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There are very few techniques that can separate signals from the convolutive mixture in the underdetermined case. We have developed a method that uses overcomplete expansion of the signal created with a time-frequency transform and that also uses the property of sparseness and a Laplacian source density model to obtain the source signals from the instantaneously mixed signals in the underdetermined case. This technique has been extended here to separate signals (a) in the case of underdetermined convolutive mixtures, and (b) in the general case of more than 2 mixtures. Here, we also propose a geometric constrained based search approach to significantly reduce the computational time of our original "dual update" algorithm. Several examples are provided. The results of signal separation from the convolutive mixtures indicate that an average signal to noise ratio improvement of 5.3 dB can be obtained.