Ultrasound breast tomography has been around for more than 40 years. Early approaches to reconstruction focused on simple algebraic reconstructions and bent ray techniques. These approaches were not able to provide high-quality and high spatial-resolution images. The advent of inverse scattering approaches resulted in a shift in image reconstruction approaches for breast tomography and a subsequent improvement in image quality. Full wave inverse solvers were developed to improve the reconstruction times without sacrificing image quality. The development of GPUs has markedly decreased the time for reconstruction using inverse scatting approaches. The development of fully 3D image solvers and hardware capable of capturing out of plane scattering have resulted in further improvement in breast tomography. This chapter discusses the state-of-the-art in ultrasound breast tomography, its history, the theory behind inverse scattering, approximations that are included to improve convergence, 3D image reconstruction, and hardware implementation of the constructions.
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