Mass Spectrometry

There have been recent advances in different techniques of mass spectrometry. However, in many of these techniques there are common mathematical frameworks: inverse problems. In this work, a few of these inverse problems are presented and an overview of the methods to handle them is given. The Bayesian inference approach is a very useful approach to handle these problems as it give the possibility to account both for prior modeling of the signals and images and for the uncertainly associated to the measurement process. It also gives the necessary tools to estimate the hyper parameters and the remaining uncertainties in the proposed solution. To illustrate this, we take the deconvolution problem which is one of the main inverse problems in mass spectrometry and go through the different regularization and Bayesian inference methods and compare their relative performances.