The Suppression of Transient Artifacts in Time Series via Convex Analysis

For the suppression of transient artifacts in time series data, we propose a non-convex generalized fused lasso penalty for the estimation of signals comprising a low-pass signal, a sparse piecewise constant signal, and additive white Gaussian noise. The proposed non-convex penalty is designed so as 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.

[1]  Antoine Liutkus,et al.  Non-negative matrix factorization for single-channel EEG artifact rejection , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[2]  Ivan W. Selesnick,et al.  Simultaneous Low-Pass Filtering and Total Variation Denoising , 2014, IEEE Transactions on Signal Processing.

[3]  R. Tibshirani,et al.  Sparsity and smoothness via the fused lasso , 2005 .

[4]  Laurent Condat,et al.  A Direct Algorithm for 1-D Total Variation Denoising , 2013, IEEE Signal Processing Letters.

[5]  Amir Rastegarnia,et al.  Artifact characterization and removal for in vivo neural recording , 2014, Journal of Neuroscience Methods.

[6]  Tong Zhang,et al.  Transient Artifact Reduction Algorithm (TARA) Based on Sparse Optimization , 2014, IEEE Transactions on Signal Processing.

[7]  O. Scherzer.  Handbook of mathematical methods in imaging , 2011 .

[8]  David A. Boas,et al.  A Systematic Comparison of Motion Artifact Correction Techniques for Functional Near-Infrared Spectroscopy , 2012, Front. Neurosci..

[9]  Mila Nikolova,et al.  Energy Minimization Methods , 2015, Handbook of Mathematical Methods in Imaging.

[10]  M. Calkins,et al.  The misclassification of blinks as saccades: implications for investigations of eye movement dysfunction in schizophrenia. , 2001, Psychophysiology.

[11]  Harry L Graber,et al.  Optomechanical imaging system for breast cancer detection. , 2011, Journal of the Optical Society of America. A, Optics, image science, and vision.

[12]  Andrew Blake,et al.  Visual Reconstruction , 1987, Deep Learning for EEG-Based Brain–Computer Interfaces.

[13]  D. Donoho,et al.  Redundant Multiscale Transforms and Their Application for Morphological Component Separation , 2004 .

[14]  Heinz H. Bauschke,et al.  Convex Analysis and Monotone Operator Theory in Hilbert Spaces , 2011, CMS Books in Mathematics.

[15]  Martin Wolf,et al.  A New Approach for Automatic Removal of Movement Artifacts in Near-Infrared Spectroscopy Time Series by Means of Acceleration Data , 2015, Algorithms.

[16]  Ivan W. Selesnick,et al.  Fused lasso with a non-convex sparsity inducing penalty , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[17]  Meltem Izzetoglu,et al.  Motion artifact cancellation in NIR spectroscopy using Wiener filtering , 2005, IEEE Transactions on Biomedical Engineering.

[18]  Ivan W. Selesnick,et al.  Sparse Regularization via Convex Analysis , 2017, IEEE Transactions on Signal Processing.

[19]  Thomas Strömberg.  The operation of infimal convolution , 1996 .

[20]  G. Dumont,et al.  Wavelet based motion artifact removal for Functional Near Infrared Spectroscopy , 2010, 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology.

[21]  R. Tibshirani,et al.  PATHWISE COORDINATE OPTIMIZATION , 2007, 0708.1485.

[22]  M Wolf,et al.  How to detect and reduce movement artifacts in near-infrared imaging using moving standard deviation and spline interpolation , 2010, Physiological measurement.

[23]  Toshihisa Tanaka,et al.  Artifact suppression from EEG signals using data adaptive time domain filtering , 2012, Neurocomputing.

[24]  Meryem A Yücel,et al.  Motion artifact detection and correction in functional near-infrared spectroscopy: a new hybrid method based on spline interpolation method and Savitzky–Golay filtering , 2018, Neurophotonics.

[25]  Ivan W. Selesnick,et al.  Sparsity-Inducing Nonconvex Nonseparable Regularization for Convex Image Processing , 2019, SIAM J. Imaging Sci..

[26]  I. Selesnick,et al.  Convex fused lasso denoising with non-convex regularization and its use for pulse detection , 2015, 2015 IEEE Signal Processing in Medicine and Biology Symposium (SPMB).