This Ph.D. work was carried out at the Biomedical ultrasound lab, Indian Institute of Technology-Game, India. The overall objective of the thesis is to develop a Compressed Sensing (CS)-based framework to reduce the number of active elements in Conventional Focused Beamforming (CFB) or Multi-element Synthetic Transmit Aperture (MSTA) based ultrasound imaging systems. The hypothesis is that it is possible to reduce the active channel count in CFB and MSTA based ultrasound system, without much compromise on the image quality, by exploiting strategic lateral under-sampling in CS approach.

Over the last decade, CS has gained much exposure and appreciation from the signal processing community. This inverse problem technique makes severe down-sampling of the signal possible. The recovery of the missing information is accomplished using convex optimization. This CS framework has already been studied to reduce data and to improve the frame rate of the ultrasound system. However, there is no prior work reported, which can reduce the active channel count using CS.

The first goal of the thesis was to investigate and develop a CS framework that is appropriate for CFB imaging. The work involves strategic design and development of novel lateral under-sampling based on Gaussian distribution to accomplish a reduction in active elements count using CS in CFB without trading off with the resulting image quality. The performance of the proposed framework was analyzed for simulation, experiment, and in-vivo data. It was found that despite reducing the number of receive elements by 75% and overall removing 90% of the data, CS using the Gaussian sampling scheme was able to recover images of comparable quality to that of full aperture data.

The next goal of the thesis was to investigate the adaptation of the CS framework developed for CFB imaging to the MSTA imaging method. In this study, the previously proposed Gaussian sampling scheme is modified to suit the MSTA imaging method. Despite reducing the number of receive elements by 50% and overall removal of 75 % of the data, the CS framework was able to recover images of comparable quality to that of the full aperture data.

The last part of the research investigates the performance of the proposed framework for the MSTA imaging method when the receive element positions are chosen optimally based on genetic algorithm (GA), which can reduce the practical implementation complexity. It was found that the CS framework using GA leads to the lowest recovery error and a 14% improvement in image contrast in comparison to the Gaussian sampling scheme. From work done in this thesis, it can be concluded that the CS framework using novel lateral-under-sampling schemes can be used to reduce the receive channel count in CFB and MSTA without degradation in the resulting image quality.