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This paper addresses the problem of speech enhancement and acoustic noise reduction by partial and set-membership adaptive algorithms combined with the symmetric decorrelating adaptive (SAD) algorithm structure. In this paper, we propose two new adaptive algorithms based on set-membership principle that improve the original set-membership algorithm behavior in speech enhancement applications. The first proposed algorithm (called Proposed 1), is based on the combination of the SAD algorithm structure with a smart control that uses decorrelating properties between the output and the mixing signal to control and update the SAD adaptive filters. The second proposed algorithm (called Proposed 2) is a modification of Proposed 1 and based on a new regularization relations of the SAD adaptive filters that use a combination between the variance of the mixing and the output signals of the SAD structures. These two proposed algorithms (Proposed 1 and Proposed 2) aim to improve the convergence speed performance and the output signal-tonoise-ratio of the original SAD algorithm when no smart control of the adaptive filters is used. The proposed algorithms have very interesting properties with non-stationary signal like speech when the SAD algorithm is, used alone, fails. The simulation results that are obtained by the comparison between the proposed algorithms (Proposed 1 and Proposed 2) and the original two-channel set-membership NLMS algorithm have shown the best performances of Proposed 1 and Proposed 2 in terms of the following criteria: systems mismatch, segmental SNR and segmental men square error.

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