Sigma Delta Quantization for Compressive Sensing

Compressive sensing is a new data acquisition technique that aims to measure sparse and compressible signals at close to their intrinsic information rate rather than their Nyquist rate. Recent results in compressive sensing show that a sparse or compressible signal can be reconstructed from very few measurements with an incoherent, and even randomly generated, dictionary. To date the hardware implementation of compressive sensing analog-todigital systems has not been straightforward. This paper explores the use of Sigma-Delta quantizer architecture to implement such a system. After examining the challenges of using Sigma-Delta with a randomly generated compressive sensing dictionary, we present efficient algorithms to compute the coefficients of the feedback loop. The experimental results demonstrate that Sigma-Delta relaxes the required analog filter order and quantizer precision. We further demonstrate that restrictions on the feedback coefficient values and stability constraints impose a small penalty on the performance of the Sigma-Delta loop, while they make hardware implementations significantly simpler.