Simulation and experimental investigation for regularization methods used in the statistically optimal near-field acoustical holography

The reconstruction of the sound field provided by the statistically optimal near-field acoustical holography (SONAH) from pressure measurements fulfilled near a sound source is an ill-posed inverse problem because of the existence of the noise signals. This paper presented two regularization methods to solve this problem in SONAH: the standard Tikhonov procedure accompanied with two parameter selection procedures, the Morozov's discrepancy principle and the Engl's criterion, which were crucial to the regularization. SONAH method performed the plane to plane calculations directly in the spatial domain, and the equations can be reformulated into an eigenvalue problem. The resulting eigenvalues and eigenvectors matched easily to regularization theory. Numeral examples and experiments show that both methods are useful for yielding a robust solution to the source field.