Wavelet Filter Parameterization for Compression of Spectral Images

Vaatimus kuvatiedon tiivistämisestä on tullut entistä ilmeisemmäksi viimeisen kymmenen vuoden aikana kuvatietoon perustuvien sovellutusten myötä. Nykyisin kiinnitetään erityistä huomiota spektrikuviin, joiden tallettaminen ja siirto vaativat runsaasti levytilaa ja kaistaa. Aallokemuunnos on osoittautunut hyväksi ratkaisuksi häviöllisessä tiedontiivistämisessä. Sen toteutus alikaistakoodauksessa perustuu aallokesuodattimiin ja ongelmana on sopivan aallokesuodattimen valinta erilaisille tiivistettäville kuville. Tässä työssä esitetään katsaus tiivistysmenetelmiin, jotka perustuvat aallokemuunnokseen. Ortogonaalisten suodattimien määritys parametrisoimalla on työn painopisteenä. Työssä todetaan myös kahden erilaisen lähestymistavan samanlaisuus algebrallisten yhtälöiden avulla. Kokeellinen osa sisältää joukon testejä, joilla perustellaan parametrisoinnin tarvetta. Erilaisille kuville tarvitaan erilaisia suodattimia sekä erilaiset tiivistyskertoimet saavutetaan eri suodattimilla. Lopuksi toteutetaan spektrikuvien tiivistys aallokemuunnoksen avulla.

Spectral Analysis of Buffers in Communication Systems

Muokatun matriisi-geometrian tekniikan kehitys yleimmäksi jonoksi on esitelty tässä työssä. Jonotus systeemi koostuu useista jonoista joilla on rajatut kapasiteetit. Tässä työssä on myös tutkittu PH-tyypin jakautumista kun ne jaetaan. Rakenne joka vastaa lopullista Markovin ketjua jossa on itsenäisiä matriiseja joilla on QBD rakenne. Myös eräitä rajallisia olotiloja on käsitelty tässä työssä. Sen esitteleminen matriisi-geometrisessä muodossa, muokkaamalla matriisi-geometristä ratkaisua on tämän opinnäytetyön tulos.

Identification of neuronal network properties from the spectral analysis of calcium imaging signals in neuronal cultures

Neuronal networks in vitro are prominent systems to study the development of connections in living neuronal networks and the interplay between connectivity, activity and function. These cultured networks show a rich spontaneous activity that evolves concurrently with the connectivity of the underlying network. In this work we monitor the development of neuronal cultures, and record their activity using calcium fluorescence imaging. We use spectral analysis to characterize global dynamical and structural traits of the neuronal cultures. We first observe that the power spectrum can be used as a signature of the state of the network, for instance when inhibition is active or silent, as well as a measure of the network's connectivity strength. Second, the power spectrum identifies prominent developmental changes in the network such as GABAA switch. And third, the analysis of the spatial distribution of the spectral density, in experiments with a controlled disintegration of the network through CNQX, an AMPA-glutamate receptor antagonist in excitatory neurons, reveals the existence of communities of strongly connected, highly active neurons that display synchronous oscillations. Our work illustrates the interest of spectral analysis for the study of in vitro networks, and its potential use as a network-state indicator, for instance to compare healthy and diseased neuronal networks.

Statistical Analysis of Spectral Images

Tämä diplomityö liittyy Spektrikuvien tutkimiseen tilastollisen kuvamallin näkökulmasta. Diplomityön ensimmäisessä osassa tarkastellaan tilastollisten parametrien jakaumien vaikutusta väreihin ja korostumiin erilaisissa valaistusolosuhteissa. Havaittiin, että tilastollisten parametrien väliset suhteet eivät riipu valaistusolosuhteista, mutta riippuvat kuvan häiriöttömyydestä. Ilmeni myös, että korkea huipukkuus saattaa aiheutua värikylläisyydestä. Lisäksi työssä kehitettiin tilastolliseen spektrimalliin perustuvaa tekstuurinyhdistämisalgoritmia. Sillä saavutettiin hyviä tuloksia, kun tilastollisten parametrien väliset riippuvuussuhteet olivat voimassa. Työn toisessa osassa erilaisia spektrikuvia tutkittiin käyttäen itsenäistä komponenttien analyysia (ICA). Seuraavia itsenäiseen komponenttien analyysiin tarkoitettuja algoritmia tarkasteltiin: JADE, kiinteän pisteen ICA ja momenttikeskeinen ICA. Tutkimuksissa painotettiin erottelun laatua. Paras erottelu saavutettiin JADE- algoritmilla, joskin erot muiden algoritmien välillä eivät olleet merkittäviä. Algoritmi jakoi kuvan kahteen itsenäiseen, joko korostuneeseen ja korostumattomaan tai kromaattiseen ja akromaattiseen, komponenttiin. Lopuksi pohditaan huipukkuuden suhdetta kuvan ominaisuuksiin, kuten korostuneisuuteen ja värikylläisyyteen. Työn viimeisessä osassa ehdotetaan mahdollisia jatkotutkimuskohteita.

