Adaptive signal processing algorithms for noncircular complex data

The complex domain provides a natural processing framework for a large class of signals encountered in communications, radar, biomedical engineering and renewable energy. Statistical signal processing in C has traditionally been viewed as a straightforward extension of the corresponding algorithms in the real domain R, however, recent developments in augmented complex statistics show that, in general, this leads to under-modelling. This direct treatment of complex-valued signals has led to advances in so called widely linear modelling and the introduction of a generalised framework for the differentiability of both analytic and non-analytic complex and quaternion functions. In this thesis, supervised and blind complex adaptive algorithms capable of processing the generality of complex and quaternion signals (both circular and noncircular) in both noise-free and noisy environments are developed; their usefulness in real-world applications is demonstrated through case studies. The focus of this thesis is on the use of augmented statistics and widely linear modelling. The standard complex least mean square (CLMS) algorithm is extended to perform optimally for the generality of complex-valued signals, and is shown to outperform the CLMS algorithm. Next, extraction of latent complex-valued signals from large mixtures is addressed. This is achieved by developing several classes of complex blind source extraction algorithms based on fundamental signal properties such as smoothness, predictability and degree of Gaussianity, with the analysis of the existence and uniqueness of the solutions also provided. These algorithms are shown to facilitate real-time applications, such as those in brain computer interfacing (BCI). Due to their modified cost functions and the widely linear mixing model, this class of algorithms perform well in both noise-free and noisy environments. Next, based on a widely linear quaternion model, the FastICA algorithm is extended to the quaternion domain to provide separation of the generality of quaternion signals. The enhanced performances of the widely linear algorithms are illustrated in renewable energy and biomedical applications, in particular, for the prediction of wind profiles and extraction of artifacts from EEG recordings

A Unifying Approach to Quaternion Adaptive Filtering: Addressing the Gradient and Convergence

A novel framework for a unifying treatment of quaternion valued adaptive filtering algorithms is introduced. This is achieved based on a rigorous account of quaternion differentiability, the proposed I-gradient, and the use of augmented quaternion statistics to account for real world data with noncircular probability distributions. We first provide an elegant solution for the calculation of the gradient of real functions of quaternion variables (typical cost function), an issue that has so far prevented systematic development of quaternion adaptive filters. This makes it possible to unify the class of existing and proposed quaternion least mean square (QLMS) algorithms, and to illuminate their structural similarity. Next, in order to cater for both circular and noncircular data, the class of widely linear QLMS (WL-QLMS) algorithms is introduced and the subsequent convergence analysis unifies the treatment of strictly linear and widely linear filters, for both proper and improper sources. It is also shown that the proposed class of HR gradients allows us to resolve the uncertainty owing to the noncommutativity of quaternion products, while the involution gradient (I-gradient) provides generic extensions of the corresponding real- and complex-valued adaptive algorithms, at a reduced computational cost. Simulations in both the strictly linear and widely linear setting support the approach

Quaternion Matrices : Statistical Properties and Applications to Signal Processing and Wavelets

Similarly to how complex numbers provide a possible framework for extending scalar signal processing techniques to 2-channel signals, the 4-dimensional hypercomplex algebra of quaternions can be used to represent signals with 3 or 4 components. For a quaternion random vector to be suited for quaternion linear processing, it must be (second-order) proper. We consider the likelihood ratio test (LRT) for propriety, and compute the exact distribution for statistics of Box type, which include this LRT. Various approximate distributions are compared. The Wishart distribution of a quaternion sample covariance matrix is derived from first principles. Quaternions are isomorphic to an algebra of structured 4x4 real matrices. This mapping is our main tool, and suggests considering more general real matrix problems as a way of investigating quaternion linear algorithms. A quaternion vector autoregressive (VAR) time-series model is equivalent to a structured real VAR model. We show that generalised least squares (and Gaussian maximum likelihood) estimation of the parameters reduces to ordinary least squares, but only if the innovations are proper. A LRT is suggested to simultaneously test for quaternion structure in the regression coefficients and innovation covariance. Matrix-valued wavelets (MVWs) are generalised (multi)wavelets for vector-valued signals. Quaternion wavelets are equivalent to structured MVWs. Taking into account orthogonal similarity, all MVWs can be constructed from non-trivial MVWs. We show that there are no non-scalar non-trivial MVWs with short support [0,3]. Through symbolic computation we construct the families of shortest non-trivial 2x2 Daubechies MVWs and quaternion Daubechies wavelets.Open Acces

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

DEVELOPMENT OF THE NASA CELESTIAL NAVIGATION METHOD FOR DYNAMIC EXTRATERRESTRIAL SURFACE NAVIGATION

The Celestial Navigation (CelNav) method was developed in conjunction with NASA Goddard Space Flight Center, to provide accurate location data for extraterrestrial surface navigation without the use of a global positioning system (GPS) or a ground/relay station. CelNav is a minimal sensor/power solution originally developed for static Lunar surface navigation. However, dynamic navigation via CelNav requires high-accuracy state estimates, due to the absence of key sensors such as a gyroscope, GPS, and a magnetometer. In this thesis, robust nonlinear state estimation techniques (the Sliding Mode Observer, the Extended Kalman Filter, and the H-Infinity Filter) are used with CelNav to accurately determine dynamic latitude, longitude, and heading, for an unmanned/manned rover or astronaut. The goal is to investigate the feasibility of implementing a nonlinear estimation technique with CelNav for dynamic extraterrestrial surface navigation when accurate location coordinates are necessary. Preliminary results show that this research shows promise as a secondary dynamic navigation system for future extraterrestrial exploration

