Signal processing applied to ultrasonic imaging

This paper describes a noncoherent ultrasonic array used to form three-dimensional images of defects in metal. The problem developed in terms of deconvolution in multiple dimensions to improve resolution of images blurred by the measuring system and degraded by noise is reduced to solution of a linear equation of the form y=Hx, where H is called the imaging operator H may be separated into the Kronecker product of smaller banded-Toeplitz matrices V⊗S⊗P. This structure is used to develop an algorithm to solve for X using least squares and singular value decomposition