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

Variational autoencoders (VAEs) are sensitive to spatially heterogeneous noise because corrupted high-frequency components can be propagated into the latent posterior and degrade reconstruction. We propose Learnable Local FFT-VAE, a VAE-oriented localized frequency correction framework that performs windowed Fourier-domain modulation before variational encoding. The proposed Localized Denoising-Correction Module extracts overlapping patches, applies local FFT, predicts patch-conditioned frequency-control parameters (α,σ,m), and reconstructs corrected inputs through inverse FFT and Hann overlap-add. This design preserves spatial locality while remaining differentiable and jointly trainable with the VAE objective. We evaluate the method on FashionMNIST, CIFAR-10, and PneumoniaMNIST under homogeneous and heterogeneous synthetic noise, and compare it with Direct VAE, AE, Local FFT-AE, best-tuned Fixed FFT-VAE, learnable Global FFT-VAE, BM3D, DnCNN, and FFDNet. The revised experiments demonstrate improvements in PSNR, SSIM, SNR, MSE, HFEN, and gradient-error, with statistical tests over random seeds. Parameter heatmaps and spectral visualizations further show that the learned local correction adapts to spatially varying corruption. PneumoniaMNIST is used only as a lightweight biomedical benchmark, and the method is not intended for clinical diagnosis.