M.Sc Thesis

M.Sc StudentWagner Noam
SubjectCompressed Beamforming with Applications to Ultrasound
DepartmentDepartment of Electrical and Computer Engineering
Supervisors PROFESSOR EMERITUS Arie Feuer
PROF. Yonina Eldar


Emerging sonography techniques often require increasing the number of transducer elements which are involved in the imaging process. Consequently, larger amounts of data must be acquired and transferred from the system front-end to the processing unit. Growing imaging demands additionally require that these larger amounts of data be employed in more computational tasks. The overall growth in data transfer and computational rates affects both machinery size and power consumption.

Within the classical sampling framework, state of the art systems reduce processing rates by exploiting the bandpass bandwidth of the detected signals. However, it has been recently shown that a much more significant sample rate reduction may be achieved, by treating ultrasound signals within the Finite Rate of Innovation framework. These ideas follow the spirit of Xampling, a framework which combines classic methods from sampling theory with recent developments in Compressed Sensing, aimed at sampling certain analog signals far below the Nyquist rate.

Applying such low-rate sampling schemes to individual transducer elements, which detect energy reflected from biological tissues, is limited by the noisy nature of the signals. This often results in erroneous parameter extraction, bringing forward the need to enhance the SNR of the low-rate samples.

In our work, we achieve SNR enhancement, by beamforming the sub-Nyquist samples obtained from multiple transducer elements. We refer to this process as “compressed beamforming”, since it transfers the beamforming operator to the domain of the low-rate samples. We present two compressed beamforming schemes. The first scheme utilizes multiple modulation and integration branches. The modulating waveforms are designed such that a dynamically focused scanline is recovered directly from the low-rate samples. The second scheme may be considered a digital equivalent of the first, where the sampling mechanism is simplified by applying digital post-processing to the low-rate samples.

FRI methods traditionally employ spectral analysis techniques in order to recover the analog signal from its low-rate samples. In our work, we propose a different recovery approach, which is based on a Compressed Sensing (CS) formulation. In addition, we generalize the stream of pulses signal model, proposed in previous works, allowing additional, unknown phase shifts of the detected pulses. This generalization results in better reconstruction of the scanlines, without any need to modify the sampling and recovery schemes.

Applying our approach to cardiac ultrasound data, we successfully image macroscopic perturbations in the tissue bulk, while achieving a nearly eight-fold reduction in sample rate, compared to standard techniques.