Regularized Least Squares Imaging for High Resolution Ultrasound

Abstract

Traditional imaging techniques in medical ultrasound are mostly based on pre-defined geometrical processing of the measurement data. In this thesis however, we focus on finding the image that would best explain the observed measurement in a least squares sense, given an ultrasound model. This enables the use of prior knowledge such as transducer impulse responses and acoustic wave field theory to be fully taken into account, resulting in a spatio-temporal imaging technique. Since performance is dependent on modeling accuracy, this thesis investigates the formulation and verification of a linear ultrasound model that also takes the transducer lens into account. Additionally, a technique to easily estimate the transducer impulse response is proposed. After defining the linear model, several techniques that solve this linear system for the image are considered, namely Tikhonov regularized least squares, Tikhonov regularized non-negative least squares, basis pursuit de-noising. Using a synthetic aperture transmission scheme, these techniques are compared to delay-and-sum beamforming in both a simulation based resolution analysis, as well as in a real experiment using a high-resolution phantom in water. Results show that the proposed imaging techniques perform significantly better than conventional delay-and-sum beamforming.