Signal Processing - January 2016 - 36

National Science Foundation (NSF) (BCS 1262297), and the U.S.
Department of Defense (W81XWH-13-1-0494). Zhe Chen was sup-
ported by a Collaborative Research in Computational Neurosci-
ence Award (1307645) from the U.S. NSF.
autHors
Wei Wu (wwumed@stanford.edu) is with the School of Automa-
tion Science and Engineering, South China University of Technol-
ogy, Guangzhou, and the Department of Psychiatry and
Behavioral Sciences, Stanford University, California. He is a Mem-
ber of the IEEE.
Srikantan Nagarajan (sri@ucsf.edu) is with the Department of
Radiology and Biomedical Imaging, University of California at San
Francisco. He is a Senior Member of the IEEE.
Zhe Chen (zhe.chen3@nyumc.org) is with the Department of
Psychiatry, Neuroscience, and Physiology, School of Medicine, New
York University. He is a Senior Member of the IEEE.
rEFErEncEs

[1] S. Baillet, J. C. Mosher, and R. M. Leahy, "Electromagnetic brain mapping,"
IEEE Signal Processing. Mag., vol. 18, no. 6, pp. 14-30, 2001.
[2] S. Sanei and J. A. Chambers, EEG Signal Processing. Hoboken, NJ: Wiley, 2007.
[3] C. Lamus, M. S. Hämäläinen, S. Temereanca, E. N. Brown, and P. L. Purdon,
"A spatiotemporal dynamic distributed solution to the MEG inverse problem," Neuroimage, vol. 63, no. 2, pp. 894-909, 2012.
[4] K. Friston, L. Harrison, J. Daunizeau, S. Kiebel, C. Phillips, N. Trujillo-Bar-
reto, R. Henson, G. Flandin et al., "Multiple sparse priors for the M/EEG inverse
problem," Neuroimage, vol. 39, no. 3, pp. 1104-1120, 2008.
[5] A. Bolstad, B. V. Veen, and R. Nowak, "Space-time event sparse penalization for
magneto-/electro-encephalography," Neuroimage, vol. 46, no. 4, pp. 1066-1081, 2009.
[6] K. J. Friston, W. Penny, C. Phillips, S. Kiebel, G. Hinton, and J. Ashburner,
"Classical and Bayesian inference in neuroimaging: Theory," Neuroimage, vol. 16,
no. 2, pp. 465-483, 2002.
[7] J. Mattout, C. Phillips, W. D. Penny, M. D. Rugg, and K. J. Friston, "MEG source
localization under multiple constraints: an extended Bayesian framework," Neuroimage, vol. 30, no. 3, pp. 753-767, 2006.
[8] M. W. Seeger and D. P. Wipf, "Variational Bayesian inference techniques," IEEE
Signal Processing. Mag., vol. 27, no. 6, pp. 81-91, 2010.
[9] D. P. Wipf, B. D. Rao, and S. Nagarajan, "Latent variable Bayesian models for
promoting sparsity," IEEE Trans. Inf. Theory, vol. 57, no. 9, pp. 6236-6255, 2011.
[10] D. P. Wipf and S. Nagarajan, "A unified Bayesian framework for MEG/EEG
source imaging," Neuroimage, vol. 44, no. 3, pp. 947-966, 2009.
[11] C. P. Robert, The Bayesian Choice: From Decision-Theoretic Foundations to
Computational Implementation, 2nd ed. New York: Springer-Verlag, 2007.
[12] W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, Markov Chain Monte
Carlo in Practice. London: Chapman & Hall/CRC, 1995.
[13] S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions, and the
Bayesian restoration of images," IEEE Trans. Pattern Anal. Mach. Intell, vol. 6,
no. 6, pp. 721-741, 1984.
[14] T. Marshall and G. Roberts, "An adaptive approach to Langevin MCMC," Stat.
Comput., vol. 22, no. 5, pp. 1041-1057, 2012.
[15] H. Attias, "Independent factor analysis," Neural Comput., vol. 11, no. 4,
pp. 803-851, 1999.
[16] B. Blankertz, R. Tomioka, S. Lemm, M. Kawanabe, and K. R. Müller, "Opti-
mizing spatial filters for robust EEG single-trial analysis," IEEE Signal Processing.
Mag., vol. 25, no. 1, pp. 41-56, 2008.
[17] W. Wu, Z. Chen, X. Gao, Y. Li, E. Brown, and S. Gao, "Probabilistic common
spatial patterns for multichannel EEG analysis," IEEE Trans. Pattern Anal. Mach.
Intell., vol. 37, no. 3, pp. 639-653, 2015.
[18] H. Kang and S. Choi, "Bayesian common spatial patterns with Dirichlet pro-
cess priors for multi-subject EEG classification," in Proc. Int. Joint Conf. Neural
Networks (IJCNN), 2012, pp. 1-6.
[19] W. Wu, Z. Chen, S. Gao, and E. N. Brown, "A hierarchical Bayesian approach
for learning sparse spatio-temporal decompositions of multichannel EEG," Neuroimage, vol. 56, no. 4, pp. 1929-1945, 2011.
[20] J. M. Zumer, H. T. Attias, K. Sekihara, and S. S. Nagarajan, "A probabilistic
algorithm integrating source localization and noise suppression for MEG and EEG
data," Neuroimage, vol. 37, no. 1, pp. 102-115, 2007.
[21] J. Sarvas, "Basic mathematical and electromagnetic concepts of the biomag-
netic inverse problem," Phys. Med. Biol., vol. 32, no. 1, pp. 11-22, 1987.

