Adaptive-spectral deep learning framework for multiscale signal denoising

Recent advances in deep learning have significantly improved signal denoising by enabling the modeling of complex and nonlinear temporal relationships. However, their performance often declines in real-world settings where data are disrupted by volatile, high-dimensional noise and irregular patterns. To address these challenges, this study presents a novel enhancement of the deep multilayer perceptron through the integration of a hierarchical Kalman filtering framework. This framework introduces a recursively filtering mechanism that combines state-space modeling, spectral decomposition, and multiscale noise isolation. It begins with a Kalman filter that separates raw inputs into trend components and residual noise. A spectral analysis stage then identifies dominant noise frequencies for targeted suppression. Following this, the model iteratively updates its internal state-space parameters based on the evolving statistical properties of the residuals, particularly their power spectral density and autocorrelation decay. To prevent overfitting, convergence thresholds are dynamically tuned based on signal complexity rather than fixed values. By refining noisy inputs into feature-rich signals, the system overcomes key limitations of standard deep multilayer perceptron such as their sensitivity to noise and difficulty modeling fine-grained temporal structures. Empirical evaluations on crude oil price dataset demonstrated substantial improvements. Compared to the deep multilayer perceptron, the proposed model achieved up to 58.2% lower mean absolute error, 82.8% reduction in mean squared error, and 57.0% lower root mean squared error, on the test set after 11 adaptive iterations. Forecasting accuracy improved progressively with each filtering step, and results showed a mean absolute percentage error reduction from 2.79% to 1.21%.