TY - GEN
T1 - Active learning versus compressive sampling
AU - Castro, Rui
AU - Haupt, Jarvis
AU - Nowak, Robert
PY - 2006
Y1 - 2006
N2 - Compressive sampling (CS), or Compressed Sensing, has generated a tremendous amount of excitement in the signal processing community. Compressive sampling, which involves non-traditional samples in the form of randomized projections, can capture most of the salient information in a signal with a relatively small number of samples, often far fewer samples than required using traditional sampling schemes. Adaptive sampling (AS), also called Active Learning, uses information gleaned from previous observations (e.g., feedback) to focus the sampling process. Theoretical and experimental results have shown that adaptive sampling can dramatically outperform conventional (non-adaptive) sampling schemes. This paper compares the theoretical performance of Compressive and adaptive sampling for regression in noisy conditions, and it is shown that for certain classes of piecewise constant signals and high SNR regimes both CS and AS are near-optimal. This result is remarkable since it is the first evidence that shows that Compressive sampling, which is non-adaptive, cannot be significantly outperformed by any other method (including adaptive sampling procedures), even in the presence of noise. The performance of CS schemes for signal detection is also investigated.
AB - Compressive sampling (CS), or Compressed Sensing, has generated a tremendous amount of excitement in the signal processing community. Compressive sampling, which involves non-traditional samples in the form of randomized projections, can capture most of the salient information in a signal with a relatively small number of samples, often far fewer samples than required using traditional sampling schemes. Adaptive sampling (AS), also called Active Learning, uses information gleaned from previous observations (e.g., feedback) to focus the sampling process. Theoretical and experimental results have shown that adaptive sampling can dramatically outperform conventional (non-adaptive) sampling schemes. This paper compares the theoretical performance of Compressive and adaptive sampling for regression in noisy conditions, and it is shown that for certain classes of piecewise constant signals and high SNR regimes both CS and AS are near-optimal. This result is remarkable since it is the first evidence that shows that Compressive sampling, which is non-adaptive, cannot be significantly outperformed by any other method (including adaptive sampling procedures), even in the presence of noise. The performance of CS schemes for signal detection is also investigated.
KW - Active Learning
KW - Adaptive Sampling
KW - Compressive Sampling
KW - Noisy Randomized Projections
UR - http://www.scopus.com/inward/record.url?scp=33748521516&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33748521516&partnerID=8YFLogxK
U2 - 10.1117/12.669725
DO - 10.1117/12.669725
M3 - Conference contribution
AN - SCOPUS:33748521516
SN - 0819462888
SN - 9780819462886
T3 - Proceedings of SPIE - The International Society for Optical Engineering
BT - Intelligent Integrated Microsystems
T2 - Intelligent Integrated Microsystems
Y2 - 19 April 2006 through 21 April 2006
ER -