[22] S. S. Nagarajan, H. T. Attias, K. E. H. II, and K. Sekihara, "A graphical
model for estimating stimulus-evoked brain responses from magnetoencepha-
lography data with large background brain activity," Neuroimage, vol. 30, no. 2,
pp. 400-416, 2006.
[23] V. Litvak and K. Friston, "Electromagnetic source reconstruction for group
studies," Neuroimage, vol. 42, no. 4, pp. 1490-1498, 2008.
[24] J. D. López, V. Litvak, J. J. Espinosa, K. Friston, and G. R. Barnes, "Algorith-
mic procedures for Bayesian MEG/EEG source reconstruction in SPM," Neuroimage, vol. 84, pp. 476-487, Jan., 2014.
[25] E. J. Candes and M. B. Wakin, "An introduction to compressive sampling,"
IEEE Signal Processing. Mag., vol. 25, no. 2, pp. 21-30, 2008.
[26] Y. Li, Z. Yu, N. Bi, Y. Xu, Z. Gu, and S. I. Amari, "Sparse representation for
brain signal processing: A tutorial on methods and applications," IEEE Signal Processing. Mag., vol. 31, no. 3, pp. 96-106, 2014.
[27] S. Ji, Y. Xue, and L. Carin, "Bayesian compressive sensing," IEEE Trans. Signal
Processing, vol. 56, no. 6, pp. 2346-2356, 2008.
[28] D. P. Wipf and S. Nagarajan, "A new view of automatic relevance determination," in
Proc. Advances in Neural Information Processing Systems, 2008, vol. 20, pp. 1625-1632.
[29] W. Wu, C. Wu, S. Gao, B. Liu, Y. Li, and X. Gao, "Bayesian estimation of ERP
components from multicondition and multichannel EEG," Neuroimage, vol. 88,
pp. 319-339, Mar., 2014.
[30] S. S. Nagarajan, H. T. Attias, K. E. Hild, and K. Sekihara, "A probabilistic
algorithm for robust interference suppression in bioelectromagnetic sensor data,"
Stat. Med., vol. 26, no. 21, pp. 3886-910, 2007.
[31] D. P. Wipf, J. P. Owen, H. T. Attias, K. Sekihara, and S. S. Nagarajan,
"Robust Bayesian estimation of the location, orientation, and time course of
multiple correlated neural sources using MEG," Neuroimage, vol. 49, no. 1,
pp. 641-655, 2010.
[32] Z. Ghahramani, "Bayesian non-parametrics and the probabilistic approach to
modelling," Philos. Trans. R. Soc. A, vol. 371, no. 1984, p. 20110553, 2013.
[33] C. E. Rasmussen and C. Williams, Gaussian Processes for Machine Learning.
Cambridge, MA: MIT Press, 2005.
[34] N. L. Hjort, C. Holmes, P. Mülcer, and S. G. Walker, Eds., Bayesian Nonparametrics. Cambridge, UK: Cambridge Univ. Press, 2010.
[35] C. J. Paciorek and M. J. Schervish, "Nonstationary covariance functions for
Gaussian process regression," in Proc. Advances in Neural Information Processing Systems, 2004, vol. 16, pp. 273-280.
[36] S. Faul, G. Gregorcic, G. Boylan, W. Marnane, G. Lightbody, and S. Connolly,
"Gaussian process modeling of EEG for the detection of neonatal seizure," IEEE
Trans. Biomed. Eng., vol. 54, no. 12, pp. 2151-2162, 2007.
[37] M. Zhong, F. Lotte, M. Girolami, and A. Lecuyer, "Classifying EEG for brain
computer interfaces using Gaussian process," Pattern Recognit. Lett., vol. 29,
