Underdetermined speech separation is a challenging problem that has been studied extensively in recent years. A promising method to this problem is based on the so-called sparse signal representation. Using this technique, we have recently developed a multi-stage algorithm, where the source signals are recovered using a pre-defined dictionary obtained by e.g. the discrete cosine transform (DCT). In this paper, instead of using the pre-defined dictionary, we present three methods for learning adaptive dictionaries for the reconstruction of source signals, and compare their performance with several state-of-the-art speech separation methods.