Spectral density

Quantum mechanics

Algorithm

Undersampling

Statistics

Aliasing

Noise power

Power (physics)

Computer science

Filter (signal processing)

Physics

Mathematics

Optics

Image (mathematics)

Sampling (signal processing)

Focus (optics)

Artificial intelligence

Colors of noise

Noise reduction

Noise (video)

Computer vision

ACM Transactions on Graphics

In this article we revisit the problem of blue noise sampling with a strong focus on the spectral properties of the sampling patterns. Starting from the observation that oscillations in the power spectrum of a sampling pattern can cause aliasing artifacts in the resulting images, we synthesize two new types of blue noise patterns: step blue noise with a power spectrum in the form of a step function and single-peak blue noise with a wide zero-region and no oscillations except for a single peak. We study the mathematical relationship of the radial power spectrum to a spatial statistic known as the radial distribution function to determine which power spectra can actually be realized and to construct the corresponding point sets. Finally, we show that both proposed sampling patterns effectively prevent structured aliasing at low sampling rates and perform well at high sampling rates.

Blue noise sampling with controlled aliasing