Some regularization methods for a thermoacoustic inverse problem

In this paper we consider the thermoacoustic inverse problem of identifying the oscillatory heat release from pressure measurements. We consider the spatially one-dimensional and time harmonic case. Three different regularization methods for the stable solution of this ill-posed inverse problem are proposed: Lavrent'ev's method, regularization by discretization, and a method based on an explicit formula combined with regularized numerical differentiation. For these methods, the results of numerical experiments are documented.