Optimized Biosignals Decomposition and Denoising using Schrodinger Operator

Abstract
In this paper, a signal reconstruction and denoising algorithm is proposed based on quantum signal processing. This algorithm is based on semi-classical signal analysis (SCSA). The SCSA consists of decomposing the pulse-shaped signal into the sum of weighted squared eigenfunctions of the negative spectrum of the Schrodinger operator. As the Schrodinger operator is nonlinear, the main challenge of this method is to find the optimal value of its parameter that ensures faithful signal reconstruction and denoising using iterative optimization. In this work, we propose the use of an optimized search algorithm to find this optimal parameter of the SCSA algorithm with less information loss and in a short time. It is based on dynamically narrowing down the initial search interval by taking into consideration the SCSA properties related to the reconstructed signal energy or the number of eigenfunctions. This process is repeated using a finer search internal until finding a suitable number of eigenfunctions for optimal reconstruction and denoising. The proposed algorithm shows encouraging results for different types of academic and biomedical signals compared to the grid search algorithm. This work will help in exploring the SCSA method for feature generation with easy implementation for future biomedical applications. A graphical user interface of the proposed algorithm is available for public use on https://github.com/EMANG-KAUST/SCSA-reconstruction.

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