## 1 Introduction  
It is well known that the larynx is the main organ of natural voice production for normal human beings to communicate, however, there are still many patients who suffer from larynx diseases or have no larynx (due to laryngectomies, which are the total removal of the larynx for the treatment of laryngeal cancer, other laryngeal lesions, and so on), which would lead to the loss of their vocal function. Therefore, various speech production substitutes have been developed and used practically in order to reconstruct speech functions [1; 2; 3; 4], including the esophageal speech and the trachea esophageal speech production methods, [PERSON]'s artificial larynx, and the electrolarynx (EL) [1]. Comparing these post- laryngectomy forms of speech production, the electrolarynx, which is a hand-held battery-powered device that is typically held against the neck at the level of the former glottis to excite the vocal tract acoustically [5], has several special advantages, such as being easier to use, production of longer sentences without special care, and being more effective in communication than other methods of voice rehabilitation in many situations. Therefore, the electrolarynx is the main method adopted for voice rehabilitation after laryngectomies, and has been clinically proven to be an important method of oral communication for laryngectomees for more than 50 years. Unfortunately, both the EL device and the resulting speech have several serious shortcomings, especially the radiated noise during phonation, which is due to the fact that part of the sound energy produced is not able to pass through the neck tissue but rather is radiated directly from the instrument itself. Data from previous studies reported that this radiated noise was about 20-25 dB when the mouth was closed [5], and varied over 4-15 dB across subjects for the same device [6]. This radiated noise, therefore, may not only cause a stronger concentration of noise energy between 400-1 KHz and 2-4 kHz in EL speech, but also result in loss of speech intelligibility [7]. In addition, the masking effect of the noise can contribute to the unnaturalness and poor quality of EL speech. Besides the acoustic shielding technology which is applied on the EL device itself [8], more and more signal processing techniques have been developed to improve EL speech [9-12]. To summarize these papers, two main speech enhancement algorithms have been developed to reduce the radiated noise of EL speech, and improve its intelligibility and naturalness. One method is the subtractive-type algorithm [12, 13], which is the most widely used, and has been shown to be an effective approach for noise canceling. Due to the simplicity of implementation, and low computational load, the spectral subtraction method is the primary choice for real time applications [9, 12]. In general, this method enhances the speech spectrum by subtracting an average noise spectrum from the noisy speech spectrum; here the noise is assumed to be uncorrelated and additive to the speech signal. The phase of the noisy speech is kept unchanged, since it is assumed that the phase distortion is not perceived by human ear. However, a serious drawback of this method is that the enhanced speech is accompanied by an unpleasant musical noise artifact which is characterized by tones with random frequencies. Although many solutions have been proposed to reduce the musical noise in the subtractive-type algorithms [11, 14-17], results performed with these algorithms show that there is a need for further improvement, especially under very low signal-noise ratio (SNR) conditions. Another method uses adaptive noise canceling [10, 18], which removes the noise components of the primary input signal that depend on the reference input signal and are based on second-order statistics. However, many other noise components in the primary input signal, which depend on the noise reference signal through higher-order statistics may exist in the enhanced speech, which affects the effect of noise reduction.