A novel TCP-PD framework: discrete orthogonal polynomial-based compressed sensing for EOG signal compression in IoT-based healthcare

Remote healthcare monitoring systems face significant challenges in managing the substantial data volumes generated by continuous physiological signal acquisition on battery-powered wearable Internet of Things (IoT) devices. This paper introduces a novel Tchebichef–Compressed Sensing–Primal–Dual (TCP-PD) framework for electrooculogram (EOG) signal compression in IoT-based healthcare applications. Unlike conventional compressed sensing approaches that rely on Fourier- or wavelet-based sparsifying transforms, the proposed methodology employs discrete Tchebichef polynomials, exploiting their inherently discrete formulation and superior energy compaction properties on EOG signals. The TCP-PD framework integrates Gaussian random measurement matrices that satisfy the Restricted Isometry Property with an optimized primal–dual reconstruction algorithm enhanced by a backtracking line search. A comprehensive evaluation on the Sleep-EDF and DROZY databases shows that the proposed method achieves a 70% compression ratio while maintaining a percent root-mean-square difference of 3.35%, a signal-to-noise ratio of 29.50 dB, and a correlation coefficient of 0.988. Comparative analysis indicates a 13.4% reduction in reconstruction error relative to wavelet-based approaches and a 40–57% improvement over traditional compression techniques. Feature-preservation analysis further confirms that blink detection (F1 score = 0.987) and saccade-timing accuracy (mean error = 4.8 ms) remain intact. A processing time of 11.3 ms per segment, together with a 70% reduction in wireless transmission energy, confirms the suitability of the framework for real-time deployment on resource-constrained wearable healthcare devices.