Novel and efficient computation of Hilbert-Huang transform on surfaces

摘要: Hilbert-Huang Transform (HHT) has proven to be extremely powerful for signal processing and analysis in 1D time series, its generalization regular tensor-product domains (e.g., 2D 3D Euclidean space) also demonstrated widespread utilities image analysis. Compared with popular Fourier transform wavelet transform, the most prominent advantage of is that, it a fully data-driven, adaptive method, especially valuable handling non-stationary nonlinear signals. Two key technical elements are: (1) Empirical Mode Decomposition (EMD) (2) Hilbert spectra computation. HHT's uniqueness results from capability reveal both global information (i.e., Intrinsic Functions (IMFs) enabled by EMD) local computation frequency, amplitude (energy) phase computation) input Despite rapid advancement past decade, theory applications on surfaces remain severely under-explored due current challenge conducting surfaces. To ameliorate, this paper takes new initiative compute Riesz surfaces, natural higher-dimensional cases, goal make theoretic breakthrough. The core our computational framework exploit relationship between fractional Laplacian operator, which can enable via eigenvalue decomposition matrix. Moreover, we integrate techniques EMD newly-proposed monogenic signals spectra, include space-frequency-energy distribution defined over characterize feature instantaneous amplitude, phase). Experiments spectral geometry detection illustrate effectiveness HHT could serve as solid foundation upcoming, more serious graphics computing fields. A method (RT) proposed.The RT depends matrix.EMD are integrated get spectra.The based potential.