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In this paper, we provide a comprehensive theory of anti-aliasing samplingpatterns that explains and revises known results, and show how patterns aspredicted by the theory can be generated via a variational optimizationframework. We start by deriving the exact spectral expression for expectederror in reconstructing an image in terms of power spectra of samplingpatterns, and analyzing how the shape of power spectra is related toanti-aliasing properties. Based on this analysis, we then formulate the problemof generating anti-aliasing sampling patterns as constrained variationaloptimization on power spectra. This allows us to not rely on any parametricform, and thus explore the whole space of realizable spectra. We show that theresulting optimized sampling patterns lead to reconstructions with less visiblealiasing artifacts, while keeping low frequencies as clean as possible.

A Comprehensive Theory and Variational Framework for Anti-aliasing Sampling Patterns