Compressed Sensing of ΔΣ Streams

Compressed sensing (CS) is often applied at the digital level. We consider the case where CS follows a ΔΣ data converter and we show that CS can be practiced directly on the ΔΣ stream. In the proposed scheme, an appropriate sensing matrix incorporates the ability to get rid of the quantization noise from the ΔΣ 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 ΔΣ data acquisition, is not needed. Furthermore, the low depth of ΔΣ streams allows CS measures to be taken without multipliers, streamlining arithmetic blocks. A test case based on electrocardiograms is used to validate the approach.