A local model of relative transfer functions involving sparsity

Abstract

We propose a model of Relative Transfer Functions between two microphones which correspond to closed target positions within a certain spatially constrained area. Each RTF is modeled as the product of two transfer functions. One corresponds to a linear-phase filter and is the common factor of all the RTFs. The second transfer function is an individual factor that should be as sparse as possible in the time domain. A learning algorithm to identify the decomposition given a set of RTFs is proposed. The common factor is the main output, which we then apply to reconstruct an unknown RTF corresponding to a position within the assumed area, when only an incomplete measurement of it is available.