High‐Order Recursive Filtering of Non‐Uniformly Sampled Signals for Image and Video Processing

Abstract

AbstractWe present a discrete‐time mathematical formulation for applying recursive digital filters to non‐uniformly sampled signals. Our solution presents several desirable features: it preserves the stability of the original filters; is well‐conditioned for low‐pass, high‐pass, and band‐pass filters alike; its cost is linear in the number of samples and is not affected by the size of the filter support. Our method is general and works with any non‐uniformly sampled signal and any recursive digital filter defined by a difference equation. Since our formulation directly uses the filter coefficients, it works out‐of‐the‐box with existing methodologies for digital filter design. We demonstrate the effectiveness of our approach by filtering non‐uniformly sampled signals in various image and video processing tasks including edge‐preserving color filtering, noise reduction, stylization, and detail enhancement. Our formulation enables, for the first time, edge‐aware evaluation of any recursive infinite impulse response digital filter (not only low‐pass), producing high‐quality filtering results in real time.