Imaging from Echoes: On Inverse Problems in Ultrasound

Ultrasound (US) imaging is currently living a revolution. On the one hand, ultrafast US imaging, a novel way of acquiring and producing US images, has paved the way to several advanced imaging modes, e.g. shear-wave elastography, ultrafast Doppler imaging and ultrafast contrast imaging. On the other hand, the mass adoption of mobile commodity devices pushes towards portable US imaging. These new paradigms require to rethink the imaging pipeline and come with a myriad of new challenges in terms of data rate, power considerations as well as software and hardware design. In this thesis, we explore several inverse problems related to these challenges, with an emphasis on data-rate reduction for imaging and localization. We follow the view of considering pulse-echo US imaging as a tomographic image reconstruction problem where sensor measurements can be seen as projections onto quadric surfaces. By appropriate parameterization of these surfaces, we devise efficient formulations of the measurement model associated with the image reconstruction problem and pave the way to large scale regularized US imaging. We introduce USSR, an UltraSound Sparse Regularization framework, which exploits the measurement model in the context of convex optimization algorithms. We describe three applications, namely sparsely regularized beamforming where high-quality images are obtained with few insonifications, compressed beamforming which aims to decrease the amount of data collected per insonification, and image restoration which exploits a model of non-stationary blur to enhance already reconstructed images. We suggest a compressive multiplexing approach for US signals. Such a technique achieves high-quality imaging with significantly fewer coaxial cables connecting the probe to the imaging system than existing methods. The compression is based on the compressive multiplexer, an analog compressed-sensing architecture, and the reconstruction relies on convex optimization algorithms. We propose two methods which exploit different low-dimensional models of US signals, namely the bandpass signal model and the pulse-stream model. We tackle the problem of localizing strong reflectors, with potential application in non-destructive evaluation and contrast-enhanced US imaging. We suggest a threefold approach composed of a time-of-flight (TOF)-sensing step, a TOF-labeling step and a localization step, which is capable of recovering the locations of strong reflectors with significantly fewer transducer elements and less sensor measurements than existing techniques. By exploring innovative methods for imaging and localization, this work contributes to a next generation of US imaging devices which will benefit from ultrafast US imaging to integrate advanced imaging modes into more and more compact systems.