Spectral Color Appearance Modeling

Kuvien laatu on tutkituimpia ja käytetyimpiä aiheita. Tässä työssä tarkastellaan värin laatu ja spektrikuvia. Työssä annetaan yleiskuva olemassa olevista pakattujen ja erillisten kuvien laadunarviointimenetelmistä painottaen näiden menetelmien soveltaminen spektrikuviin. Tässä työssä esitellään spektriväriulkomuotomalli värikuvien laadunarvioinnille. Malli sovelletaan spektrikuvista jäljennettyihin värikuviin. Malli pohjautuu sekä tilastolliseen spektrikuvamalliin, joka muodostaa yhteyden spektrikuvien ja valokuvien parametrien välille, että kuvan yleiseen ulkomuotoon. Värikuvien tilastollisten spektriparametrien ja fyysisten parametrien välinen yhteys on varmennettu tietokone-pohjaisella kuvamallinnuksella. Mallin ominaisuuksien pohjalta on kehitetty koekäyttöön tarkoitettu menetelmä värikuvien laadunarvioinnille. On kehitetty asiantuntija-pohjainen kyselymenetelmä ja sumea päättelyjärjestelmä värikuvien laadunarvioinnille. Tutkimus osoittaa, että spektri-väri –yhteys ja sumea päättelyjärjestelmä soveltuvat tehokkaasti värikuvien laadunarviointiin.

Spectral properties of the Laplacian of multiplex networks.

One of the more challenging tasks in the understanding of dynamical properties of models on top of complex networks is to capture the precise role of multiplex topologies. In a recent paper, Gómez et al. [ Phys. Rev. Lett. 110 028701 (2013)], some of the authors proposed a framework for the study of diffusion processes in such networks. Here, we extend the previous framework to deal with general configurations in several layers of networks and analyze the behavior of the spectrum of the Laplacian of the full multiplex. We derive an interesting decoupling of the problem that allow us to unravel the role played by the interconnections of the multiplex in the dynamical processes on top of them. Capitalizing on this decoupling we perform an asymptotic analysis that allow us to derive analytical expressions for the full spectrum of eigenvalues. This spectrum is used to gain insight into physical phenomena on top of multiplex, specifically, diffusion processes and synchronizability.

Combining T2-preparation with spectral and spatial selectivity for improved coronary MRA

