Sparse Nonnegative Matrix Factor 2D Deconvolution 
Morten Mørup, Mikkel N. Schmidt

Abstract  Se instead "Shift Invariant Sparse Coding for Image and Music Data"
We introduce the nonnegative matrix factor 2D deconvolution
(NMF2D) model, which decomposes a matrix into a 2dimensional
convolution of two factor matrices. This model is an extension of
the nonnegative 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 KullbackLeibler divergence respectively.
Next, we introduce a sparse nonnegative matrix factor 2D
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. 
Type  Technical report 
Journal/Book/Conference  Technical Report 
Year  2006 
Publisher  Technical University of Denmark 
Electronic version(s)  [pdf] 
BibTeX data  [bibtex] 
IMM Group(s)  Intelligent Signal Processing 