Deep Task-Based Analog-To-Digital Conversion

Analog-To-digital converters (ADCs) allow physical signals to be processed using digital hardware. Their conversion consists of two stages: Sampling, which maps a continuous-Time signal into discrete-Time, and quantization, i.e., representing the continuous-Amplitude quantities using a finite number of bits. ADCs typically implement generic uniform conversion mappings that are ignorant of the task for which the signal is acquired, and can be costly when operating in high rates and fine resolutions. In this work we design task-oriented ADCs which learn from data how to map an analog signal into a digital representation such that the system task can be efficiently carried out. We propose a model for sampling and quantization that facilitates the learning of non-uniform mappings from data. Based on this learnable ADC mapping, we present a mechanism for optimizing a hybrid acquisition system comprised of analog combining, tunable ADCs with fixed rates, and digital processing, by jointly learning its components end-To-end. Then, we show how one can exploit the representation of hybrid acquisition systems as deep networks to optimize the sampling and quantization rates given the task by utilizing Bayesian meta-learning techniques. We evaluate the proposed deep task-based ADC in two case studies: The first considers synthetic multi-variate symbol detection, where multiple analog signals are simultaneously acquired in order to recover a set of discrete symbols. The second application is beamforming of analog channel data acquired in ultrasound imaging. Our numerical results demonstrate that the proposed approach achieves performance which is comparable to operating with high sampling rates and fine resolution quantization, while operating with reduced overall bit rate. For instance, we demonstrate that deep task-based ADCs enable accurate reconstruction of ultrasound images while using 12.5% of the overall number of bits used by conventional ADCs.