no. 3, pp. 354-359, 2008.
[38] A. Fyshe, E. Fox, D. Dunson, and T. Mitchell, "Hierarchical latent dictionaries
for models of brain activation," in Proc. 15th Int. Conf. Artificial Intelligence and
Statistics (AISTATS), 2012, pp. 409-421.
[39] H. Kang and S. Choi, "Bayesian common spatial patterns for multi-subject
EEG classification," Neural Netw., vol. 57, pp. 39-50, Sept. 2014.
[40] A. Ossadtchi, S. Baillet, J. C. Mosher, D. Thyerlei, W. Sutherling, and
R. M. Leahy, "Automated interictal spike detection and source localization in mag-
netoencephalography using independent components analysis and spatio-temporal
clustering," Clin. Neurophysiol., vol. 115, no. 3, pp. 508-522, 2004.
[41] J. P. Owen, D. P. Wipf, H. T. Attias, K. Sekihara, and S. S. Nagarajan, "Perfor-
mance evaluation of the CHAMPAGNE source reconstruction algorithm on simu-
lated and real M/EEG data," Neuroimage, vol. 60, no. 1, pp. 305-323, 2012.
[42] R. N. Henson, G. Flandin, K. J. Friston, and J. Mattout, "A parametric empiri-
cal Bayesian framework for fMRI-constrained MEG/EEG source reconstruction,"
Hum. Brain Mapp., vol. 31, no. 10, pp. 1512-1531, 2010.
[43] S. J. Kiebel, M. I. Garrido, R. Moran, C. Chen, and K. J. Friston, "Dynamic causal
modeling for EEG and MEG," Hum. Brain Mapp., vol. 30, no. 6, pp. 1866-1876, 2009.
[44] Z. Zhang, T. Jung, S. Makeig, and B. D. Rao, "Compressed sensing of EEG for
wireless telemonitoring with low energy consumption and inexpensive hardware,"
IEEE Trans. Biomed. Eng., vol. 60, no. 1, pp. 221-224, 2013.
[45] D. Heckerman, "A tutorial on learning with Bayesian networks," in Learning in
Graphical Models, M. I. Jordan, Ed. Cambridge, MA: MIT Press, 1999, pp. 301-354.
[46] J. Lee and T. Hastie, "Structure learning of mixed graphical models," in Proc.
16th Int. Conf. Artificial Intelligence and Statistics, 2013, pp. 388-396.
[47] B. Babdi, G. Obregon-Henao, C. Lamus, M. S. Hämäläinen, E. N. Brown, and
P. L. Purdon, "A subspace pursuit-based iterative greedy hierarchical solution to the
neuromagnetic inverse problem." Neuroimage, vol. 87, pp. 427-443, Feb., 2014.
[48] H. Cecotti and A. Graser, "Convolutional neural networks for P300 detection
with application to brain-computer interfaces," IEEE Trans. Pattern Anal. Mach.
Intell., vol. 33, no. 3, pp. 433-445, 2011.
[49] L. Deng and D. Yu, "Deep learning: methods and applications," Found. Trends
Signal Processing, vol. 7, no. 3-4, pp. 197-387, 2014.
[50] E. Pan and Z. Han. (2014). Non-parametric Bayesian learning with deep
learning structure and its application in wireless network. [Online]. Available:
https://arxiv.org/pdf/1410.4599v2.pdf

IEEE SIGNAL PROCESSING MAGAZINE [36] jANuARy 2016

[SP]
https://www.arxiv.org/pdf/1410.4599v2.pdf
Table of Contents for the Digital Edition of Signal Processing - January 2016
