Comparison of methods for sparse representation of musical signals

Within the last few decades, several new signal processing tools have appeared. These have mainly been compared using constructed signals, signals designed to show the advantage of a new method over already existing methods. We evaluate the following methods on "real" signals: basis pursuit; minimum fuel neural networks; matching pursuit; best orthogonal basis; alternating projections; methods of frames. The methods are applied on a number of excerpts sampled from a small collection of music, and their ability to express music signals in a sparse manner is evaluated. The sparseness is measured by a number of sparseness measures and results are shown on the ℓ ¹ norm of the coefficients, using a dictionary containing a Dirac basis, a discrete cosine transform, and a wavelet packet. Evaluated only on sparseness, matching pursuit is the best method, and it is also relatively fast.