Noise Cancellation with Static Mixtures of a Nonstationary Signal and Stationary Noise
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Noise Cancellation with Static Mixtures of a Nonstationary Signal and Stationary Noise Sharon Gannot Electrical Engineering Faculty, Technion, Technion City, Haifa 32000, Israel Email: [email protected]
Arie Yeredor Department of Electrical Engineering-Systems, Tel Aviv University, P.O. Box 39040, Tel Aviv 69978, Israel Email: [email protected] Received 27 January 2002 and in revised form 18 June 2002 We address the problem of cancelling a stationary noise component from its static mixtures with a nonstationary signal of interest. Two different approaches, both based on second-order statistics, are considered. The first is the blind source separation (BSS) approach which aims at estimating the mixing parameters via approximate joint diagonalization of estimated correlation matrices. Proper exploitation of the nonstationary nature of the desired signal, in contrast to the stationarity of the noise, allows the parameterization of the joint diagonalization problem in terms of a nonlinear weighted least squares (WLS) problem. The second approach is a denoising approach, which translates into direct estimation of just one of the mixing coefficients via solution of a linear WLS problem, followed by the use of this coefficient to create a noise-only signal to be properly eliminated from the mixture. Under certain assumptions, the BSS approach is asymptotically optimal, yet computationally more intense, since it involves an iterative nonlinear WLS solution, whereas the second approach only requires a closed-form linear WLS solution. We analyze and compare the performance of the two approaches and provide some simulation results which confirm our analysis. Comparison to other methods is also provided. Keywords and phrases: blind source separation, denoising, stationarity, nonstationarity, static mixture.
1.
INTRODUCTION
In many applications in signal processing and communications, a desired signal is contaminated by some unknown, statistically independent, noise signal. Multisensor arrays are often used for the purpose of separating, or denoising, the desired signal. Each sensor receives a linear combination of the desired signal and noise so that, by properly combining the received signals, enhancement of the desired signal is possible. This problem can be regarded either as a denoising or as a blind source separation (BSS) problem. The difference between these two approaches lies within the treatment of the noise signal: while the former regards the noise merely as a disturbance, the latter regards it as another source signal to be separated from the desired one. A major practical difference between the two approaches to this problem lies in their computational complexity: while the BSS approach involves approximate joint diagonalization, which amounts to the solution of a nonlinear weighted
least squares (WLS) problem, the denoising approach only requires the solution of a linear WLS problem. It is therefore interesting to compare the performance of the two approaches in order to gauge the benefit of using the co
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