Singer quad apertures and super fast decoding

Abstract

Abstract A new class of coded aperture is introduced, the Singer quad aperture, which is the Cartesian product of two unwrapped Singer product apertures. Formulae for the signal-to-noise ratio (SNR) of Singer quad apertures are derived, allowing optimal Singer quad apertures to be identified, and the CPU time required to decode them is quantified. This allows a systematic comparison to be made of the theoretical performance of Singer quad apertures against both conventionally wrapped Singer apertures, and also Singer product apertures. For very large images, equivalently for images at very high resolution, the SNR of Singer quad apertures should be asymptotically as good as either of these other two classes of apertures, but Singer product apertures should decode faster than either, and by a factor which increases with increasing image size. Initial results from numerical simulations indicate that these theoretical predictions are likely to be true in practice.