Measures and algorithms for best basis selection

A general framework based on majorization, Schur-concavity, and concavity is given that facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed diversity measures useful for best basis selection. Admissible sparsity measures are given by the Schur-concave functions, which are the class of functions consistent with the partial ordering on vectors known as majorization. Concave functions form an important subclass of the Schur-concave functions which attain their minima at sparse solutions to the basis selection problem. Based on a particular functional factorization of the gradient, we give a general affine scaling optimization algorithm that converges to a sparse solution for measures chosen from within this subclass.