Frequency Domain Compressive Sampling for Ultrasound Imaging

Compressed sensing or compressive sampling is a recent theory that originated in the applied mathematics field. It suggests a robust way to sample signals or images below theclassic Shannon-Nyquist theorem limit. This technique has led to many applications, and has especially been successfully used in diverse medical imaging modalities such as magnetic resonance imaging, computed tomography, or photoacoustics. This paper first revisits the compressive sampling theory and then proposes several strategies to perform compressive sampling in the context of ultrasound imaging. Finally, we show encouraging results in 2D and 3D, on high- and low-frequency ultrasound images