Quantitative imaging complements structural imaging by providing quantitative estimations
of subsurface material properties as opposed to the sizes, shapes and
positions of scatterers available from structural methods. The ability to reconstruct
material properties from a series of wave measurements is extremely valuable in
a range of applications as it potentially allows diagnostic technology with superior
sensitivity and selectivity. Breast cancer, for example, is stiffer and hence of
higher sound velocity than the surrounding tissue, so reconstructing velocity from
ultrasonic measurements could allow cancer detection. Using this concept, breast ultrasound
tomography has the potential to significantly improve the cost, safety and
reliability of breast cancer screening and diagnosis over mammography, the gold-standard.
Key to unlocking this potential is the availability of an accurate, fast,
robust and high-resolution algorithm to reconstruct wave velocity. This thesis introduces
HARBUT, the Hybrid Algorithm for Robust Breast Ultrasound Tomography,
a new imaging approach combining the complementary strengths of low resolution
bent-ray tomography and high resolution diffraction tomography. HARBUT's theoretical
foundation is explained and applied to simulated and experimental, in-vivo,
breast ultrasound tomography data, confirming that it generates a step change in
image quality over existing techniques, revealing lesions that would not be visible on
a mammogram. This thesis also shows how, by combining data from many slices, the
out-of-plane resolution can be significantly improved compared to treating each slice
independently. HARBUT is applied to alternative problems including guided wave
tomography, which aims to quantify the remaining wall thickness of a potentially
corroded, inaccessible plate-like structure. Thickness estimates within 1mm for a
10mm nominal thickness plate were demonstrated for both simulated and experimental
data. The thesis finally investigates HARBUT's performance with limited
view configurations, and introduces VISCIT, the Virtual Image Space Component
Iterative Technique, which accounts for the missing data, significantly improving
the reconstructed image.