This papers focuses on underdetermined Independent Component
  Analysis, that is, the separation of N sources from M linear
  mixtures when M<N. Sparsity is achieved by exploiting the 
  near Laplacian distribution of music and speech signals 
  in the short-time Fourier domain.
  Given the mixing matrix, a most sparse
  representation of the sources is obtained by solving a
  low-dimensional linear programming (LP) problem for each of 
  the data points independently. For M=2 we propose 
  a shortest path, closed-form solution to this LP 
  problem that represents each data
  point as a linear combination of the pair of directions 
  that enclose it. The mixing matrix can be estimated either by maximizing a
  likelihood function, using the above LP optimitazion at the internal
  step, or with a clustering algorithm that can give a much
  faster solution. In this work, for M=2, we use a clustering algorithm,
  based on a triangular potential function,
  that infers both the the mixing matrix and the number of sources.

  Several experiments are described involving music and speech
  signals, including the separation of up to six sources from two
  mixtures.