514 research outputs found
Octonion sparse representation for color and multispectral image processing
A recent trend in color image processing combines the quaternion algebra with dictionary learning methods. This paper aims to present a generalization of the quaternion dictionary learning method by using the octonion algebra. The octonion algebra combined with dictionary learning methods is well suited for representation of multispectral images with up to 7 color channels. Opposed to the classical dictionary learning techniques that treat multispectral images by concatenating spectral bands into a large monochrome image, we treat all the spectral bands simultaneously. Our approach leads to better preservation of color fidelity in true and false color images of the reconstructed multispectral image. To show the potential of the octonion based model, experiments are conducted for image reconstruction and denoising of color images as well as of extensively used Landsat 7 images
Hypercomplex algebras for dictionary learning
This paper presents an application of hypercomplex algebras combined with dictionary learning for sparse representation of multichannel images. Two main representatives of hypercomplex algebras, Clifford algebras and algebras generated by the Cayley-Dickson procedure are considered. Related works reported quaternion methods (for color images) and octonion methods, which are applicable to images with up to 7 channels. We show that the current constructions cannot be generalized to dimensions above eight
Robust GNSS Carrier Phase-based Position and Attitude Estimation Theory and Applications
Mención Internacional en el título de doctorNavigation information is an essential element for the functioning of robotic platforms and
intelligent transportation systems. Among the existing technologies, Global Navigation Satellite
Systems (GNSS) have established as the cornerstone for outdoor navigation, allowing for
all-weather, all-time positioning and timing at a worldwide scale. GNSS is the generic term
for referring to a constellation of satellites which transmit radio signals used primarily for
ranging information. Therefore, the successful operation and deployment of prospective
autonomous systems is subject to our capabilities to support GNSS in the provision of
robust and precise navigational estimates.
GNSS signals enable two types of ranging observations: –code pseudorange, which is a
measure of the time difference between the signal’s emission and reception at the satellite
and receiver, respectively, scaled by the speed of light; –carrier phase pseudorange, which
measures the beat of the carrier signal and the number of accumulated full carrier cycles.
While code pseudoranges provides an unambiguous measure of the distance between satellites
and receiver, with a dm-level precision when disregarding atmospheric delays and clock offsets,
carrier phase measurements present a much higher precision, at the cost of being ambiguous by
an unknown number of integer cycles, commonly denoted as ambiguities. Thus, the maximum
potential of GNSS, in terms of navigational precision, can be reach by the use of carrier phase
observations which, in turn, lead to complicated estimation problems.
This thesis deals with the estimation theory behind the provision of carrier phase-based
precise navigation for vehicles traversing scenarios with harsh signal propagation conditions.
Contributions to such a broad topic are made in three directions. First, the ultimate positioning
performance is addressed, by proposing lower bounds on the signal processing realized at the
receiver level and for the mixed real- and integer-valued problem related to carrier phase-based
positioning. Second, multi-antenna configurations are considered for the computation of a
vehicle’s orientation, introducing a new model for the joint position and attitude estimation
problems and proposing new deterministic and recursive estimators based on Lie Theory.
Finally, the framework of robust statistics is explored to propose new solutions to code- and
carrier phase-based navigation, able to deal with outlying impulsive noises.La información de navegación es un elemental fundamental para el funcionamiento de sistemas
de transporte inteligentes y plataformas robóticas. Entre las tecnologías existentes, los
Sistemas Globales de Navegación por Satélite (GNSS) se han consolidado como la piedra
angular para la navegación en exteriores, dando acceso a localización y sincronización temporal
a una escala global, irrespectivamente de la condición meteorológica. GNSS es el término
genérico que define una constelación de satélites que transmiten señales de radio, usadas
primordinalmente para proporcionar información de distancia. Por lo tanto, la operatibilidad y
funcionamiento de los futuros sistemas autónomos pende de nuestra capacidad para explotar
GNSS y estimar soluciones de navegación robustas y precisas.
Las señales GNSS permiten dos tipos de observaciones de alcance: –pseudorangos de
código, que miden el tiempo transcurrido entre la emisión de las señales en los satélites y su
acquisición en la tierra por parte de un receptor; –pseudorangos de fase de portadora, que
miden la fase de la onda sinusoide que portan dichas señales y el número acumulado de ciclos
completos. Los pseudorangos de código proporcionan una medida inequívoca de la distancia
entre los satélites y el receptor, con una precisión de decímetros cuando no se tienen en
cuenta los retrasos atmosféricos y los desfases del reloj. En contraposición, las observaciones
de la portadora son super precisas, alcanzando el milímetro de exactidud, a expensas de ser
ambiguas por un número entero y desconocido de ciclos. Por ende, el alcanzar la máxima
precisión con GNSS queda condicionado al uso de las medidas de fase de la portadora, lo
cual implica unos problemas de estimación de elevada complejidad.
Esta tesis versa sobre la teoría de estimación relacionada con la provisión de navegación
precisa basada en la fase de la portadora, especialmente para vehículos que transitan escenarios
donde las señales no se propagan fácilmente, como es el caso de las ciudades. Para ello,
primero se aborda la máxima efectividad del problema de localización, proponiendo cotas
inferiores para el procesamiento de la señal en el receptor y para el problema de estimación
mixto (es decir, cuando las incógnitas pertenecen al espacio de números reales y enteros). En
segundo lugar, se consideran las configuraciones multiantena para el cálculo de la orientación de un vehículo, presentando un nuevo modelo para la estimación conjunta de posición y
rumbo, y proponiendo estimadores deterministas y recursivos basados en la teoría de Lie. Por
último, se explora el marco de la estadística robusta para proporcionar nuevas soluciones de
navegación precisa, capaces de hacer frente a los ruidos atípicos.Programa de Doctorado en Ciencia y Tecnología Informática por la Universidad Carlos III de MadridPresidente: José Manuel Molina López.- Secretario: Giorgi Gabriele.- Vocal: Fabio Dovi
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
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