Serial Quantization for Sparse Time Sequences

Sparse signals are encountered in a broad range of applications. In order to process these signals using digital hardware, they must first be sampled and quantized using an analog-to-digital convertor (ADC), which typically operates in a serial scalar manner. In this work, we propose an serial quantization of sparse time sequences (SQuaTS) method inspired by group testing theory. This method is designed to reliably and accurately quantize sparse signals acquired in a sequential manner using the serial scalar ADCs. Unlike previously proposed approaches that combine quantization and compressed sensing (CS), our SQuaTS scheme updates its representation on each incoming analog sample and does not require the complete signal to be observed or stored in analog prior to quantization. We characterize the asymptotic tradeoff between the accuracy and quantization rate of SQuaTS as well as its computational burden. We also propose a variation of SQuaTS that trades the quantization rate for computational efficiency. Next, we show how SQuaTS can be naturally extended to distributed quantization scenarios, where a set of jointly sparse time sequences are acquired individually and processed jointly. Our numerical results demonstrate that SQuaTS is capable of achieving substantially improved representation accuracy over previous CS-based schemes without requiring the complete set of analog signal samples to be observed prior to signal quantization, making this method an attractive approach for acquiring sparse time sequences.