Total Variation Reconstruction From Quasi-Random Samples

Pseudo-random numbers are often used for generating incoherent uniformly distributed sample distributions. However randomness is a sufficient -- not necessary -- condition to ensure incoherence. If one wants to reconstruct an image from few samples, choosing a globally optimized set of evenly distributed points could capture the visual content more efficiently. This work compares classical random sampling with a simple construction based on properties of the fractional Golden ratio sequence and the Hilbert space filling curve. Images are then reconstructed using a total variation prior. Results show improvements in terms of peak signal to noise ratio over pseudo-random sampling.