A Dual-Domain Denoising Network for Nonstationary Signals with Learned Wavelet Bases

Abstract

The restoration of nonstationary signals contaminated by complex noise distributions remains a fundamental challenge in signal processing, particularly within biomedical engineering, seismic analysis, and structural health monitoring. Traditional denoising methodologies, which predominantly rely on fixed basis transformations or purely time-domain filtering, often fail to preserve high-frequency transient features while effectively suppressing noise. This paper introduces the Dual-Domain Denoising Network (D3N), a novel deep learning architecture that integrates a learnable wavelet transform with a dual-path attention mechanism. Unlike standard Convolutional Neural Networks (CNNs) that operate solely in the spatial or temporal domain, the D3N explicitly decomposes signals into time-frequency representations using trainable lifting schemes, allowing the network to adapt the basis functions to the specific spectral characteristics of the input data. We propose a parallel architecture that processes global temporal dependencies via a recurrent attention branch and local spectral features via a sparse wavelet coding branch. Extensive experiments on synthetic and real-world datasets, including ECG and seismic time-series, demonstrate that the proposed method significantly outperforms state-of-the-art baselines in terms of Signal-to-Noise Ratio (SNR) and Root Mean Square Error (RMSE).