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 |
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