  The standard technique used by commercial medical ultrasound systems to form
B-mode images is delay and sum (DAS) beamforming. However, DAS often results in
limited image resolution and contrast, which are governed by the center
frequency and the aperture size of the ultrasound transducer. A large number of
elements leads to improved resolution but at the same time increases the data
size and the system cost due to the receive electronics required for each
element. Therefore, reducing the number of receiving channels while producing
high quality images is of great importance. In this paper, we introduce a
nonlinear beamformer called COnvolutional Beamforming Algorithm (COBA), which
achieves significant improvement of lateral resolution and contrast. In
addition, it can be implemented efficiently using the fast Fourier transform.
Based on the COBA concept, we next present two sparse beamformers with closed
form expressions for the sensor locations, which result in the same beam
pattern as DAS and COBA while using far fewer array elements. Optimization of
the number of elements shows that they require a minimal number of elements
which is on the order of the square root of the number used by DAS. The
performance of the proposed methods is tested and validated using simulated
data, phantom scans and in vivo cardiac data. The results demonstrate that COBA
outperforms DAS in terms of resolution and contrast and that the suggested
beamformers offer a sizable element reduction while generating images with an
equivalent or improved quality in comparison to DAS.
