Online Bayesian estimation for solving electromagetic NDE inverse problems

Flaw profile estimation from measurements is a typical inverse problem in electromagnetic nondestructive evaluation (NDE). This paper proposes a novel state-space approach to combat the ill-posedness in the solution to the inverse problem, particularly in the presence of measurement noise. The inversion approach formulates the inverse problem as a tracking problem with state and measurement equations. This state-space model resembles the classical discrete-time tracking problem, and enables the application of Bayesian non-linear filters based on sequential Monte Carlo methods in conjunction with numerical models that represent the measurement process (i.e. solution of forward problem). The proposed approach is applied to simulated NDE measurements from known flaw shapes. Functional models of the NDE inspection process are used as the measurement model and a probabilistic state transition model is defined for the proposed technique. Initial results of applying the proposed approach to eddy current NDE inverse problems indicate the feasibility of the proposed method.