Einstein matrix-optimized multiscale frequency band fusion framework for speech denoising

Frequency-domain speech enhancement plays a critical role in improving speech quality under complex noise conditions. However, current methods often suffer from limited feature granularity and constrained model complexity. To overcome these limitations, we propose a novel architecture, Einstein matrix-based Fast Fourier Transform with Multi-Band Frequency Feature fusion (EinFFT-MBFF). The model includes two key modules: a quadratic Fast Fourier Transform (FFT) module that projects signals into a high-dimensional “hyper-frequency” domain, where trainable matrix transformations extract fine-grained spectral features; and a multi-scale fusion mechanism that captures both global and local frequency characteristics via parallel sub-networks. To further improve robustness, a dynamic mixed data augmentation strategy is employed by diversifying noise-speech combinations during training. Experiments on DR-VCTK, FSD50K, and REVERB datasets show that under reverberant conditions, the model achieves relative improvements of 1.058% in Wideband Perceptual Evaluation of Speech Quality (WB-PESQ), 1.076% in Narrowband PESQ (NB-PESQ), and 8.15% in Short-Time Objective Intelligibility (STOI). In non-reverberant settings, improvements reach 0.96%, 0.989%, and 5.61%, respectively. Compared with state-of-the-art methods, EinFFT-MBFF achieves better noise suppression and more stable convergence, while preserving computational efficiency through the inherent cross-channel interaction capabilities of the Einstein matrix.