Sub-Nyquist Medical Ultrasound Imaging: En Route to Cloud Processing Alon Eilam * , Tanya Chernyakova * , Yonina C. Eldar * and Arcady Kempinski ** * Department of Electrical Engineering, Technion, Israel Institute of Technology, Haifa, Israel Email: aeilam@tx.technion.ac.il, ctanya@tx.technion.ac.il, yonina@ee.technion.ac.il ** GE Healthcare, Haifa, Israel Email: arcady.kempinski@med.ge.com Abstract—In medical ultrasound imaging, a pulse of known shape is transmitted into the respective medium, and the received echoes are sampled and digitally processed in a way referred to as beamforming to form an ultrasound image. Applied spatially, beamforming allows to improve resolution and signal-to-noise ratio. The structure of medical ultrasound signals allow for significant reduction of both sampling and processing rates by relying on ideas of Xampling, sub-Nyquist sampling and frequency domain beamforming. In this paper we present an implementation on an ultrasound machine using sub-Nyquist sampling and processing and the obtained imaging results. The provided system configuration exploits the advantages of beamforming in the frequency domain, which is performed at a low-rate. Our results prove that the concept of porting heavy computational tasks to the cloud is feasible for medical ultrasound, leading to potential of considerable reduction in future ultrasound machines size, power consumption and cost. Index Terms—Array Processing, Ultrasound, Beamforming, Com- pressed Sensing, Sub-Nyquist I. I NTRODUCTION Diagnostic ultrasound has been used for decades to visualize body structures. The overall imaging process is described as follows: An energy pulse is transmitted along a narrow beam. During its propagation echoes are scattered by acoustic impedance perturbations in the tissue, and detected by the elements of the transducer. Collected data are sampled and digitally processed in a way referred to as beam- forming, which results in signal-to-noise ratio (SNR) enhancement. Such a beamformed signal forms a line in the image. According to the classic Shannon-Nyquist theorem [1], the sam- pling rate at each transducer element should be at least twice the bandwidth of the detected signal. In legacy systems, rates up to 3-10 times the modulation frequency are required in order to avoid artifacts caused by digital implementation of beamforming in the time domain [2]. Such rates can be up to 4 times the Nyquist rate of the detected signal. Taking into account the number of transducer elements and the number of lines in an image, the amount of sampled data that needs to be digitally processed is enormous, motivating methods to reduce sampling rates. Reduction of processing rate is possible within the classical sam- pling framework, by exploiting the fact that the signal is modulated onto a carrier and occupies only a portion of its entire baseband bandwidth. Accordingly, state-of-the-art systems digitally demodulate down-sample the data at the system’s front-end. However, this does not change the sampling rate since demodulation takes place in the digital domain. In addition, resulting processing rate may be reduced up to 1/4 of the standard beamforming rate, but the signal becomes complex in this setup, and the number of samples effectively is only twice smaller. A different approach to sampling rate reduction was introduced in [3]. Tur et. al. regard the ultrasound signal detected by each receiver within the framework of finite rate of innovation (FRI) [4], modeling it as L replicas of a known pulse-shape, caused by scattering of the transmitted pulse from reflectors, located along the transmitted beam. Such an FRI signal is fully described by 2L parameters, correspond- ing to the replica’s delays and amplitudes. These parameters can be extracted from a small set of the signal’s Fourier series coefficients. A mechanism, referred to as Xampling, derived in [5], [6] extracts such a set of coefficients from 4L real-valued samples. This work is continued in [7], where Wagner et. al. introduce a generalized scheme, referred to as compressed beamforming, which allows to compute the Fourier series coefficients of the beamformed signal from the low-rate samples of signals detected at each element. The problem of reconstruction of the beamformed signal from a small number of its Fourier series coefficients is solved via a compressed sensing (CS) technique, while assuming a small number L of replicas. This approach allows to reconstruct an image comprised of macroscopic perturbations, but did not treat the speckle, which is of significant importance in medical imaging. A solution to the problem of speckle retaining was proposed in [8], where Chernyakova et al. extended the notion of compressed beamforming to beamforming in frequency and proposed alternative approach for reconstruction of the signal from partial frequency data. Beamforming in frequency exploits the low bandwidth of the signal and allows to bypass the oversampling required for beamforming in time. Arbitrary set of discrete Fourier transform (DFT) coefficients of the beamformed signal can be computed as a linear combination of DFT coefficients of the detected signals. The latter can be computed from low-rate generalized samples of the detected signals, obtained by Xampling scheme. Once partial beamformed frequency data is obtained, appropriate CS techniques can be used to recover the beamformed signal. Such a framework, utilizing sub-Nyquist sampling, frequency domain beamforming and CS techniques for signal recovery allows for significant reduction in both sampling and processing rates, while retaining sufficient image quality. In this paper we introduce the implementation of beamforming in frequency and sub-Nyquist processing on a stand alone ultrasound machine and show that such processing is feasible and is not just a theoretical framework. Low-rate processing is performed on the data obtained in real-time by scanning a phantom with an 64 element probe. The proposed approach allows for significant rate redaction with respect to the lowest processing rates that are achievable today. The achieved saving in data and processing rates enable beamforming by remote servers in a computer network cloud. This approach is expected to have a significant impact on system size, power con- sumption and cost. It consolidates with the trend of cloud computing in general [9] and its proposed application in medical ultrasound imaging systems [10].