Time-warping estimation via stationarity-based learning of the de-warped signal

Summary

The paper introduces TWET (Time-Warping Estimation Trainable), a neural model that estimates a time-warping function from a single observation y(t) = x(γ(t)), where the latent signal x is assumed wide-sense stationary. Building on the approximation that smooth warping shifts wavelet coefficients along the scale axis (Proposition 1), TWET de-warps the wavelet modulus by interpolation along scales and minimizes a differentiable stationarity criterion — the average temporal variance of the de-warped coefficients — plus a smoothness penalty on δ(u) = log_q γ'(u). A hierarchical architecture of four dilated-convolution residual blocks (16 filters, GELU, LayerNorm) with a final across-scale convolution predicts δ per sample, with a zero-mean constraint removing shift ambiguity. On 50 synthetic 1-second test signals (44.1 kHz), TWET attains lower deformation-derivative error (MSE 0.0070 vs 0.0424 for JEFAS and 0.0564 for WSB) and far lower runtime (0.0008 s vs 13.5 s and 1.7 s), though JEFAS remains better on its own likelihood criterion rJ. On three real audio recordings trained signal-specifically, stationarity indices are comparable to or better than JEFAS and clearly better than WSB. Limitations: acknowledged train/test distribution similarity, no variance estimates, GPU-batched runtime measurement, and several unreported hyperparameters.