a National Polytechnic School of Algiers (NPSA), 10 Rue des Frères OUDEK, El Harrach 16200, Algeria b University of Blida 1, Signal Processing and Image Laboratory (LATSI), Route de Soumaa, B.P. 270, Blida 09000, Algeria article info Article history: Received 20 February 2015 Received in revised form 12 November 2015 Accepted 16 November 2015 Keywords: Noise cancellation Discrete wavelet transform SAD Convolutive mixture Speech enhancement abstract In this paper, we address the problem of noise reduction and speech enhancement by adaptive filtering algorithm. Recently, the well known forward blind source separation (FBSS) structure has been largely studied and intensively used to reduce acoustic noise components and to enhance speech signal. The FBSS structure is often combined with adaptive algorithms to accelerate the adaptation of the cross-filters, and to improve noise suppression at the output. In this paper, we propose to use a wavelet transform decomposition in the FBSS structure by using a two-channel forward wavelet symmetric adap- tive decorrelating (WFSAD) algorithm. The proposed WFSAD algorithm provides a better compromise between time and frequency resolution and improves robustness of the noise reduction process when compared with the classical two-channel forward symmetric adaptive decorrelating (FSAD) algorithm. Simulation results prove the efficiency of the proposed WFBSS algorithm in comparison with conven- tional ones in terms of several objective and subjective criteria. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction In recent years, particular attention has been paid to acoustic noise cancellation and speech enhancement techniques, in many applications and systems such as in teleconferencing and hand- free telephony [1–3]. In these applications, the desired speech sig- nal is often corrupted by noise signals, such as coherent noises, incoherent noises, diffuse noises, and double talk. Several tech- niques and algorithms have been proposed to reduce noise components. These last techniques are mostly based upon the use of a number of microphones. Several single, two-channel and multi-channel algorithms have been proposed in speech enhance- ment [4–9]. We can classify these methods in terms of adaptive and non adaptive behavior of the used algorithms [10–13]. The methods, including adaptive algorithms, give best results with non-stationary signals [14,15]. Other approaches that are often used in speech enhancement and acoustic noise reduction are based on the used of blind source separation (BSS) to retrieve speech from noisy observations [16]. The BSS systems are helpful in the situation when there is no infor- mation about the input signal and the mixtures in a crosstalk removal of two-sensor system [17,18]. The performance of speech enhancement systems based on adaptive filtering is reliant to the equality of the noise reference. However, speech leakage into the noise reference causes signal distortion and poor noise reduction. This is due to the fact that the algorithm decorrelates the output speech signal and the noise reference, which makes no sense in the case of speech signal leakage [19,20]. A number of these algo- rithms that suppress the acoustic noise components at the output are based on the decorrelation of the signal estimate with a signal free noise estimate. This free noise signal is obtained by adding a symmetric filter to the classical adaptive noise cancellation (ANC) structure. Forward (FBSS) and backward (BBSS) are mainly used in speech enhancement application. Several algorithms are employed with the FBSS and BBSS structures in noise reduction and speech enhancement applications [21,20]. The first two-channel algorithm used in this context is the sym- metric adaptive decorrelating (SAD) algorithm that is based on the least mean square (LMS) approach [21]. This algorithm allows the estimated speech signal to be retrieved from two noisy observa- tions generated by convolutive mixtures of two mutually indepen- dent sources signals. This two-sensor algorithm is known by its simple implementation and low complexity. Another algorithm used in literature is the LMS in its single channel, two-channel and multichannel form [22]. Furthermore, several techniques have been proposed to improve the convergence speed of the LMS and the normalized (NLMS) algorithms [23]. This improvement is http://dx.doi.org/10.1016/j.apacoust.2015.11.011 0003-682X/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: khadidja.ghribi@g.enp.edu.dz (K. Ghribi), m_djendi@yahoo.fr (M. Djendi), daoud.berkani@g.enp.edu.dz (D. Berkani). Applied Acoustics 105 (2016) 55–66 Contents lists available at ScienceDirect Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust