A Robust Multivariate Thresholding Function for Sparse and Biomedical Signal Reconstruction

This paper presents a computationally efficient Multivariate Mixture Model Thresholding (MMMT) technique for sparse signal denoising and recovery, with the goal of improving data quality in modern sensing and biomedical systems. The proposed method extends classical thresholding approaches by modeling nonzero signal coefficients using a multivariate Gaussian mixture prior, thereby capturing cross-channel and intercomponent dependencies commonly observed in multi-sensor and physiological signals. The thresholding rule is analytically derived through maximum a posteriori (MAP) estimation within a majorization-minimization (MM) optimization framework, while the associated model parameters are adaptively estimated using an expectation-maximization (EM) algorithm. Experimental results on noisy sinusoidal signals and synthetic ECG data demonstrate that MMMT consistently achieves higher correlation with ground-truth signals and improved preservation of pulse amplitude and morphological characteristics compared with benchmark methods, including the l1-fused lasso and convex-non-convex (CNC) fused lasso. Quantitative evaluations based on correlation metrics, signal-to-noise ratio (SNR), and peak signal-to-noise ratio (PSNR) further confirm the effectiveness of the proposed approach. Owing to its scalability, robustness, and strong statistical interpretability, MMMT provides a promising framework for real-time ECG signal enhancement. Although the proposed framework is general and can be adapted to other biomedical modalities such as EEG, CT, and MRI, experimental validation in this study is limited to ECG signals.