A Robust Estimator-Based Nonlinear Filtering Approach to Piecewise Biosignal Reconstruction

Many biophysical measurements involve source signals possessing piecewise characteristic. Recovery of the piecewise source from the noisy measurements through the linear filtering schemes fails due to the oversmoothing effect at jump discontinuities. Similarly, most of the nonlinear filters underperform at large noise level/outliers. In this paper, we propose a Huberized nonlinear filtering approach, which is penalized by the robust estimators, such as Huber, reversed-Huber (Berhu), and the total variation (TV) functions. By addressing the small residual values quadratically and large ones by their absolute errors, the effectiveness of the proposed methods is enhanced. The hidden sparsity structures of various piecewise signals are exploited. The convexity of the proposed cost functions ensures a global solution. The new approach outperforms the state-of-the-art methods by preserving the smoothness and sharp transitions of piecewise biosignals.