Methods and apparatuses are disclosed that model the lineshapes of mass
spectrometry data. Ions can be modeled with an initial distribution that
models molecules as having multiple positions and/or energies prior to
traveling in the mass spectrometer. These initial distributions can be
pushed forward by time of flight functions. Fitting can be performed
between the modeled lineshapes and empirical data. Filtering can greatly
reduce dimensions of the empirical data, remove noise, compress the data,
recover lost and/or damaged data.