TY - JOUR
T1 - Regime change
T2 - Bit-depth versus measurement-rate in compressive sensing
AU - Laska, Jason N.
AU - Baraniuk, Richard G.
N1 - Funding Information:
Manuscript received October 15, 2011; revised January 30, 2012; accepted March 14, 2012. Date of publication April 16, 2012; date of current version June 12, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Jean‐Christophe Pesquet. This work was supported by the grants NSF CCF-0431150, CCF-0728867, and CCF-0926127, DARPA/ONR N66001-11-C-4092, N66001-11-1-4090, ONR N00014-08-1-1067, N00014-08-1-1112, and N00014-11-1-0714, AFOSR FA9550-09-1-0432, ARO MURI W911NF-07-1-0185 and W911NF-09-1-0383, and the Texas Instruments Leadership University Program.
PY - 2012/7
Y1 - 2012/7
N2 - 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.
AB - 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.
KW - Analog-to-digital conversion
KW - compressed sensing
KW - quantization
UR - http://www.scopus.com/inward/record.url?scp=84862605117&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84862605117&partnerID=8YFLogxK
U2 - 10.1109/TSP.2012.2194710
DO - 10.1109/TSP.2012.2194710
M3 - Article
AN - SCOPUS:84862605117
SN - 1053-587X
VL - 60
SP - 3496
EP - 3505
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 7
M1 - 6184331
ER -