Resumen de Non-negative matrix descompostion for single-cannel source separation in biomedical signal processing applications
Source separation in digital signal processing consists of finding best estimates of the signals involved in a signal mixture. Although, in most cases a detailed information about the sources is not known in advance, a partial separation is still possible. One of possible methods is non negative matrix factorization NMF. In spite of its increasing popularity in the biomedical signal processing community, a little attention is paid to its serious drawbacks which often make impossible the straightforward use of the available “off-shelf” algorithm.
One of them is a random initialization of an algorithm what often leads to a local minimum and irreproducible results. The selection of the non-negative rank of individual sources is often misleading. A usual shortcut to this problem is to assign rank according to the number of sources and then to tune it up by some iterative trial and error input matrix decomposition procedure. Such an approach is computationally costly and is not guaranteed to converge to optimal rank for each source. Moreover, a synthesis of time-domain waveforms from the low rank source descriptions is often hard, due to the fact that the original phases are unknown.
In the present thesis we address the aforementioned drawbacks and introduce new algorithm features, namely: unambiguous non-negative rank estimation and initialization with carefully designed structures. All proposed methods have been compared to at least two-state-of art reference methods.
