Ultrasonic B-Scan Imaging: Theory of Image Formation and a Technique for Restoration

This paper presents a theory for ultrasonic B-scan image formation. Our theory is based on the assumption that imaging is done using broadband signals and that all the information in the returned echos is utilized for image formation, as opposed to only the video detected envelopes. We also assume that the image is formed from the backscattered returns caused by inhomogeneities within soft tissue structures. In other words, we do not take into account the contributions from the specularly reflecting surfaces that represent large impedance discontinuities. (Surfaces that only represent small impedance changes and are visible to the transducer are accounted for by our theory.) Our main reason for this omission is the fact that although the contributions of the surfaces with large impedance changes are important to the delineation of features in some 3-scan images, it is the presentation of the backscattered echos from small inhomogeneities within the tissues that is more severely distorted by the radiation and the electromechanical properties of the transducer. Also, it is currently believed that the backscattered echoes from the small inhomogeneities within the tissues carry important pathological information. Our theory is also limited to the case of Linearly scanned transducers with unfocused apertures. A major result of our theory is an analytical expression for the point spread function of the image degradation. As expected, this function is position variant. To simplify the computations required for image restoration, we have presented approximations that reduce the point spread function to the position-invariant form. We have shown experimentally that the resulting restoration filters retain their effectiveness over several centimeters of the object thickness. This has led us to conclude that the B-scan images of thick objects may be restored by using piecewise position-invariant techniques.