Quaternion singular spectrum analysis of electroencephalogram With application in sleep analysis

A novel quaternion-valued singular spectrum analysis (SSA) is introduced for multichannel analysis of electroencephalogram (EEG). The analysis of EEG typically requires the decomposition of data channels into meaningful components despite the notoriously noisy nature of EEG - which is the aim of SSA. However, the singular value decomposition involved in SSA implies the strict orthogonality of the decomposed components, which may not reflect accurately the sources which exhibit similar neural activities. To allow for the modelling of such co-channel coupling, the quaternion domain is considered for the first time to formulate the SSA using the augmented statistics. As an application, we demonstrate how the augmented quaternion-valued SSA (AQSSA) can be used to extract the sources, even at a signal-to-noise ratio as low as -10 dB. To illustrate the usefulness of our quaternion-valued SSA in a rehabilitation setting, we employ the proposed SSA for sleep analysis to extract statistical descriptors for five-stage classification (Awake, N1, N2, N3 and REM). The level of agreement using these descriptors was 74% as quantified by the Cohen's kappa

Latent variable regression and applications to planetary seismic instrumentation

The work presented in this thesis is framed by the concept of latent variables, a modern data analytics approach. A latent variable represents an extracted component from a dataset which is not directly measured. The concept is first applied to combat the problem of ill-posed regression through the promising method of partial least squares (PLS). In this context the latent variables within a data matrix are extracted through an iterative algorithm based on cross-covariance as an optimisation criterion. This work first extends the PLS algorithm, using adaptive and recursive techniques, for online, non-stationary data applications. The standard PLS algorithm is further generalised for complex-, quaternion- and tensor-valued data. In doing so it is shown that the multidimensional algebras facilitate physically meaningful representations, demonstrated through smart-grid frequency estimation and image-classification tasks. The second part of the thesis uses this knowledge to inform a performance analysis of the MEMS microseismometer implemented for the InSight mission to Mars. This is given in terms of the sensor's intrinsic self-noise, the estimation of which is achieved from experimental data with a colocated instrument. The standard coherence and proposed delta noise estimators are analysed with respect to practical issues. The implementation of algorithms for the alignment, calibration and post-processing of the data then enabled a definitive self-noise estimate, validated from data acquired in ultra-quiet, deep-space environment. A method for the decorrelation of the microseismometer's output from its thermal response is proposed. To do so a novel sensor fusion approach based on the Kalman filter is developed for a full-band transfer-function correction, in contrast to the traditional ill-posed frequency division method. This algorithm was applied to experimental data which determined the thermal model coefficients while validating the sensor's performance at tidal frequencies 1E-5Hz and in extreme environments at -65C. This thesis, therefore, provides a definitive view of the latent variables perspective. This is achieved through the general algorithms developed for regression with multidimensional data and the bespoke application to seismic instrumentation.Open Acces

Face Recognition in Color Using Complex and Hypercomplex Representation

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-540-72847-4_29Color has plenty of discriminative information that can be used to improve the performance of face recognition algorithms, although it is difficult to use it because of its high variability. In this paper we investigate the use of the quaternion representation of a color image for face recognition. We also propose a new representation for color images based on complex numbers. These two color representation methods are compared with the traditional grayscale and RGB representations using an eigenfaces based algorithm for identity verification. The experimental results show that the proposed method gives a very significant improvement when compared to using only the illuminance information.Work supported by the Spanish Project DPI2004-08279-C02-02 and the Generalitat Valenciana - Consellería d’Empresa, Universitat i Ciència under an FPI scholarship.Villegas, M.; Paredes Palacios, R. (2007). Face Recognition in Color Using Complex and Hypercomplex Representation. En Pattern Recognition and Image Analysis: Third Iberian Conference, IbPRIA 2007, Girona, Spain, June 6-8, 2007, Proceedings, Part I. Springer Verlag (Germany). 217-224. https://doi.org/10.1007/978-3-540-72847-4_29S217224Yip, A., Sinha, P.: Contribution of color to face recognition. Perception 31(5), 995–1003 (2002)Torres, L., Reutter, J.Y., Lorente, L.: The importance of the color information in face recognition. In: ICIP, vol. 3, pp. 627–631 (1999)Jones III, C., Abbott, A.L.: Color face recognition by hypercomplex gabor analysis. In: FG2006, University of Southampton, UK, pp. 126–131 (2006)Hamilton, W.R.: On a new species of imaginary quantities connected with a theory of quaternions. In: Proc. Royal Irish Academy, vol. 2, pp. 424–434 (1844)Zhang, F.: Quaternions and matrices of quaternions. Linear Algebra And Its Applications 251(1-3), 21–57 (1997)Pei, S., Cheng, C.: A novel block truncation coding of color images by using quaternion-moment preserving principle. In: ISCAS, Atlanta, USA, vol. 2, pp. 684–687 (1996)Sangwine, S., Ell, T.: Hypercomplex fourier transforms of color images. In: ICIP, Thessaloniki, Greece, vol. 1, pp. 137–140 (2001)Bihan, N.L., Sangwine, S.J.: Quaternion principal component analysis of color images. In: ICIP, Barcelona, Spain, vol. 1, pp. 809–812 (2003)Chang, J.-H., Pei, S.-C., Ding, J.J.: 2d quaternion fourier spectral analysis and its applications. In: ISCAS, Vancouver, Canada, vol. 3, pp. 241–244 (2004)Li, S.Z., Jain, A.K.: 6. In: Handbook of Face Recognition. Springer (2005)Gross, R., Brajovic, V.: An image preprocessing algorithm for illumination invariant face recognition. In: Kittler, J., Nixon, M.S. (eds.) AVBPA 2003. LNCS, vol. 2688, p. 1055. Springer, Heidelberg (2003)Lee, K., Ho, J., Kriegman, D.: Nine points of light: Acquiring subspaces for face recognition under variable lighting. In: CVPR, vol. 1, pp. 519–526 (2001)Zhang, L., Samaras, D.: Face recognition under variable lighting using harmonic image exemplars. In: CVPR, vol. 1, pp. 19–25 (2003)Villegas, M., Paredes, R.: Comparison of illumination normalization methods for face recognition. In: COST 275, University of Hertfordshire, UK, pp. 27–30 (2005)Turk, M., Pentland, A.: Face recognition using eigenfaces. In: CVPR, Hawaii, pp. 586–591 (1991)Bihan, N.L., Mars, J.: Subspace method for vector-sensor wave separation based on quaternion algebra. In: EUSIPCO, Toulouse, France (2002)XM2VTS (CDS00{1,6}), http://www.ee.surrey.ac.uk/Reseach/VSSP/xm2vtsdbLuettin, J., Maître, G.: Evaluation protocol for the extended M2VTS database (XM2VTSDB). IDIAP-COM 05, IDIAP (1998

