Rakeness and beyond in zero-complexity digital compressed sensing: A down-to-bits case study

Compressed sensing can be seen as a lossy data compression stage processing vectors of digital words that correspond to time windows of the signal to acquire. We here show that if the second-order statistical features of such a signal are known, they may be exploited to obtain extremely high compression ratios by means of an almost zero-complexity hardware that is limited to signed adders and very few other elementary algebraic blocks. Optimization is obtained and demonstrated against non-optimized compressed sensing both by specializing classical rakeness-based design and by employing and even simpler and novel principal-component-based method that in some cases may outperform the former. Simulations are performed taking into account bit-wise operations and yield the true compression ratios that would be produced by the real system entailing only very low-depth fixed-point arithmetic. In the case of real-workd ECGs, good reconstruction with bitwise compression ratios up to 9 is demonstrated.