A new blind method for separating M+1M+1 sources from MM mixtures

In this paper, we consider the problem of underdetermined blind source separation (UBSS), i.e., there are more sources than mixtures. By exploiting the time–frequency (TF) sparsity of the source signals, some TF–UBSS algorithms have recently been proposed in the literature. These algorithms require that the number of active sources at any TF point should not exceed one or be strictly less than the number of mixtures. In this paper, we show that if the number of sources is greater than the number of mixtures by one, the sparsity assumption can be further relaxed. Especially, it is allowed to have as many sources as mixtures at any TF point in this case. Then we propose a new TF–UBSS method to recover the sources. The relaxation on the maximum number of active sources at TF points ensures that the TF-based methods can be used in a wider range of applications.