TY - JOUR
T1 - Democracy in action
T2 - Quantization, saturation, and compressive sensing
AU - Laska, Jason N.
AU - Boufounos, Petros T.
AU - Davenport, Mark A.
AU - Baraniuk, Richard G.
N1 - Funding Information:
✩ This work was supported by the grants NSF CCF-0431150, CCF-0728867, CCF-0926127, CNS-0435425, CNS-0520280, and DMS-1004718, DARPA/ONR N66001-08-1-2065, ONR N00014-07-1-0936, N00014-08-1-1067, N00014-08-1-1112, and N00014-08-1-1066, AFOSR FA9550-07-1-0301 and FA9550-09-1-0432, ARO MURI W911NF-07-1-0185 and W911NF-09-1-0383, and the Texas Instruments Leadership University Program. * Corresponding author. E-mail addresses: [email protected] (J.N. Laska), [email protected] (P.T. Boufounos), [email protected] (M.A. Davenport), [email protected] (R.G. Baraniuk).
PY - 2011/11
Y1 - 2011/11
N2 - Recent theoretical developments in the area of compressive sensing (CS) have the potential to significantly extend the capabilities of digital data acquisition systems such as analog-to-digital converters and digital imagers in certain applications. To date, most of the CS literature has been devoted to studying the recovery of sparse signals from a small number of linear measurements. In this paper, we study more practical CS systems where the measurements are quantized to a finite number of bits; in such systems some of the measurements typically saturate, causing significant nonlinearity and potentially unbounded errors. We develop two general approaches to sparse signal recovery in the face of saturation error. The first approach merely rejects saturated measurements; the second approach factors them into a conventional CS recovery algorithm via convex consistency constraints. To prove that both approaches are capable of stable signal recovery, we exploit the heretofore relatively unexplored property that many CS measurement systems are democratic, in that each measurement carries roughly the same amount of information about the signal being acquired. A series of computational experiments indicate that the signal acquisition error is minimized when a significant fraction of the CS measurements is allowed to saturate (10-30% in our experiments). This challenges the conventional wisdom of both conventional sampling and CS.
AB - Recent theoretical developments in the area of compressive sensing (CS) have the potential to significantly extend the capabilities of digital data acquisition systems such as analog-to-digital converters and digital imagers in certain applications. To date, most of the CS literature has been devoted to studying the recovery of sparse signals from a small number of linear measurements. In this paper, we study more practical CS systems where the measurements are quantized to a finite number of bits; in such systems some of the measurements typically saturate, causing significant nonlinearity and potentially unbounded errors. We develop two general approaches to sparse signal recovery in the face of saturation error. The first approach merely rejects saturated measurements; the second approach factors them into a conventional CS recovery algorithm via convex consistency constraints. To prove that both approaches are capable of stable signal recovery, we exploit the heretofore relatively unexplored property that many CS measurement systems are democratic, in that each measurement carries roughly the same amount of information about the signal being acquired. A series of computational experiments indicate that the signal acquisition error is minimized when a significant fraction of the CS measurements is allowed to saturate (10-30% in our experiments). This challenges the conventional wisdom of both conventional sampling and CS.
KW - Compressive sensing
KW - Consistent reconstruction
KW - Quantization
KW - Saturation
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U2 - 10.1016/j.acha.2011.02.002
DO - 10.1016/j.acha.2011.02.002
M3 - Article
AN - SCOPUS:79960557614
SN - 1063-5203
VL - 31
SP - 429
EP - 443
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
IS - 3
ER -