Spectral-Domain Local Statistics with Missing-Data Support for Cartesian and Polar Grids

TL;DR

This paper introduces a spectral-domain method for computing local statistics on incomplete gridded data, supporting Cartesian and polar grids with boundary-aware operators and stability safeguards.

Contribution

It combines normalized convolution with boundary-condition modeling using DCT and RFFT, enabling accurate local statistics on incomplete data with open-source implementation.

Findings

Mitigates wrap-around artifacts in Cartesian boundary scenarios

Effective outlier detection in synthetic 3D tests

Supports real-radar polar data analysis with stable results

Abstract

This paper presents a method for computing local mean, variance, standard deviation, and effective sample count on incomplete gridded data using boundary-aware spectral operators. The framework combines normalized convolution with explicit boundary-condition modeling: reflective Discrete Cosine Transform (DCT) for non-periodic Cartesian axes and periodic Real Fast Fourier Transform (RFFT) for circular azimuth processing in polar geometry. Stability safeguards (denominator floor, prefill fallback, and variance clamp) are specified for under-supported regions. We evaluate the framework across three targeted scenarios: a Cartesian boundary-condition check demonstrating the mitigation of wrap-around artifacts, a synthetic 3D outlier-identification test, and a real-radar polar application. Results establish bounded, support-aware interpretation of local statistics while preserving a concise reproducibility path through the open-source 'dct\_toolkit' implementation.