Continuous Wavelet Neural Operators for Acoustic Speech Enhancement

We introduce the Wavelet Neural Operator (WNO) framework for continuous acoustic speech enhancement. Standard neural audio models parameterize maps between finite-dimensional Euclidean vectors, suffering from discretization bias and performance degradation across varying sampling rates. In contrast, WNO learns a continuous operator G : L^2([0, T]) -> L^2([0, T]) directly parameterized by orthogonal multiresolution wavelet bases. We propose a Hierarchical U-WNO architecture incorporating Inter-Scale Wavelet Gated Attention to model phase-locked cross-octave speech harmonics. Under strict parameter-matched controls (~622k parameters), we evaluate denoising fidelity across diverse acoustic noise conditions, sample-rate invariance, and real-time CPU edge execution (0.053 RTF).