On the possibility of using the maximum entropy method in ultrasonic nondestructive testing for scatterer visualization from a set of echo signals

We have studied the possibility of solving the inverse scattering problem in the Born approximation, i.e., the reconstruction of scatterer images from the measured set of echo signals. We have considered generalization of the classical combined SAFT (C-SAFT) algorithm to the case of multiple reflections from uneven boundaries of the tested object taking into account the transformation of the wave type for several positions of the antenna grid, which makes it possible to obtain high-quality scatterer images. Representation of the direct problem in matrix form makes it possible to switch to solving the inverse problem, which can be solved using the Tikhonov regularization procedure, because it is an ill-posed. We have considered the possibility of using the entropy of the image estimate as the stabilizing functional that forms the essence of the maximum entropy method (MEM). The advantage of the MEM over the conventionally used linear C-SAFT method has been shown. The ray model taking into account reflections of rays from the boundaries of the tested object with uneven boundaries has been used for constructing the function estimate. We have demonstrated the ability of the MEM to obtain the scatterer images with superresolution and to suppress the “side lobes” of the function of the point scattering on the collapsed set of echo signals. The use of echo signals reflected from the boundaries of the tested object makes it possible to reconstruct the scatterer shape more exactly. Examples of images reconstructed by the MEM on echo signals obtained in the numerical and model experiments have been presented.