Time domain compressive beam forming of ultrasound signals

Ultrasound imaging is a wide spread technique used in medical imaging as well as in non-destructive testing. The technique offers many advantages such as real-time imaging, good resolution, prompt acquisition, ease of use, and low cost compared to other techniques such as x-ray imaging. However, the maximum frame rate achievable is limited as several beams must be emitted to compute a single image. For each emitted beam, one must wait for the wave to propagate back and forth, thus imposing a limit to the frame rate. Several attempts have been made to use less beams while maintaining image quality. Although efficiently increasing the frame rate, these techniques still use several transmit beams. Compressive Sensing (CS), a universal data completion scheme based on convex optimization, has been successfully applied to a number of imaging modalities over the past few years. Using a priori knowledge of the signal, it can compute an image using less data allowing for shorter acquisition times. In this paper, it is shown that a valid CS framework can be derived from ultrasound propagation theory, and that this framework can be used to compute images of scatterers using only one plane wave as a transmit beam.