The Signal Projection Method: A General Approach to Active Imaging With Arrays

Using a generic model of how active array imaging systems operate, a formal definition of the image as a projection of the reflected wave field onto the wave field emitted to probe the medium is proposed. This definition is applied to the case of imaging in homogeneous and isotropic media to which, by using the frequency-domain solution of the wave equation, the relationship between the calculated image, the emitted and received signals, the positions of the transducers, the speed of the waves used, and the reflectivity of the medium is shown at each point. Then, a general algorithm for the formation of images of a region in this kind of media is derived. Finally, using real and simulated ultrasound signals, images obtained with the proposed signal projection method are compared with those produced by the “de facto” standard delay and sum-based algorithms.