Sparse approximation of ion-mobility spectrometry profiles by binomial splines

Employing discrete binomial splines instead of the Gaussian distributions, we construct and test an algorithm for analyzing ion-mobility spectrometry profiles. Following the standard framework of sparse approximation, we compose the dictionary of atoms given by shifted binomial splines of different orders, and we incrementally pick up, by means of the orthogonal matching pursuit, atoms for their linear combination to approximate a given profile. The only non-standard attribute is that both profile and atoms are non-negative and consequently that the coefficients should also be non-negative. That forces us to introduce a different criterion of sparseness other than the usual absolute sum of the coefficients. Through numerical simulations for randomly synthesized profiles corrupted with white noises of different levels, we find an optimal value of the weight for blending fitness (less approximation errors) and sparseness (fewer major coefficients) to choose a best sparse approximation. Application to several real profiles is presented.