Notice
This is not the latest version of this item. The latest version can be found at:https://dspace.mit.edu/handle/1721.1/137942.2
Near-optimal Coded Apertures for Imaging via Nazarov’s Theorem
Author(s)
Ajjanagadde, Ganesh; Thrampoulidis, Christos; Yedidia, Adam; Wornell, Gregory
DownloadSubmitted version (361.2Kb)
Open Access Policy
Open Access Policy
Creative Commons Attribution-Noncommercial-Share Alike
Terms of use
Metadata
Show full item recordAbstract
© 2019 IEEE. We characterize the fundamental limits of coded aperture imaging systems up to universal constants by drawing upon a theorem of Nazarov regarding Fourier transforms. Our work is performed under a simple propagation and sensor model that accounts for thermal and shot noise, scene correlation, and exposure time. Focusing on mean square error as a measure of linear reconstruction quality, we show that appropriate application of a theorem of Nazarov leads to essentially optimal coded apertures, up to a constant multiplicative factor in exposure time. Additionally, we develop a heuristically efficient algorithm to generate such patterns that explicitly takes into account scene correlations. This algorithm finds apertures that correspond to local optima of a certain potential on the hypercube, yet are guaranteed to be tight. Finally, for i.i.d. scenes, we show improvements upon prior work by using spectrally flat sequences with bias. The development focuses on 1D apertures for conceptual clarity; the natural generalizations to 2D are also discussed.
Date issued
2019Journal
ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Ajjanagadde, Ganesh, Thrampoulidis, Christos, Yedidia, Adam and Wornell, Gregory. 2019. "Near-optimal Coded Apertures for Imaging via Nazarov’s Theorem." ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 2019-May.
Version: Original manuscript