Butterworth as Attention: Anisotropic Spectral Gating for Pansharpening

Pansharpening fuses high-resolution panchromatic (PAN) images with low-resolution multispectral (LMS) images. For spatial-spectral fusion, Fast Fourier Transform (FFT)-based methods provide a global receptive field to capture long-range dependencies and naturally separate frequency components. However, most existing approaches directly transplant spatial operators like convolution or self-attention, while disregarding the fundamental structure of the spectrum: a strict spatial correspondence where each coordinate represents a specific frequency component, and a highly non-uniform, radially decaying energy distribution. To address this, we revisit the classical Butterworth filter, a frequencydomain operator defined directly on spectral coordinates that is inherently suited for processing such structured representations. We generalize the standard isotropic Butterworth filter into an anisotropic, learnable frequency-domain gating mechanism, establishing an efficient alternative to self-attention, and propose the Anisotropic Butterworth Fusion Network (ABFNet). Its core is a novel dual-branch gating module that employs learnable anisotropic Butterworth filters to perform adaptive direction-aware feature selection, integrating global context and local details with linear complexity. Extensive experiments show that ABFNet achieves state-of-the-art (SOTA) performance on pansharpening benchmarks with low computational overhead. Furthermore, its superior accuracy on CIFAR-100 classification validates the broader applicability of this frequency-domain learning paradigm.