Cardiovascular disease is the leading cause of death worldwide. Within this subset, coronary artery disease (CAD) is the most prevalent. Magnetic resonance angiography (MRA) is an emerging technique that provides a safe, non-invasive way of assessing CAD progression. To generate contrast between tissues, MR images are weighted according to the magnetic properties of those tissues. In cardiac MRI, T2 contrast, which is governed by the rate of transverse signal loss, is often created through the use of a T2-Preparation module. T2-Preparation, or T2-Prep, is a magnetization preparation scheme used to improve blood/myocardium contrast in cardiac MRI. T2-Prep methods generally use a non-selective +90°, 180°, 180°, -90° train of radiofrequency (RF) pulses (or variant thereof), to tip magnetization into the transverse plane, allow it to evolve, and then to restore it to the longitudinal plane. A key feature in this process is the combination of a +90° and -90° RF pulse. By changing either one of these, a mismatch occurs between signal excitation and restoration. This feature can be exploited to provide additional spectral or spatial selectivity. In this work, both of these possibilities are explored. The first - spectral selectivity - has been examined as a method of improving fat saturation in coronary MRA. The second - spatial selectivity - has been examined as a means of reducing imaging time by decreasing the field of view, and as a method of reducing artefacts originating from the tissues surrounding the heart. Two additional applications, parallel imaging and self-navigation, are also presented. This thesis is thus composed of four sections. The first, "A Fat Signal Suppression for Coronary MRA at 3T using a Water-Selective Adiabatic T2-Preparation Technique", was originally published in the journal Magnetic Resonance in Medicine (MRM) with co-authors Ruud B. van Heeswijk and Matthias Stuber. The second, "Combined T2-Preparation and 2D Pencil Beam Inner Volume Selection", again with co-authors Ruud van Heeswijk and Matthias Stuber, was also published in the journal MRM. The third, "A cylindrical, inner volume selecting 2D-T2-Prep improves GRAPPA-accelerated image quality in MRA of the right coronary artery", written with co-authors Jerome Yerly and Matthias Stuber, has been submitted to the "Journal of Cardiovascular Magnetic Resonance", and the fourth, "Combined respiratory self-navigation and 'pencil-beam' 2D-T2 -Prep for free-breathing, whole-heart coronary MRA", with co¬authors Jerome Chaptinel, Giulia Ginami, Gabriele Bonanno, Simone Coppo, Ruud van Heeswijk, Davide Piccini, and Matthias Stuber, is undergoing internal review prior to submission to the journal MRM. -- Les maladies cardiovasculaires sont la cause principale de décès dans le monde : parmi celles-ci, les maladies coronariennes sont les plus répandues. L'angiographie par résonance magnétique (ARM) est une technique émergente qui fournit une manière sûre, non invasive d'évaluer la progression de la coronaropathie. Pour obtenir un contraste entre les tissus, les images d'IRM sont pondérées en fonction des propriétés magnétiques de ces tissus. En IRM cardiaque, le contraste en T2, qui est lié à la décroissance du signal transversal, est souvent créé grâce à l'utilisàtion d'un module de préparation T2. La préparation T2, ou T2-Prep, est un système de préparation de l'aimantation qui est utilisé pour améliorer le contraste entre le sang et le myocarde lors d'une IRM cardiaque. Les méthodes de T2-Prep utilisent généralement une série non-sélective d'impulsions de radiofréquence (RF), typiquement [+ 90°, 180°, 180°, -90°] ou une variante, qui bascule l'aimantation dans le plan transversal, lui permet d'évoluer, puis la restaure dans le plan longitudinal. Un élément clé de ce processus est la combinaison des impulsions RF de +90° et -90°. En changeant l'une ou l'autre des impulsions, un décalage se produit entre l'excitation du signal et de la restauration. Cette fonction peut être exploitée pour fournir une sélectivité spectrale ou spatiale. Dans cette thèse, les deux possibilités sont explorées. La première - la sélectivité spectrale - a été examinée comme une méthode d'améliorer la saturation de la graisse dans l'IRM coronarienne. La deuxième - la sélectivité spatiale - a été étudiée comme un moyen de réduire le temps d'imagerie en diminuant le champ de vue, et comme une méthode de réduction des artefacts provenant des tissus entourant le coeur. Deux applications supplémentaires, l'imagerie parallèle et la self-navigation, sont également présentées. Cette thèse est ainsi composée de quatre sections. La première, "A Fat Signal Suppression for Coronary MRA at 3T using a Water-Selective Adiabatic T2-Preparation Technique", a été publiée dans la revue médicale Magnetic Resonance .in Medicine (MRM) avec les co-auteurs Ruud B. van Heeswijk et Matthias Stuber. La deuxième, Combined T2-Preparation and 2D Pencil Beam Inner Volume Selection", encore une fois avec les co-auteurs Ruud van Heeswijk et Matthias Stuber, a également été publiée dans le journal MRM. La troisième, "A cylindrical, inner volume selecting 2D-T2-Prep improves GRAPPA- accelerated image quality in MRA of the right coronary artery", écrite avec les co-auteurs Jérôme Yerly et Matthias Stuber, a été présentée au "Journal of Cardiovascular Magnetic Resonance", et la quatrième, "Combined respiratory self-navigation and 'pencil-beam' 2D-T2 -Prep for free-breathing, whole-heart coronary MRA", avec les co-auteurs Jérôme Chaptinel, Giulia Ginami, Gabriele Bonanno , Simone Coppo, Ruud van Heeswijk, Davide Piccini, et Matthias Stuber, subit un examen interne avant la soumission à la revue MRM.

