Multidimensional inverse problems in ultrasonic imaging

Abstract

This chapter describes the reconstruction of reflectivity profiles from ultrasonic back-scattered echoes as an inverse problem involving incomplete and noisy measurements. Given pulse-echo measurements from a synthetically created one-dimensional or two-dimensional array of sensors, the chapter highlights that the maximum likelihood estimate of the reflectivity profile requires the pseudoinverse of the array point spread function (PSF). As a consequence of the physical properties, the point spread function is shown to be highly structured block Toeplitz linear operator and is a function of the sensor and array characteristics. The chapter reviews the literature in the field of ultrasonic dig..