Non-negative matrix completion for bandwidth extension: A convex optimization approach

Bandwidth extension is the problem of recovering missing bandwidth in audio signals that have been band-passed, typically for compression purposes. One approach that has been shown to be successful for bandwidth extension is non-negative matrix factorization (NMF). The disadvantage of NMF is that it is non-convex and intractable to solve in general. However, in bandwidth extension, only the reconstruction is needed and not the explicit factors. We formulate bandwidth extension as a convex optimization problem, propose a simple algorithm, and demonstrate the effectiveness of this approach on practical examples.