IEEE Transactions on Signal Processing
Underdetermined blind source separation based on relaxed sparsity condition of sources
IEEE Transactions on Signal Processing
Underdetermined blind separation of non-sparse sources using spatial time-frequency distributions
Digital Signal Processing
A new blind method for separating M+1 sources from M mixtures
Computers & Mathematics with Applications
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This paper concerns underdetermined linear instantaneous and convolutive blind source separation (BSS), i.e., the case when the number of observed mixed signals is lower than the number of sources. We propose partial BSS methods, which separate supposedly nonstationary sources of interest (while keeping residual components for the other, supposedly stationary, ldquonoiserdquo sources). These methods are based on the general differential BSS concept that we introduced before. In the instantaneous case, the approach proposed in this paper consists of a differential extension of the FastICA method (which does not apply to underdetermined mixtures). In the convolutive case, we extend our recent time-domain fast fixed-point C-FICA algorithm to underdetermined mixtures. Both proposed approaches thus keep the attractive features of the FastICA and C-FICA methods. Our approaches are based on differential sphering processes, followed by the optimization of the differential nonnormalized kurtosis that we introduce in this paper. Experimental tests show that these differential algorithms are much more robust to noise sources than the standard FastICA and C-FICA algorithms.