Sparse Approximation of Ion-Mobility Spectrometry Profiles by Minutely Shifted Discrete B-splines

Employing discrete B-splines instead of the Gaussian distribution, we construct an algorithm for the analysis of ionmobility spectrometry profiles. The algorithm is suitable for hardware implementation because the discrete B-splines are supported by a simple digital filter to compute their weighted sum and their correlations with a given signal. Minutely shifted discrete B-splines are deployed of which weighted sum is to approximate a given profile with non-negative weights. Closely neighboring discrete B-splines are almost linearly dependent so that they may cause numerical instability in the approximation process. But numerical experiments deny this anxiety at least for the final results. Varying the width of discrete B-splines, we obtain a number of different approximations. Out of sufficiently precise approximations, we choose the sparse one in the sense that it comprises few discrete B-splines with large weights.