An efficient computation of discrete orthogonal moments for bio-signals reconstruction

Abstract

Bio-signals are extensively used in diagnosing many diseases in wearable devices. In signal processing, signal reconstruction is one of the essential applications. Discrete orthogonal moments (DOMs) are effective analysis tools for signals that can extract digital information without redundancy. The propagation of numerical errors is a significant challenge for the computation of DOMs at high orders. This problem damages the orthogonality property of these moments, which restricts the ability to recover the signal's distinct and unique components with no redundant information. This paper proposes a stable computation of DOMs based on QR decomposition methods: the Gram–Schmidt, Householder, and Given Rotations methods. It also presents a comparative study on the performance of the types of moments: Tchebichef, Krawtchouk, Charlier, Hahn, and Meixner moments. The proposed algorithm's evaluation is done using the MIT-BIH arrhythmia dataset in terms of mean square error and peak signal to noise ratio. The results demonstrate the superiority of the proposed method in computing DOMs, especially at high moment orders. Moreover, the results indicate that the Householder method outperforms Gram–Schmidt and Given Rotations methods in execution time and reconstruction quality. The comparative results show that Tchebichef, Krawtchouk, and Charlier moments have superior reconstruction quality than Hahn and Meixner moments, and Tchebichef generally has the highest performance in signal reconstruction.

Efficient Analysis of Large-Size Bio-Signals Based on Orthogonal Generalized Laguerre Moments of Fractional Orders and Schwarz–Rutishauser Algorithm

“…The results also outperform the introduced algorithm compared to FrGLMs-HM at each order in terms of PSNR and MSE. A comparative investigation of other existing algorithms [8,18,20,36] in reconstruction quality is summarized in Table 4. Figures 7 and 8 A comparative investigation of other existing algorithms [8,18,20,36] in reconstruction quality is summarized in Table 4.…”

“…Hosny et al [15] suggested an efficient Algorithm for the compression of different types of bio-medical signals based on discrete Tchebichef moments and the Artificial Bee Colony (ABC). Fathi et al [16][17][18] introduced different algorithms based on different types of DOMs for the efficient energy compression of bio-medical signals: ECG and FPCG. Such algorithms reveal high superiority concerning remote healthcare monitoring systems.…”

“…Also, to overcome the highly time-consuming problem, they used a recurrence formula based on a normalization factor. The third problem vanished using the most common QR decomposition algorithms: the Gram-Schmidt Method (GSM), Householder Method (HM), and Given Rotations Method (GRM) [18].…”

An efficient compression technique for Foetal phonocardiogram signals in remote healthcare monitoring systems

“…The STM32f429 discovery system comprises an ARM Cortex-M4base 32-bit microcontroller from STMicroelectronics. It operates at a maximum frequency of 180 MHz, which this study utilizes for data compression [27]. The development board offers a direct memory access technique (DMA) for fPCG measuring devices accessing memory directly.…”

“…The superiority in Compression time, Compression speed, and computational efficiency are thanks to using a recurrence relation completely independent of Charlier polynomials computation, which is no longer dependent on the factorial and power functions. In addition, using HOM in the proposed algorithm leads to speeding the compression, which is considered the best way of QR decomposition in signal reconstruction quality and execution time [27].…”