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.

中文翻译：

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稀疏时间序列的串行量化


在广泛的应用中都会遇到稀疏信号。为了使用数字硬件处理这些信号，必须首先使用模数转换器 (ADC) 对它们进行采样和量化，模数转换器通常以串行标量方式运行。在这项工作中，我们受群体测试理论的启发，提出了一种稀疏时间序列的串行量化（SQuaTS）方法。该方法旨在可靠且准确地量化使用串行标量 ADC 以顺序方式采集的稀疏信号。与之前提出的结合量化和压缩感知 (CS) 的方法不同，我们的 SQuaTS 方案更新其在每个传入模拟样本上的表示，并且不需要在量化之前观察或以模拟形式存储完整信号。我们描述了 SQuaTS 的准确性和量化率及其计算负担之间的渐近权衡。我们还提出了 SQuaTS 的变体，以量化率换取计算效率。接下来，我们展示如何将 SQuaTS 自然地扩展到分布式量化场景，其中单独获取一组联合稀疏时间序列并联合处理。我们的数值结果表明，与之前基于 CS 的方案相比，SQuaTS 能够显着提高表示精度，而无需在信号量化之前观察完整的模拟信号样本集，这使得该方法成为获取稀疏时间序列的有吸引力的方法。