Stair blue noise sampling

A common solution to reducing visible aliasing artifacts in image reconstruction is to employ sampling patterns with a blue noise power spectrum. These sampling patterns can prevent discernible artifacts by replacing them with incoherent noise. Here, we propose a new family of blue noise distributions, Stair blue noise, which is mathematically tractable and enables parameter optimization to obtain the optimal sampling distribution. Furthermore, for a given sample budget, the proposed blue noise distribution achieves a significantly larger alias-free low-frequency region compared to existing approaches, without introducing visible artifacts in the mid-frequencies. We also develop a new sample synthesis algorithm that benefits from the use of an unbiased spatial statistics estimator and efficient optimization strategies.