Blind color deconvolution, normalization, and classification of histological images using general super Gaussian priors and Bayesian inference

This work was sponsored in part by the Agencia Es-tatal de Investigacion under project PID2019-105142RB-C22/AEI/10.13039/50110 0 011033, Junta de Andalucia under project PY20_00286,and the work by Fernando Perez-Bueno was spon-sored by Ministerio de Economia, Industria y Competitividad un-der FPI contract BES-2017-081584. Funding for open access charge: Universidad de Granada/CBUA.Background and Objective: Color variations in digital histopathology severely impact the performance of computer-aided diagnosis systems. They are due to differences in the staining process and acquisition system, among other reasons. Blind color deconvolution techniques separate multi-stained images into single stained bands which, once normalized, can be used to eliminate these negative color variations and improve the performance of machine learning tasks. Methods: In this work, we decompose the observed RGB image in its hematoxylin and eosin components. We apply Bayesian modeling and inference based on the use of Super Gaussian sparse priors for each stain together with prior closeness to a given reference color-vector matrix. The hematoxylin and eosin components are then used for image normalization and classification of histological images. The proposed framework is tested on stain separation, image normalization, and cancer classification problems. The results are measured using the peak signal to noise ratio, normalized median intensity and the area under ROC curve on five different databases. Results: The obtained results show the superiority of our approach to current state-of-the-art blind color deconvolution techniques. In particular, the fidelity to the tissue improves 1,27 dB in mean PSNR. The normalized median intensity shows a good normalization quality of the proposed approach on the tested datasets. Finally, in cancer classification experiments the area under the ROC curve improves from 0.9491 to 0.9656 and from 0.9279 to 0.9541 on Camelyon-16 and Camelyon-17, respectively, when the original and processed images are used. Furthermore, these figures of merits are better than those obtained by the methods compared with. Conclusions: The proposed framework for blind color deconvolution, normalization and classification of images guarantees fidelity to the tissue structure and can be used both for normalization and classification. In addition, color deconvolution enables the use of the optical density space for classification, which improves the classification performance.Agencia Es-tatal de Investigacion PID2019-105142RB-C22/AEI/10.13039/50110 0 011033Junta de Andalucia PY20_00286Ministerio de Economia, Industria y Competitividad under FPI BES-2017-081584Universidad de Granada/CBU

A review of laser scanning for geological and geotechnical applications in underground mining

Laser scanning can provide timely assessments of mine sites despite adverse challenges in the operational environment. Although there are several published articles on laser scanning, there is a need to review them in the context of underground mining applications. To this end, a holistic review of laser scanning is presented including progress in 3D scanning systems, data capture/processing techniques and primary applications in underground mines. Laser scanning technology has advanced significantly in terms of mobility and mapping, but there are constraints in coherent and consistent data collection at certain mines due to feature deficiency, dynamics, and environmental influences such as dust and water. Studies suggest that laser scanning has matured over the years for change detection, clearance measurements and structure mapping applications. However, there is scope for improvements in lithology identification, surface parameter measurements, logistic tracking and autonomous navigation. Laser scanning has the potential to provide real-time solutions but the lack of infrastructure in underground mines for data transfer, geodetic networking and processing capacity remain limiting factors. Nevertheless, laser scanners are becoming an integral part of mine automation thanks to their affordability, accuracy and mobility, which should support their widespread usage in years to come

Employing data fusion & diversity in the applications of adaptive signal processing

The paradigm of adaptive signal processing is a simple yet powerful method for the class of system identification problems. The classical approaches consider standard one-dimensional signals whereby the model can be formulated by flat-view matrix/vector framework. Nevertheless, the rapidly increasing availability of large-scale multisensor/multinode measurement technology has render no longer sufficient the traditional way of representing the data. To this end, the author, who from this point onward shall be referred to as `we', `us', and `our' to signify the author myself and other supporting contributors i.e. my supervisor, my colleagues and other overseas academics specializing in the specific pieces of research endeavor throughout this thesis, has applied the adaptive filtering framework to problems that employ the techniques of data diversity and fusion which includes quaternions, tensors and graphs. At the first glance, all these structures share one common important feature: invertible isomorphism. In other words, they are algebraically one-to-one related in real vector space. Furthermore, it is our continual course of research that affords a segue of all these three data types. Firstly, we proposed novel quaternion-valued adaptive algorithms named the n-moment widely linear quaternion least mean squares (WL-QLMS) and c-moment WL-LMS. Both are as fast as the recursive-least-squares method but more numerically robust thanks to the lack of matrix inversion. Secondly, the adaptive filtering method is applied to a more complex task: the online tensor dictionary learning named online multilinear dictionary learning (OMDL). The OMDL is partly inspired by the derivation of the c-moment WL-LMS due to its parsimonious formulae. In addition, the sequential higher-order compressed sensing (HO-CS) is also developed to couple with the OMDL to maximally utilize the learned dictionary for the best possible compression. Lastly, we consider graph random processes which actually are multivariate random processes with spatiotemporal (or vertex-time) relationship. Similar to tensor dictionary, one of the main challenges in graph signal processing is sparsity constraint in the graph topology, a challenging issue for online methods. We introduced a novel splitting gradient projection into this adaptive graph filtering to successfully achieve sparse topology. Extensive experiments were conducted to support the analysis of all the algorithms proposed in this thesis, as well as pointing out potentials, limitations and as-yet-unaddressed issues in these research endeavor.Open Acces

Journal of Telecommunications and Information Technology, 2014, nr 2

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