Multivariate Curve Resolution (MCR) aims to blindly recover the concentration profile and the source spectra without any prior supervised calibration step. It is well known that imposing additional constraints like positiveness, closure and others may improve the quality of the solution. When a physico-chemical model of the process is known, this can be also introduced constraining even more the solution. In this paper, we apply MCR to Ion Mobility Spectra. Since instrumental models suggest that peaks are of Gaussian shape with a width depending on the instrument resolution, we introduce that each source is characterized by a linear superposition of Gaussian peaks of fixed spread. We also prove that this model is able to fit wider peaks departing from pure Gaussian shape. Instead of introducing a non-linear Gaussian peak fitting, we use a very dense model and rely on a least square solver with L1-norm regularization to obtain a sparse solution. This is accomplished via Least Absolute Shrinkage and Selection Operator (LASSO). Results provide nicely resolved concentration profiles and spectra improving the results of the basic MCR solution.