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Near-optimal Coded Apertures for Imaging via Nazarov’s Theorem
Name
1810.12871.pdf
Description
Submitted version
Size
361.25 KB
Format
Adobe PDF
Checksum (MD5)
882a71b4ebd4cbd7b5221b7e9879226d
Author(s)
Ajjanagadde, Ganesh
Thrampoulidis, Christos
Yedidia, Adam
Wornell, Gregory
Date Issued
2019
Journal
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
Abstract
© 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.
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
10.1109/ICASSP.2019.8682254
