HOPs: a new tomographic reconstruction algorithm for non destructive acoustic testing of concrete structures

Tomographic reconstruction is a typically ill posed inverse problem, and the computations of solutions are extremely sensitive to data errors, model errors, and rounding errors. Therefore the problem is overdetermined, the solutions are ambiguous, and computational problems are severely ill conditioned. In this paper, a new iterative algorithm has been implemented with the purpose of evaluating the reliability of acous-tic tomography in the characterization and non destructive testing of buildings structures. In particular, the new algorithm performs a direct procedure in order to find a solution that minimizes the mean squared error. Using a well know benchmark for 2D tomography, the performances of the algorithm have been compared with traditional algebraic iterative reconstruction methods for discretizations of inverse problems, such as ART and SIRT. Finally, the iterative algorithm has been applied on a case study considering the tion of the acoustic wave that crosses a selected section of a concrete structure.