RBHAT: Robust Bootstrap-Hurst Adaptive Thresholding — Code and Data Archive

This repository archives the complete code and data supporting the paper "Robust Bootstrap-Hurst Adaptive Thresholding for Stationary Wavelet Denoising in Data-Driven Multiresolution Analysis" by Ntebogang Dinah Moroke (2026), submitted to Frontiers in Signal Processing, Statistical Signal Processing section. RBHAT is a four-stage statistical signal processing framework that models scale-wise wavelet detail coefficients as particle trajectories governed by a Fractional Langevin Equation, using Huber M-estimation and Moving Block Bootstrap resampling to estimate a scale-specific persistence index at each decomposition level, and applying a fractal-corrected adaptive threshold T_j = σ̂_j √(2 ln N) · φ(Ĥ_j) that elevates the threshold for persistent signal trajectories and depresses it for anti-persistent noise fluctuations. Contents: code/rbhat.py — Complete Python 3.12 implementation of all four RBHAT stages: Hankel-SVD preprocessing, Stationary Wavelet Transform decomposition, Huber-MBB robust Hurst estimation, and fractal-corrected adaptive thresholding code/reproduce_experiments.py — Reproduces all Monte Carlo benchmarks, financial metrics, and ablation results reported in the paper data/fbm_clean_seed2015.npz — Pre-generated fractional Brownian motion signals, H ∈ {0.3, 0.5, 0.7, 0.9}, N=1024, M=30 trials, base seed 2015 data/jse_garch_t_seed2017.npz — JSE-calibrated GARCH(1,1)-t log-return series, N=2048, μ=2.8×10⁻⁴, α₁=0.082, β₁=0.906, ν=5.8, seed 2017 data/ecg_noisy_seed42.npz — scipy/PhysioNet electrocardiogram (N=1024, 360 Hz) with documented noise: baseline wander (0.1 Hz, 0.3 Hz) and Student-t(ν=4) muscle artefact, seed 42 Reproducibility seeds: Monte Carlo fBm generation: 2015 | MBB resampling: trial_index offset | JSE GARCH simulation: 2017 Dependencies: Python ≥ 3.10, numpy, scipy, PyWavelets (pip install numpy scipy PyWavelets) Related dataset: JSE securities panel (87 assets, 2015–2025, Eskom load-shedding period): https://doi.org/10.5281/zenodo.20008530