It-Based Filter for a Sequential Monte Carlo Inversion Strategy

Abstract

In this article, we propose and develop an information-theoretic filter for a three-step Sequential Monte Carlo(SMC) inversion procedure. The last stage in this procedure corresponds to a filter, which selects/rejects samplesaccording to a noise level, only known approximately up to a certain order of magnitude. Therefore, we have designedan information-theoretic (IT)-based filter which selects this noise level instead of choosing an approximate but stillarbitrary value for it. A cut-off level is calculated using an optimization scheme based on the principle of relevantinformation (PRI). The PRI has been used to balance the minimization of the entropy of the prior PDF with thediscrepancy between the original data and the solution found by the SMC procedure. Finally, we briefly analyze theperformance of the filter for the computation of both solution and approximate noise level in simulated cases of anapplication inverse problem.