Time-domain Reconstruction Methods for Ultrasonic Array Imaging : A Statistical Approach

Abstract: This thesis is concerned with reconstruction techniques for ultrasonic array imaging based on a statistical approach. The reconstruction problem is posed as the estimation of an image consisting of scattering strengths. To solve the estimation problem, a time-domain spatially-variant model of the imaging system is developed based on the spatial impulse response method. The image reconstruction is formulated as a linearized inverse-scattering problem in which the time and space discrete natures of the imaging setup as well as measurement uncertainties are taken into account. The uncertainties are modeled in terms of a Gaussian distribution. The scattering strengths are estimated using two prior probability density functions (PDF’s), Gaussian and exponential PDF’s. For the Gaussian PDF, the maximum a posteriori (MAP) approach results in an analytical solution in the form of a linear spatio-temporal filter which deconvolves the diffraction distortion due to the finite-sized transducer. The exponential distribution leads to a positivity constrained quadratic programming (PCQP) problem that is solved using efficient optimization algorithms. In contrast to traditional beamforming methods (based on delay-and-summation), the reconstruction approach proposed here accounts both for diffraction effects and for the transducer’s electro-mechanical characteristics. The simulation and experimental results presented show that the performances of the linear MAP and nonlinear PCQP estimators are superior to classical beamforming in terms of resolution and sidelobe level, and that the proposed methods can effectively reduce spatial aliasing errors present in the conventional beamforming methods.