Transient Artifacts Suppression in Time Series via Convex Analysis
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This book chapter addresses the suppression of transient artifacts in time series data. We categorize the transient artifacts into two general types: spikes and brief waves with zero baseline, and step discontinuities. We propose a sparse-assisted optimization problem for the estimation of signals comprising a low-pass signal, a sparse piecewise constant signal, a piecewise constant signal, and additive white Gaussian noise. For better estimation of the artifacts, in turns better suppression performance, we propose a non-convex generalized conjoint penalty that can be designed to preserve the convexity of the total cost function to be minimized, thereby realizing the benefits of a convex optimization framework (reliable, robust algorithms, etc.). Compared to the conventional use of ℓ1 norm penalty, the proposed non-convex penalty does not underestimate the true amplitude of signal values. We derive a fast proximal algorithm to implement the method. The proposed method is demonstrated on the suppression of artifacts in near-infrared spectroscopic (NIRS) measures.
KeywordsSparse signal processing Fused lasso Non-convex regularization Artifact reduction Convex optimization Morphological component analysis
The authors thank Randall Barbour for important discussions. This work was supported by NSF (grant CCF-1525398).
- 2.Ayaz, H., Izzetoglu, M., Shewokis, P. A., & Onaral, B. (2010). Sliding-window motion artifact rejection for functional near-infrared spectroscopy. In 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology (pp. 6567–6570).Google Scholar
- 4.Bayram, I., Chen, P.-Y., & Selesnick, I. (2014, May). Fused lasso with a non-convex sparsity inducing penalty. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).Google Scholar
- 10.Damon, C., Liutkus, A., Gramfort, A., & Essid, S. (2013). Non-negative matrix factorization for single-channel EEG artifact rejection. In IEEE International Conference on Acoustics, Speech and Signal Processing (pp. 1177–1181).Google Scholar
- 11.Feng, Y., Graber, H., & Selesnick, I. (2018). The suppression of transient artifacts in time series via convex analysis. In 2018 IEEE Signal Processing in Medicine and Biology Symposium (SPMB) (pp. 1–6).Google Scholar
- 21.Parekh, A. & Selesnick, I. W. (2015). Convex fused lasso denoising with non-convex regularization and its use for pulse detection. In IEEE Signal Processing in Medicine and Biology Symposium (SPMB) (pp. 1–6).Google Scholar
- 22.Rockafellar, R. T. (1972). Convex analysis. Princeton: Princeton University Press.Google Scholar