Subspace constrained regularization for corrosion detection with magnetic induction tomography

This work addresses the problem of detecting the corrosion in reinforced concrete columns through magnetic induction tomography. Aside the inherent ill-posedness of the associated image reconstruction problem, the particular task presents two other challenges. Accounting for the available prior information the resulted posterior probability density of the solution is shown to be binomial and thus renders deterministic approaches based on point estimators problematic. Moreover, the realistically large dimension of the model space makes statistical methods computationally inefficient, often requiring huge numbers of samples in order to achieve a reasonable solution. The proposed approach exploits the domain's nominal electrical conductivity profile and some electrochemical properties of corrosion by implementing a statistical sampling method to compute the integral of the posterior density projected on a lower dimensional subspace, making the inverse problem computationally tractable. The basis spanning the projection subspace is constructed by taking assumptions on the plausible level sets of the corroded material within the domain. Some numerical results are presented to demonstrate the performance of the algorithm for the particular application, as well as its limitations in reconstructing domain inhomogeneities irrelevant to the corrosion phenomenon.