Compressive Sensing in Medical Ultrasonography

Sammanfattning: The recently introduced compressive sensing (CS) theory allows – under certain assumptions – to recover a signal sampled below the Nyquist sampling limit. Compressive sensing can be applied for two purposes. First, to decrease the number of samples needed to capture the information, thus allowing faster acquisitions. Second, to improve the reconstruction of signals/images in fields where constraints on the physical acquisition setup yield very sparse data sets. This thesis focuses on medical ultrasonography, with the two following applications: First, 3D imaging using a matrix array of sensors. In this field, a major difficulty concerns the number of elements that are used to acquire the image. For technical reasons, only a fraction of the sensors can be used, which leads to a typical application for the CS theory. Second, duplex acquisitions for B-mode/Doppler imaging. Duplex acquisition implies the alternation between two modes of emission, thus giving sparse velocity measurements. Compressive sensing offers a way to recover the Doppler signal by circumventing the Nyquist-Shannon sampling theorem.