A Bayesian approach for nonlinear inverse scattering tomographic imaging

The authors propose a new method to solve the nonlinear inverse problem of tomographic imaging using microwave or ultrasound probing, beyond the classical first order Born or Rytov approximations. The relation between the data and the measurement is given by two coupled nonlinear equations. The authors set this problem as one of estimation and propose a solution within the Bayesian probability framework. The maximum a posteriori estimate determination leads to a multi-modal criterion minimisation. Global minimisation using simulated annealing is not practicable due to the high calculation cost. The authors propose a feasible deterministic relaxation algorithm inspired by the graduated nonconvexity principle to perform this minimisation