Physics based sparsity level determination for acoustic scattered far-field prediction.

Sparse reconstruction using the equivalent source method has shown promise in acoustic field prediction from near-field measurements. The sparsity level of the representation coefficients needs to be known or estimated. In this letter, for scattered far-field prediction, the lower bound of sparsity level is derived from the effective rank of the far-field transfer matrix and used as a pre-set hyperparameter for orthogonal matching pursuit. The minimum number of measurements is then determined under the compressed sensing theory. Simulated and tank data show the effectiveness of this approach, which combines physical propagation and compressed sensing and is easy to implement.