Hyperspectral (HS) Imagery helps to capture information using specialized sensors to extract detailed data at numerous narrow wavelengths. Hyperspectral imaging provides both spatial and spectral characteristics of regions or objects for subsequent analysis. Unfortunately, various noise sources decrease the interpretability of these images as well as the correlation between neighbouring pixels, hence both reduce the classification performance. This study focuses on developing an ensemble algorithm that enables to denoise the spectral signals while decorrelating the spatio-spectral features concurrently. The developed method is called Wavelet High Dimensional Model (W-HDMR) and combines High Dimensional Model Representation (HDMR) with the Discrete Wavelet Transform (DWT). Through W-HDMR, denoised and decorrelated features are extracted from the HS cubes. HDMR decorrelates each dimension in HS data while DWT denoises the spectral signals. The classification performance of W-HDMR as a new feature extraction technique for HS images is assessed by exploiting a Support Vector Machines algorithm. The results indicate that the proposed W-HDMR method is an efficient feature extraction technique and is considered an adequate tool in the HS classification problem.

Modern non-stationary signal denoisers increasingly replace a global wavelet threshold by a detect-then-act (gated) rule that first localises an artefact in the time–scale plane and then suppresses it selectively. Such gates couple sub-bands, and it has been unclear how to quantify, in a basis-intrinsic and interpretable way, how much of the denoising performance is produced by that coupling. We introduce the interaction budget $I=1-{\sum }_j{S}_j$ and prove that it equals the normalised $L^2$-distance of the performance functional to the space of band-additive functions; hence, $I=0$ for any band-diagonal operator and $I>0$ exactly when the gate couples bands. We then (i) give an exact pairwise identity for a binary gate, a two-point lower bound, and a sharp if-and-only-if condition on the gate; (ii) identify a coupling-strength functional with the leading-order law $I\left(\kappa \right)=(\mathcal{C}/V_0){\kappa }^2+o\left({\kappa }^2\right)$; and (iii) bound the second-order HDMR/EMPR truncation error, which vanishes for single-trigger gates. Finally, for coloured noise—where the sub-band factors are correlated, and I alone conflates the two effects—an EMPR product-support decomposition separates operator-induced from correlation-induced interaction, with a correlation-invariant operator signature and a permutation-based estimator. Controlled experiments confirm all results.

Modern non-stationary signal denoisers increasingly replace a global wavelet threshold by a \emph{detect-then-act} (gated) rule that first localises an artefact in the time--scale plane and then suppresses it selectively. Such gates couple sub-bands, and it has been unclear how to quantify, in a basis-intrinsic and interpretable way, \emph{how much} of the denoising performance is produced by that coupling. We introduce the \emph{interaction budget} $I=1-\sum_j S_j$ and prove that it equals the normalised $L^2$-distance of the performance functional to the space of band-additive functions; hence $I=0$ for any band-diagonal operator and $I>0$ exactly when the gate couples bands. We then (i) give an exact pairwise identity for a binary gate, a two-point lower bound, and a sharp iff-condition on the gate; (ii) identify a coupling-strength functional with the leading-order law $I(\kappa)=(\mathcal C/V_0)\kappa^2+o(\kappa^2)$; and (iii) bound the second-order HDMR/EMPR truncation error, which vanishes for single-trigger gates. Finally, for coloured noise---where the sub-band factors are correlated and $I$ alone conflates the two effects---an EMPR product-support decomposition \emph{separates} operator-induced from correlation-induced interaction, with a correlation-invariant operator signature and a permutation-based estimator. Controlled experiments confirm all results.