$E_{1}$-Formality of complex algebraic varieties

Let $X$ be a smooth complex algebraic variety. Morgan showed that the rational homotopy type of $X$ is a formal consequence of the differential graded algebra defined by the first term $E_{1}(X,W)$ of its weight spectral sequence. In the present work, we generalize this result to arbitrary nilpotent complex algebraic varieties (possibly singular and/or non-compact) and to algebraic morphisms between them. In particular, our results generalize the formality theorem of Deligne, Griffiths, Morgan and Sullivan for morphisms of compact Kähler varieties, filling a gap in Morgan"s theory concerning functoriality over the rationals. As an application, we study the Hopf invariant of certain algebraic morphisms using intersection theory.

Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

Role of Selected Spectral Attributes in the Perception of Synthetic Vowels

This thesis is an experimental study regarding the identification and discrimination of vowels, studied using synthetic stimuli. The acoustic attributes of synthetic stimuli vary, which raises the question of how different spectral attributes are linked to the behaviour of the subjects. The spectral attributes used are formants and spectral moments (centre of gravity, standard deviation, skewness and kurtosis). Two types of experiments are used, related to the identification and discrimination of the stimuli, respectively. The discrimination is studied by using both the attentive procedures that require a response from the subject, and the preattentive procedures that require no response. Together, the studies offer information about the identification and discrimination of synthetic vowels in 15 different languages. Furthermore, this thesis discusses the role of various spectral attributes in the speech perception processes. The thesis is divided into three studies. The first is based only on attentive methods, whereas the other two concentrate on the relationship between identification and discrimination experiments. The neurophysiological methods (EEG recordings) reveal the role of attention in processing, and are used in discrimination experiments, while the results reveal differences in perceptual processes based on the language, attention and experimental procedure.

A Cartan-Eilenberg approach to Homotopical Algebra

In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects by an extension property analogous to the classical lifting property of projective modules. We define a Cartan-Eilenberg category as a category with strong and weak equivalences such that there is an equivalence of categories between its localisation with respect to weak equivalences and the relative localisation of the subcategory of cofibrant objects with respect to strong equivalences. This equivalence of categories allows us to extend the classical theory of derived additive functors to this non additive setting. The main examples include Quillen model categories and categories of functors defined on a category endowed with a cotriple (comonad) and taking values on a category of complexes of an abelian category. In the latter case there are examples in which the class of strong equivalences is not determined by a homotopy relation. Among other applications of our theory, we establish a very general acyclic models theorem.

Computational Techniques for Spectral Image Analysis

Multispectral images are becoming more common in the field of remote sensing, computer vision, and industrial applications. Due to the high accuracy of the multispectral information, it can be used as an important quality factor in the inspection of industrial products. Recently, the development on multispectral imaging systems and the computational analysis on the multispectral images have been the focus of a growing interest. In this thesis, three areas of multispectral image analysis are considered. First, a method for analyzing multispectral textured images was developed. The method is based on a spectral cooccurrence matrix, which contains information of the joint distribution of spectral classes in a spectral domain. Next, a procedure for estimating the illumination spectrum of the color images was developed. Proposed method can be used, for example, in color constancy, color correction, and in the content based search from color image databases. Finally, color filters for the optical pattern recognition were designed, and a prototype of a spectral vision system was constructed. The spectral vision system can be used to acquire a low dimensional component image set for the two dimensional spectral image reconstruction. The data obtained by the spectral vision system is small and therefore convenient for storing and transmitting a spectral image.

Identification of acetates in elasmopalpulus lignosellus pheromone glands using a newly created mass spectral database and kóvats retention indices

Based on a specially created mass spectral database utilizing 23 tetradecenyl and 22 hexadecenyl acetate standards along with Kóvats retention indices obtained on a very polar stationary phase [poly (biscyanopropyl siloxane)] (SP 2340), (Z)-9-hexadecenyl acetate, (Z)-11-hexadecenyl acetate and (E)-8-hexadecenyl acetate were identified in active pheromone extracts of Elasmopalpus lignosellus. This identification was more efficient than our previous study using gas chromatography/mass spectrometry with a dimethyl disulfide derivative where we could only identify the first two acetates. The acetate composition of the pheromone gland differed from region to region in Brazil and from that from the Tifton (GA, USA) population, suggesting polymorphism or a different sub-species.