Recovering lost information in analog-to-digital conversion
The famous Shannon-Nyquist theorem has become a landmark in analog to digital conversion and the development of digital signal processing algorithms. However, in many modern applications, the signal bandwidths have increased tremendously, while the acquisition capabilities have not scaled sufficiently fast. Furthermore, the resulting high rate digital data requires storage, communication and processing at very high rates which is computationally expensive and requires large amounts of power. In the context of medical imaging sampling at high rates often translates to high radiation dosages, increased scanning times, bulky medical devices, and limited resolution. In this talk we consider a general framework for sub-Nyquist sampling and processing in space, time and frequency which allows to dramatically reduce the number of antennas, sampling rates and band occupancy in a variety of applications. Our framework relies on exploiting signal structure and the processing task. We consider applications of these ideas to a variety of problems in communications, radar and ultrasound imaging and show several demos of real-time sub-Nyquist prototypes including a wireless ultrasound probe, sub-Nyquist MIMO radar, cognitive radio, shared spectrum radar, and an analog combiner prototype. We then show how these ideas can be used to overcome fundamental resolution limits in optical microscopy and ultrasound imaging and demonstrate sub-Nyquist devices operating beyond the standard resolution limits combining high spatial resolution with short integration time.