  We address the issue of applying quantized compressed sensing (CS) on
low-energy telemonitoring. So far, few works studied this problem in
applications where signals were only approximately sparse. We propose a
two-stage data compressor based on quantized CS, where signals are compressed
by compressed sensing and then the compressed measurements are quantized with
only 2 bits per measurement. This compressor can greatly reduce the
transmission bit-budget. To recover signals from underdetermined, quantized
measurements, we develop a Bayesian De-quantization algorithm. It can exploit
both the model of quantization errors and the correlated structure of
physiological signals to improve the quality of recovery. The proposed data
compressor and the recovery algorithm are validated on a dataset recorded on 12
subjects during fast running. Experiment results showed that an averaged 2.596
beat per minute (BPM) estimation error was achieved by jointly using compressed
sensing with 50% compression ratio and a 2-bit quantizer. The results imply
that we can effectively transmit n bits instead of n samples, which is a
substantial improvement for low-energy wireless telemonitoring.
