A phase and space coherent direct imaging method.

A direct imaging algorithm for point and extended targets is presented. The algorithm is based on a physical factorization of the response matrix of a transducer array. The factorization is used to transform a passive target problem to an active source problem and to extract principal components (tones) in a phase consistent way. The multitone imaging function can superpose multiple tones (spatial diversity/aperture of the array) and frequencies (bandwidth of the probing signal) based on phase coherence. The method is a direct imaging algorithm that is simple and efficient since no forward solver or iteration is needed. Robustness of the algorithm with respect to noise is demonstrated via numerical examples.