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.