1999 Flight Mechanics Symposium

This conference publication includes papers and abstracts presented at the Flight Mechanics Symposium held on May 18-20, 1999. Sponsored by the Guidance, Navigation and Control Center of Goddard Space Flight Center, this symposium featured technical papers on a wide range of issues related to orbit-attitude prediction, determination, and control; attitude sensor calibration; attitude determination error analysis; attitude dynamics; and orbit decay and maneuver strategy. Government, industry, and the academic community participated in the preparation and presentation of these papers

Maximizing the Number of Spatial Nulls with Minimum Sensors

In this paper, we attempt to unify two array processing frameworks viz, Acoustic Vector Sensor (AVS) and two level nested array to enhance the Degrees of Freedom (DoF) significantly beyond the limit that is attained by a Uniform Linear Hydrophone Array (ULA) with specified number of sensors. The major focus is to design a line array architecture which provides high resolution unambiguous bearing estimation with increased number of spatial nulls to mitigate the multiple interferences in a deep ocean scenario. AVS can provide more information about the propagating acoustic field intensity vector by simultaneously measuring the acoustic pressure along with tri-axial particle velocity components. In this work, we have developed Nested AVS array (NAVS) ocean data model to demonstrate the performance enhancement. Conventional and MVDR spatial filters are used as the response function to evaluate the performance of the proposed architecture. Simulation results show significant improvement in performance viz, increase of DoF, and localization of more number of acoustic sources and high resolution bearing estimation with reduced side lobe level

Wavefield characteristics and spatial incoherency - a comparative study from Argostoli rock- and soil-site dense seismic arrays

International audienceThe current article presents the results from the analysis of the seismic events recorded from a dense array located on a rock site at Argostoli, Cephalonia Island, Greece. The objective of the study is to explore to what extent the non-direct, diffracted surface waves influence the seismic wavefield at a rock site, to investigate the loss of coherency of ground motions and to compare the results with those from a previously studied similar array located at an adjacent small, shallow sedimentary valley. The array consists of 21 velocimeters encompassing a central station in four concentric circles with diameters 20, 60, 180 and 360 m. The analyzed seismic dataset includes 40 events with magnitudes ranging from 2 to 5 and epicentral distance up to 200 km. MUSIQUE algorithm has been used to analyze the seismic wavefield by extracting the backazimuth and slowness of the dominant incoming waves and identifying the Love and Rayleigh waves. Lagged coherency has been estimated for all the available station pairs in the array and the results from the entire dataset have been averaged at four separation distance intervals, 10-20, 20-30, 30-40, 80-90 m. The results were also compared with those from a similar array located on an adjacent small, shallow sedimentary valley. The analysis suggests that about 20percent energy of the wavefield could be characterized as diffracted Love and Rayleigh waves, primarily arriving from the north-east and north-south directions, respectively. The spatial coherency estimations at the rock site are, generally, observed to be larger than those from the sedimentary array, especially at frequencies below 5 Hz. The directionality of coherency estimates observed from the soil array is absent in case of the rock array data. Comparison with the widely-quoted parametric models reveals that there is little correlation between the decay of coherency observed at the rock site and the models. The significant difference observed between the results of the rock and soil array indicate that the spatial incoherency is largely site dependent and could be potentially associated with the formation of locally generated wavefiel