1 Cognitive Systems, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark
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.