Regularization, Maximum Entropy and Probabilistic Methods in Mass Spectrometry Data Processing Problems

This paper is a synthetic overview of regularization, maximum entropy and probabilistic methods for some inverse problems such as deconvolution and Fourier synthesis problems which arise in mass spectrometry. First we present a unified description of such problems and discuss the reasons why simple naı̈ve methods cannot give satisfactory results. Then we briefly present the main classical deterministic regularization methods, maximum entropy-based methods and the probabilistic Bayesian estimation framework for such problems. The main idea is to show how all these different frameworks converge to the optimization of a compound criterion with a data adequation part and an a priori part. We will however see that the Bayesian inference framework gives naturally more tools for inferring the uncertainty of the computed solutions, for the estimation of the hyperparameters or for handling the myopic or blind inversion problems. Finally, based on Bayesian inference, we present a few advanced methods particularly designed for some mass spectrometry data processing problems. Some simulation results illustrate mainly the effect of the prior laws or equivalently the regularization functionals on the results one can obtain in typical deconvolution or Fourier synthesis problems arising in different mass spectrometry technique.