Traffic-utilisation measurements for network monitoring are corrupted by additive noise and statistical drift: time-dependent change in the signal's mean, variance, distributional shape, or tail behaviour. Static wavelet denoising, calibrated under stationary independent and identically distributed (i.i.d.) Gaussian assumptions, becomes mismatched under drift and, at moderate-to-high signal-to-noise ratio (SNR), over-suppresses useful structure and degrades monitoring decisions. We propose a drift-aware framework treating adaptive wavelet denoising as a preprocessing layer optimised for two tasks: anomaly detection, recovering the multi-scale transient load bursts that noise and drift obscure, and capacity estimation, recovering the operational required capacity $C_{95}$ (95th percentile of utilisation). Because localised bursts are multi-scale structure a wavelet preserves but a low-pass filter removes, detection discriminates denoiser families. A four-detector gate (Page-Hinkley, variance-ratio, Jensen-Shannon, Anderson-Darling) determines when to invoke a learned policy, and a Proximal Policy Optimization agent selects a per-window wavelet configuration over a mixed discrete-continuous action space. Unlike prior work, the reward is downstream task utility, not reconstruction fidelity. The denoiser is benchmarked, per drift type and input SNR, against a low-pass moving-average filter, VisuShrink, SureShrink, BayesShrink, and a Wiener filter. Defining the anomaly target on the clean signal and the drift gate on the corruption keeps both stages non-circular.
Data encountered in practice are frequently contaminated by additive noise, and wavelet shrinkage remains a fundamental tool for recovering underlying signals in nonparametric estimation. Classical procedures such as hard and soft thresholding decide whether to retain a wavelet coefficient almost entirely from its magnitude. Although effective in many settings, these rules can be too rigid for coefficients whose magnitudes fall in an intermediate region where the distinction between signal and noise is uncertain. We propose MLShrink, a two-threshold wavelet denoising procedure that combines wavelet shrinkage with machine learning. Coefficients below a lower threshold are discarded, coefficients above an upper threshold are retained, and coefficients in the intermediate band are classified using local wavelet-domain features. In this way, MLShrink preserves the simplicity of classical thresholding away from the decision boundary while allowing data-adaptive decisions for ambiguous coefficients. The paper also develops a theoretical framework tailored to this architecture. We show that MLShrink is a nonexpansive support-selection rule, derive an oracle-based risk decomposition showing that excess denoising risk is determined by classification errors on the undecided band, and establish an oracle-consistency result under suitable assumptions on classifier performance. Simulation experiments on standard benchmark signals indicate that MLShrink is competitive with several established wavelet shrinkage methods and is especially effective for signals with irregular, edge-rich, or non-smooth structure. These findings suggest that learned decisions on the intermediate threshold band provide a useful and interpretable connection between classical wavelet denoising and modern statistical learning.