We introduce the non-negative matrix factor 2-D deconvolution
(NMF2D) model, which decomposes a matrix into a 2-dimensional
convolution of two factor matrices. This model is an extension of
the non-negative matrix factor deconvolution (NMFD) recently
introduced by Smaragdis (2004). We derive and prove
the convergence of two algorithms for NMF2D based on minimizing the
squared error and the Kullback-Leibler divergence respectively.
Next, we introduce a sparse non-negative matrix factor 2-D
deconvolution model that gives easy interpretable decompositions
and devise two algorithms for computing this form of factorization. The
developed algorithms have been used for source separation
and music transcription.
|Publication status||Published - 2006|