Complex-Valued Neural Networks with Adaptive Frequency Attention for Image Denoising - Marjono Marjono; Avin Maulana; Anggi Gustiningsih Hapsani (CAUCHY: Jurnal Matematika Murni dan Aplikasi, 2026)
Image denoising encompasses various noise types; in this work, we focus specifically on periodic interference, which introduces coherent frequency-domain artifacts that are challenging to remove using conventional real-valued convolutional neural networks (CNNs). This paper introduces a Complex-Valued Neural Network with Adaptive Frequency Attention (CVNN-AFA) tailored to periodic noise removal, integrating complex-domain feature propagation with explicit radial frequency-band modulation. The proposed architecture employs complex convolutions, complex batch normalization, and ModReLU activations to jointly model amplitude and phase information. An Adaptive Frequency Attention (AFA) module operates in the Fourier domain and partitions the spectrum into low-, mid-, and high-frequency radial bands using distance-based masks, enabling adaptive band-wise reweighting aligned with interference characteristics. Experiments on the BSDS500 dataset augmented with synthetic periodic noise evaluate both low-noise and moderate-to-high noise regimes under matched training budgets and strong real-valued frequency-aware baselines. Results indicate that CVNN-AFA achieves competitive performance overall and provides consistent, moderate improvements in low-amplitude settings, while the real-valued frequency-aware baseline remains more robust under extreme corruption levels. Qualitative and spectral analyses suggest that the proposed approach offers incremental attenuation of periodic components while maintaining comparable detail preservation. These findings are specific to the controlled periodic noise scenarios evaluated in this study.