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We characterize the fundamental limits of coded aperture imaging systems upto universal constants by drawing upon a theorem of Nazarov regarding Fouriertransforms. Our work is performed under a simple propagation and sensor modelthat accounts for thermal and shot noise, scene correlation, and exposure time.Focusing on mean square error as a measure of linear reconstruction quality, weshow that appropriate application of a theorem of Nazarov leads to essentiallyoptimal coded apertures, up to a constant multiplicative factor in exposuretime. Additionally, we develop a heuristically efficient algorithm to generatesuch patterns that explicitly takes into account scene correlations. Thisalgorithm finds apertures that correspond to local optima of a certainpotential 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 sequenceswith bias. The development focuses on 1D apertures for conceptual clarity; thenatural generalizations to 2D are also discussed.

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