Rényi Entropy-Based Shrinkage with RANSAC Refinement for Sparse Time-Frequency Distribution Reconstruction

Vedran Jurdana ()
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Vedran Jurdana: Department of Automation and Electronics, Faculty of Engineering, University of Rijeka, 51000 Rijeka, Croatia

Mathematics, 2025, vol. 13, issue 13, 1-25

Abstract: Compressive sensing in the ambiguity domain facilitates high-performance reconstruction of time-frequency distributions (TFDs) for non-stationary signals. However, identifying the optimal regularization parameter in the absence of prior knowledge remains a significant challenge. The Rényi entropy-based two-step iterative shrinkage/thresholding (RTwIST) algorithm addresses this issue by incorporating local component estimates to guide adaptive thresholding, thereby improving interpretability and robustness. Nevertheless, RTwIST may struggle to accurately isolate components in cases of significant amplitude variations or component intersections. In this work, an enhanced RTwIST framework is proposed, integrating the random sample consensus (RANSAC)-based refinement stage that iteratively extracts individual components and fits smooth trajectories to their peaks. The best-fitting curves are selected by minimizing a dedicated objective function that balances amplitude consistency and trajectory smoothness. Experimental validation on both synthetic and real-world electroencephalogram (EEG) signals demonstrates that the proposed method achieves superior reconstruction accuracy, enhanced auto-term continuity, and improved robustness compared to the original RTwIST and several state-of-the-art algorithms.

Keywords: time-frequency distributions; sparse signal reconstruction; Rényi entropy; compressive sensing; RANSAC (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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