Sparse reconstruction of incomplete relative transfer function: Discrete and continuous time domain

Relative transfer functions (RTF) between microphones can often be estimated accurately but only for certain frequencies. For example, this happens in situations where the RTF is estimated from a noise-free signal of a target source whose spectrum does not span the whole frequency range. By combining a conventional RTF estimator and a selection of the active frequencies, an incomplete measurement of the RTF is obtained. We propose to retrieve the whole RTF estimate through finding the sparsest representation of the incomplete measurement in the discrete or continuous time-domain and compare both approaches. The RTF estimates are evaluated in terms of attenuation rate that measures the target signal cancellation at the output of a blocking matrix. It is shown by experiments that the reconstructed estimate can achieve significantly better attenuation than the initial (complete) estimate.