Research on ECG signal reconstruction based on improved weighted nuclear norm minimization and approximate message passing algorithm

Bing Zhang; Xishun Zhu; Fadia Ali Khan; Sajjad Shaukat Jamal; Alanoud Al Mazroa; Rab Nawaz

doi:10.3389/fninf.2024.1454244

Research on ECG signal reconstruction based on improved weighted nuclear norm minimization and approximate message passing algorithm

Front Neuroinform. 2024 Oct 8:18:1454244. doi: 10.3389/fninf.2024.1454244. eCollection 2024.

Authors

Bing Zhang¹, Xishun Zhu², Fadia Ali Khan³, Sajjad Shaukat Jamal⁴, Alanoud Al Mazroa⁵, Rab Nawaz⁶

Affiliations

¹ School of Intelligent Manufacturing, Nanyang Institute of Technology, Nanyang, Henan, China.
² School of Mathematics and Statistics, Hainan Normal University, Haikou, China.
³ Department of Computer Science, HITEC University, Taxila, Pakistan.
⁴ Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia.
⁵ Department of Information Systems, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
⁶ School of Computer Science and Electronic Engineering, University of Essex, Colchester, United Kingdom.

Abstract

In order to improve the energy efficiency of wearable devices, it is necessary to compress and reconstruct the collected electrocardiogram data. The compressed data may be mixed with noise during the transmission process. The denoising-based approximate message passing (AMP) algorithm performs well in reconstructing noisy signals, so the denoising-based AMP algorithm is introduced into electrocardiogram signal reconstruction. The weighted nuclear norm minimization algorithm (WNNM) uses the low-rank characteristics of similar signal blocks for denoising, and averages the signal blocks after low-rank decomposition to obtain the final denoised signal. However, under the influence of noise, there may be errors in searching for similar blocks, resulting in dissimilar signal blocks being grouped together, affecting the denoising effect. Based on this, this paper improves the WNNM algorithm and proposes to use weighted averaging instead of direct averaging for the signal blocks after low-rank decomposition in the denoising process, and validating its effectiveness on electrocardiogram signals. Experimental results demonstrate that the IWNNM-AMP algorithm achieves the best reconstruction performance under different compression ratios and noise conditions, obtaining the lowest PRD and RMSE values. Compared with the WNNM-AMP algorithm, the PRD value is reduced by 0.17∼4.56, the P-SNR value is improved by 0.12∼2.70.

Keywords: ECG; approximate message passing algorithm; compressed sensing; non-local similarity; weighted nuclear norm minimization.

Grants and funding

The authors declare that financial support was received for the research, authorship, and/or publication of this article. This work was supported by the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP 2/30/45, the National Natural Science Foundation of China (Grant No. 61863027), the Doctoral Research Startup Fund (Grant No. NGBJ-2024-02).