Compressed Sensing of ΔΣ Streams

Compressed sensing (CS) is often applied at the digital level. We consider the case where CS follows a Δ Σ data converter and we show that CS can be practiced directly on the Δ Σ stream. In the proposed scheme, an appropriate sensing matrix incorporates the ability to get rid of the quantization noise from the Δ Σ modulator. We also show that a suitable sparsity basis enables the CS information recovery to be practiced directly at the Nyquist rate and that decimation, which is typically inherent in Δ Σ data acquisition, is not needed. Furthermore, the low depth of Δ Σ streams allows CS measures to be taken without multipliers, streamlining arithmetic blocks. A test case based on electrocardiograms is used to validate the approach.