Reconstruction of spatially varying sound speed distributions from pulse-echo data

Traditional ultrasonic brightness mode (B-Mode) images are plagued by poor image quality due to the limited observational coverage. This has motivated research in alternative imaging modes, such as tomographic reconstruction of sound speed distributions. Historically, sound speed tomography has typically been performed in transmission-mode, which requires specialized hardware configurations and is limited to acoustically transparent tissue such as the female breast. For this reason, integration of sound speed tomography in medical settings has been slow. Recent results from Jaeger et al. (2015) have demonstrated that sound speed tomography can be performed in pulse-echo mode by exploiting cross-correlations of post-beamformed data acquired from multiple steered plane wave excitations. Unlike traditional sound speed tomography setups, pulse-echo sound speed tomography only requires a single linear array transducer, which is commonly available in a clinical setting. While the evidence presented in Jaeger et al. (2015) is exciting, the theoretical analysis in that result was lacking. In particular, no attempt was given to characterize the spatial Fourier coverage of the underlying correlation measurements. Furthermore, Jaeger's simulation results were not realistic, as they neglected heterogeneous distortions to the point spread functions due to refraction. In this work, we attempt to address these oversights. This thesis is organized as follows. To begin, the fundamentals of pulse echo sound speed tomography are reviewed. Second, the underlying model is reformulated as a convolutional model. Using this convolutional model, the spatial Fourier coverage of pulse-echo sound speed tomography is derived and shown to be complementary to that of standard B-Mode and diffraction tomography. Finally a simulation study is conducted utilizing the simulation package k-Wave~to evaluate the degeneration due to refraction