Compressed sensing vs. active learning

R.M. Castro, J. Haupt, R. Nowak

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review


    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 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 presence of noise.
    Original languageEnglish
    Title of host publicationProceedings IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'06, Toulouse, France, May 14-19, 2006)
    PublisherInstitute of Electrical and Electronics Engineers
    ISBN (Print)1-4244-0469-X
    Publication statusPublished - 2006


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