Comparison of Methods for Sparse Representation of Musical Signals

Within the last few decades a number of new signal processing tools has appeared. These have mainly been compared using constructed signals, signals designed to show the advantage of a new method over already existing methods. In this paper we evaluate the methods Basis Pursuit, Minimum Fuel Neural Networks, Matching Pursuit, Best Orthogonal Basis, Alternating Projections and Methods of Frames on “real” signals. The methods are applied on a number of excerpts sampled from a small collection of music, and their ability to expresmusic signals in a sparse manner is evaluated. The sparseness is measured by a number of sparseness measures and results are shown on the ℓ1 norm of the coefficients, using a dictionary containing a Dirac basis, a Discrete Cosine Transform, and a Wavelet Packet. Evaluated only on the sparseness Matching Pursuit is the best method, and it is also relatively fast.