Baseline wander removal for bioelectrical signals by quadratic variation reduction

Abstract

Baseline wander is a low-frequency additive noise affecting almost all bioelectrical signals, in particular the ECG. In this paper, we propose a novel approach to baseline wander estimation and removal for bioelectrical signals, based on the notion of quadratic variation reduction. The quadratic variation is meant as a measure of variability for vectors or sampled functions, and is a consistent measure in this regard. Baseline wander is estimated solving a constrained convex optimization problem where quadratic variation enters as a constraint. The solution depends on a single parameter whose value is not critical, as proven by a sensitivity analysis. Numerical results confirm the effectiveness of the approach, which outperforms state-of-the-art algorithms. The algorithm compares favorably also in terms of computational complexity, which is linear in the size of the vector to detrend. This makes it suitable for real-time applications as well as for applications on devices with reduced computing power, such as handheld devices.