Unsupervised denoising of the non-invasive fetal electrocardiogram with sparse domain Kalman filtering and vectorcardiographic loop alignment.

Objective.Even though the electrocardiogram (ECG) has potential to be used as a monitoring or diagnostic tool for fetuses, the use of non-invasive fetal ECG is complicated by relatively high amounts of noise and fetal movement during the measurement. Moreover, machine learning-based solutions to this problem struggle with the lack of clean reference data, which is difficult to obtain. To solve these problems, this work aims to incorporate fetal rotation correction with ECG denoising into a single unsupervised end-to-end trainable method.Approach.This method uses the vectorcardiogram (VCG), a three-dimensional representation of the ECG, as an input and extends the previously introduced Kalman-LISTA method with a Kalman filter for the estimation of fetal rotation, applying denoising to the rotation-corrected VCG.Main results.The resulting method was shown to outperform denoising auto-encoders by more than 3 dB while achieving a rotation tracking error of less than 33∘. Furthermore, the method was shown to be robust to a difference in signal to noise ratio between electrocardiographic leads and different rotational velocities.Significance.This work presents a novel method for the denoising of non-invasive abdominal fetal ECG, which may be trained unsupervised and simultaneously incorporates fetal rotation correction. This method might prove clinically valuable due the denoised fetal ECG, but also due to the method's objective measure for fetal rotation, which in turn might have potential for early detection of fetal complications.

Deep Learing for Sparse Domain Kalman Filtering With Applications on ECG Denoising and Motility Estimation.

OBJECTIVE: The reconstruction of an input based on a sparse combination of signals, known as sparse coding, has found widespread use in signal processing. In this work, the combination of sparse coding with Kalman filtering is explored and its potential is shown on two use-cases. METHODS: This work extends the Iterative Shrinkage and Thresholding Algorithm with a Kalman filter in the sparse domain. The resulting method may be implemented as a deep unfolded neural network and may be applied to any signal which has a sparse representation and a known or assumed relation between consecutive measurements. This method is evaluated on the use cases of noise reduction in the electrocardiogram (ECG) and the estimation of object motility. RESULTS: For ECG denoising, the proposed method achieved an improvement in Signal-to-Noise ratio of 18.6 dB, which is comparable to state-of-the-art. In motility estimation, a correlation of 0.84 with ground truth simulations was found. CONCLUSION: The proposed method was shown to have advantages over sparse coding and Kalman filtering alone. Due to the low complexity and high generalizability of the proposed method, the implementation of context-specific knowledge or an extension to other applications can be readily made. SIGNIFICANCE: The presented Kalman-ISTA algorithm is a resource-efficient method combining the promise of both sparse coding and Kalman filtering, making it well-suited for various applications.