Compressive sampling for streaming signals with sparse frequency content

Compressive sampling (CS) has emerged as significant signal processing framework to acquire and reconstruct sparse signals at rates significantly below the Nyquist rate. However, most of the CS development to-date has focused on finite-length signals and representations. In this paper we discuss a streaming CS framework and greedy reconstruction algorithm, the Streaming Greedy Pursuit (SGP), to reconstruct signals with sparse frequency content. Our proposed sampling framework and the SGP are explicitly intended for streaming applications and signals of unknown length. The measurement framework we propose is designed to be causal and implementable using existing hardware architectures. Furthermore, our reconstruction algorithm provides specific computational guarantees, which makes it appropriate for real-time system implementations. Our experimental results on very long signals demonstrate the good performance of the SGP and validate our approach.