Near-optimal Coded Apertures for Imaging via Nazarov’s Theorem
© 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 correla...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Institute of Electrical and Electronics Engineers (IEEE)
2021
|
| Online Access: | https://hdl.handle.net/1721.1/137942 |
| _version_ | 1826209756005531648 |
|---|---|
| author | Ajjanagadde, Ganesh Thrampoulidis, Christos Yedidia, Adam Wornell, Gregory |
| author_facet | Ajjanagadde, Ganesh Thrampoulidis, Christos Yedidia, Adam Wornell, Gregory |
| author_sort | Ajjanagadde, Ganesh |
| collection | MIT |
| description | © 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. |
| first_indexed | 2024-09-23T14:28:56Z |
| format | Article |
| id | mit-1721.1/137942 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:28:56Z |
| publishDate | 2021 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1379422021-11-10T03:14:30Z Near-optimal Coded Apertures for Imaging via Nazarov’s Theorem Ajjanagadde, Ganesh Thrampoulidis, Christos Yedidia, Adam Wornell, Gregory © 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. 2021-11-09T15:59:32Z 2021-11-09T15:59:32Z 2019 2021-01-25T18:31:03Z Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/137942 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. en 10.1109/ICASSP.2019.8682254 ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Ajjanagadde, Ganesh Thrampoulidis, Christos Yedidia, Adam Wornell, Gregory Near-optimal Coded Apertures for Imaging via Nazarov’s Theorem |
| title | Near-optimal Coded Apertures for Imaging via Nazarov’s Theorem |
| title_full | Near-optimal Coded Apertures for Imaging via Nazarov’s Theorem |
| title_fullStr | Near-optimal Coded Apertures for Imaging via Nazarov’s Theorem |
| title_full_unstemmed | Near-optimal Coded Apertures for Imaging via Nazarov’s Theorem |
| title_short | Near-optimal Coded Apertures for Imaging via Nazarov’s Theorem |
| title_sort | near optimal coded apertures for imaging via nazarov s theorem |
| url | https://hdl.handle.net/1721.1/137942 |
| work_keys_str_mv | AT ajjanagaddeganesh nearoptimalcodedaperturesforimagingvianazarovstheorem AT thrampoulidischristos nearoptimalcodedaperturesforimagingvianazarovstheorem AT yedidiaadam nearoptimalcodedaperturesforimagingvianazarovstheorem AT wornellgregory nearoptimalcodedaperturesforimagingvianazarovstheorem |