# Near-Optimal Coded Apertures for Imaging via Nazarov's Theorem

arXiv: https://arxiv.org/abs/1810.12871 · HTML: https://mlsanity.com/paper/1810.12871/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2018.

## Built on by (most cited first, 1 of 1)

- [Can Shadows Reveal Biometric Information?](https://mlsanity.com/paper/2209.10077/) (2022)

## Abstract (arXiv)

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.