Hassan Gaber, Hosny Khalid M, Fathi Islam S
Department of Computer Science, Faculty of computers and information, Arish University, Al-Arish, 45511, Egypt.
Department of Information Technology, Faculty of Computers and Informatics, Zagazig University, 44519, Zagazig, Egypt.
Sci Rep. 2025 Aug 19;15(1):30337. doi: 10.1038/s41598-025-16086-2.
Orthogonal Tchebichef moments of fractional order (FrTMs) serve as descriptors for signals and images. Many fields, including signal analysis and watermarking, have relied heavily on such moments. This study addresses three critical limitations in existing approaches: the computational burden of higher-order moment calculations, numerical instability affecting reconstruction accuracy, and orthogonality deterioration in large-scale signal processing. Furthermore, using the QR decomposition approach is crucial to maintain the orthogonality of the higher-order moments. We introduce an improved computational framework with three main scientific contributions as development of an optimized set of three interrelated second-order recurrence equations for normalized FrTMs, implementation of the Schwarz-Rutishauser algorithm as an alternative to classical QR decomposition methods, maintaining orthogonality with substantially lower computational overhead; and integration of these innovations into a comprehensive system for biomedical signal reconstruction and watermarking. The method in question was tested on two benchmark datasets the MIT-BIH arrhythmia and CHB-MIT Scalp EEG. The findings indicate that the proposed methodology exhibits significantly higher performance levels than current methodologies, with a 64.3% improvement in PSNR (reaching 147.08 dB compared to 89.74 dB in existing approaches), 89.7% reduction in MSE (0.0092 versus 0.09 average), and 84.1% decrease in bit error rate (0.25 versus 1.57) for watermarking applications. Processing time was also reduced by 64.3% compared to competing methods, making this approach substantially more efficient for implementation in Internet of Healthcare Things (IoHT) contexts.
分数阶正交切比雪夫矩（FrTMs）用作信号和图像的描述符。包括信号分析和水印技术在内的许多领域都严重依赖于此类矩。本研究解决了现有方法中的三个关键局限性：高阶矩计算的计算负担、影响重建精度的数值不稳定性以及大规模信号处理中的正交性退化。此外，使用QR分解方法对于保持高阶矩的正交性至关重要。我们引入了一种改进的计算框架，有三项主要科学贡献，即开发一组优化的、相互关联的二阶递推方程用于归一化FrTMs，实施施瓦茨 - 鲁蒂沙伊泽算法作为经典QR分解方法的替代方法，以显著更低的计算开销保持正交性；以及将这些创新集成到一个用于生物医学信号重建和水印的综合系统中。所讨论的方法在两个基准数据集——麻省理工学院 - 贝斯以色列女执事医疗中心心律失常数据集和CHB - 麻省理工学院头皮脑电图数据集上进行了测试。研究结果表明，所提出的方法表现出比当前方法显著更高的性能水平，在水印应用中，峰值信噪比提高了64.3%（达到147.08 dB，而现有方法为89.74 dB），均方误差降低了89.7%（分别为0.0092和0.09的平均值），误码率降低了84.1%（分别为0.25和1.57）。与竞争方法相比，处理时间也减少了64.3%，这使得该方法在医疗物联网（IoHT）环境中的实施效率大大提高。
