A simple overcomplete ICA algorithm by non-orthogonal pair optimizations

Overcomplete ICA is a method for solving blind source separation problems if the number of observed signals is less than that of source ones. In this paper, we propose an overcomplete ICA algorithm based on a simple contrast function which is defined as the sum of the covariances of the squares of signals over all the pairs. By applying non-orthogonal pair optimizations to the function, a simple ICA algorithm is derived. Theoretical analysis and numerical experiments suggest the validity of the proposed algorithm.