@TECHREPORT\{IMM2006-04116,
    author       = "M. M{\o}rup and M. N. Schmidt",
    title        = "Sparse Non-negative Matrix Factor {2-D} Deconvolution",
    year         = "2006",
    number       = "",
    series       = "",
    institution  = "Technical University of Denmark",
    address      = "",
    type         = "",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/4116-full.html",
    abstract     = "Se instead {''}Shift Invariant Sparse Coding for Image and Music Data{''} 

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."
}