An Integrated Framework of Frequency-Domain Denoising with Learnable Parameters in Variational Autoencoders

Variational Autoencoders (VAEs) have demonstrated substantial utility in generative modeling, however their performance is often compromised when inputs are corrupted by noise or measurement artifacts. Traditional approaches to preprocessing either fail to adapt to spatially heterogeneous noise or result in excessive smoothing of high-frequency features. In this study, we propose an automatic learnable FFT-VAE framework that integrates learnable frequency-domain denoising and correction parameters with generative modeling. The method predicts per-pixel parameters (\((\alpha)\),\((\sigma)\) , and\((m)\)), which dynamically control the contribution of high-frequency components, the bandwidth of the low-pass filter, and spatial confidence, respectively. This adaptive approach allows the network to suppress noise while preserving structural details in a data-driven manner, eliminating the need for manual hyperparameter tuning. We tested the method on synthetic FashionMNIST datasets under multiple Gaussian noise levels and demonstrate the efficacy of the proposed framework. Compared to baseline configurations, the automatic learnable FFT-VAE method achieves higher reconstruction fidelity, improved PSNR, SSIM, and SNR, and produces more coherent latent representations. We also tested the method in the MedMNIST dataset as a real-world application. The results indicate that the method not only enhances denoising performance but also facilitates the extraction of meaningful features for downstream analytical or diagnostic tasks.