A theoretical foundation for the ridges of a scalogram (the squared modulus of the analytic wavelet transform) treated as a set-valued random process connecting local maxima along the scale axis, for signals following the adaptive harmonic model contaminated by stationary Gaussian noise. Establishes almost-sure uniqueness of the ridge point at each time and upper hemicontinuity of the ridge process, and derives signal-to-noise-ratio-dependent bounds on ridge deviation between noisy and clean signals using new maximal inequalities for the complex modulus of nonstationary Gaussian processes (via the Borell-TIS inequality and Dudley's theorem).
This paper builds a rigorous probabilistic foundation for scalogram ridges used in nonstationary time-series analysis. The scalogram is the squared modulus of the analytic wavelet transform (AWT); it…