Sparse signal representation based algorithms with application to ultrasonic array imaging

Abstract

We address one- and two-layer ultrasonic array imaging. We use an array of transducers to inspect the internal structure of a given specimen. In the case of one-layer imaging we also address the problem of mode conversion. We propose a sparse signal representation based method for imaging solid materials in the presence of mode conversion phenomenon. In the case of two-layer imaging we model the signal propagation effect using Huygens principle and Rayleigh-Sommerfeld diffraction formula. We then use this model to develop a sparse signal representation based imaging technique for a test sample immersed in water. Moreover, we develop a new sparse Bayesian technique. In the model that we develop, the reflectivity coefficients of the desired reflectors are nonnegative real numbers and sparse in nature. Therefore, we use Weibull distribution function with two hyperparameters, namely the shape parameter and the scaling parameter, to model the prior distribution function of the reflectivity coefficients of the reflectors. As we show, the Weibull distribution, whose scale parameter obeys the inverse Gamma distribution, will enforce sparsity. We then propose a method for estimating the shape parameter of the Weibull distribution using Mellin transform.