The recently introduced compressive sensing (CS) framework enables digital
signal acquisition systems to take advantage of signal structures beyond
bandlimitedness. Indeed, the number of CS measurements required for stable
reconstruction is closer to the order of the signal complexity than the Nyquist
rate. To date, the CS theory has focused on real-valued measurements, but in
practice, measurements are mapped to bits from a finite alphabet. Moreover, in
many potential applications the total number of measurement bits is
constrained, which suggests a tradeoff between the number of measurements and
the number of bits per measurement. We study this situation in this paper and
show that there exist two distinct regimes of operation that correspond to
high/low signal-to-noise ratio (SNR). In the measurement compression (MC)
regime, a high SNR favors acquiring fewer measurements with more bits per
measurement; in the quantization compression (QC) regime, a low SNR favors
acquiring more measurements with fewer bits per measurement. A surprise from
our analysis and experiments is that in many practical applications it is
better to operate in the QC regime, even acquiring as few as 1 bit per
measurement.

本文研究了基于有限字母表编码的测量压缩和数据压缩的压缩感知框架，在高信噪比和低信噪比两种情况下，通过测量位数和每个测量数据的位数之间的权衡来实现稳定重建，并发现在许多实际应用中，以低信噪比进行量化压缩 (obtained more measurements with fewer bits per measurement) 通常更好。