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This paper addresses the problem of speech separation and enhancement frommultichannel convolutive and noisy mixtures, \emph{assuming known mixingfilters}. We propose to perform the speech separation and enhancement task inthe short-time Fourier transform domain, using the convolutive transferfunction (CTF) approximation. Compared to time-domain filters, CTF has muchless taps, consequently it has less near-common zeros among channels and lesscomputational complexity. The work proposes three speech-source recoverymethods, namely: i) the multichannel inverse filtering method, i.e. themultiple input/output inverse theorem (MINT), is exploited in the CTF domain,and for the multi-source case, ii) a beamforming-like multichannel inversefiltering method applying single source MINT and using power minimization,which is suitable whenever the source CTFs are not all known, and iii) aconstrained Lasso method, where the sources are recovered by minimizing the$\ell_1$-norm to impose their spectral sparsity, with the constraint that the$\ell_2$-norm fitting cost, between the microphone signals and the mixing modelinvolving the unknown source signals, is less than a tolerance. The noise canbe reduced by setting a tolerance onto the noise power. Experiments undervarious acoustic conditions are carried out to evaluate the three proposedmethods. The comparison between them as well as with the baseline methods ispresented.

Multichannel Speech Separation and Enhancement Using the Convolutive Transfer Function