Image quality improvement in ultrasonic nondestructive testing by the maximum entropy method

We consider the possibility of solving the inverse scattering problem in the linear approximation (in the form of a convolution equation) by reducing it to a system of linear algebraic equations and minimizing the residual. Since the problem is an ill-posed one, the Tikhonov regularization proves useful. The possibility of using the entropy of the image estimate as a stabilizing functional is considered, which is the key idea of the maximum entropy method. The single-frequency and multifrequency versions of the method are realized. The advantage of the maximum entropy method over the conventional linear methods of solving the inverse scattering problem is shown. The superresolution and sidelobe suppression abilities of the maximum entropy method are demonstrated. The method is shown to be stable to measurement noise and multiplicative interference in the form of aperture decimation. Examples of the image reconstruction by the maximum entropy method from model and experimental data are presented.