Wang, Yiran. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 70-73). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Overview of the subject --- p.6 / Chapter 1.2 --- Motivation --- p.8 / Chapter 2 --- Inverse Medium Scattering Problem --- p.11 / Chapter 2.1 --- Mathematical Formulation --- p.11 / Chapter 2.1.1 --- Absorbing Boundary Conditions --- p.12 / Chapter 2.1.2 --- Applications --- p.14 / Chapter 2.2 --- Preliminary Results --- p.17 / Chapter 2.2.1 --- Weak Formulation --- p.17 / Chapter 2.2.2 --- About the Unique Determination --- p.21 / Chapter 3 --- Unconstrained Optimization: Steepest Decent Method --- p.25 / Chapter 3.1 --- Recursive Linearization Method Revisited --- p.25 / Chapter 3.1.1 --- Frechet differentiability --- p.26 / Chapter 3.1.2 --- Initial guess --- p.28 / Chapter 3.1.3 --- Landweber iteration --- p.30 / Chapter 3.1.4 --- Numerical Results --- p.32 / Chapter 3.2 --- Steepest Decent Analysis --- p.35 / Chapter 3.2.1 --- Single Wave Case --- p.36 / Chapter 3.2.2 --- Multiple Wave Case --- p.39 / Chapter 3.3 --- Numerical Experiments and Discussions --- p.43 / Chapter 4 --- Constrained Optimization: Augmented Lagrangian Method --- p.51 / Chapter 4.1 --- Method Review --- p.51 / Chapter 4.2 --- Problem Formulation --- p.54 / Chapter 4.3 --- First Order Optimality Condition --- p.56 / Chapter 4.4 --- Second Order Optimality Condition --- p.60 / Chapter 4.5 --- Modified Algorithm --- p.62 / Chapter 5 --- Conclusions and Future Work --- p.68 / Bibliography --- p.70

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (p. 134-137).

published_or_final_version / abstract / toc / Physics / Master / Master of Philosophy

Thesis (M. Phil.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 102-120).

We are concerned with the quantum inverse scattering problem. The corresponding Marchenko integral equation is solved by using the collocation method together with piece-wise polynomials, namely, Hermite splines. The scarcity of experimental data and the lack of phase information necessitate the generation of the input reflection coefficient by choosing a specific profile and then applying our method to reconstruct it. Various aspects of the single and coupled channels inverse problem and details about the numerical techniques employed are discussed. We proceed to apply our approach to synthetic seismic reflection data. The transformation of the classical one-dimensional wave equation for elastic displacement into a Schr¨odinger-like equation is presented. As an application of our method, we consider the synthetic reflection travel-time data for a layered substrate from which we recover the seismic impedance of the medium. We also apply our approach to experimental seismic reflection data collected from a deep water location in the North sea. The reflectivity sequence and the relevant seismic wavelet are extracted from the seismic reflection data by applying the statistical estimation procedure known as Markov Chain Monte Carlo method to the problem of blind deconvolution. In order to implement the Marchenko inversion method, the pure spike trains have been replaced by amplitudes having a narrow bell-shaped form to facilitate the numerical solution of the Marchenko integral equation from which the underlying seismic impedance profile of the medium is obtained. / Physics / D.Phil.(Physics)

Les tâches qui consistent à comprendre automatiquement le contenu d’un signal naturel, comme une image ou un son, sont en général difficiles. En effet, dans leur représentation naïve, les signaux sont des objets compliqués, appartenant à des espaces de grande dimension. Représentés différemment, ils peuvent en revanche être plus faciles à interpréter. Cette thèse s’intéresse à une représentation fréquemment utilisée dans ce genre de situations, notamment pour analyser des signaux audio : le module de la transformée en ondelettes. Pour mieux comprendre son comportement, nous considérons, d’un point de vue théorique et algorithmique, le problème inverse correspondant : la reconstruction d’un signal à partir du module de sa transformée en ondelettes. Ce problème appartient à une classe plus générale de problèmes inverses : les problèmes de reconstruction de phase. Dans un premier chapitre, nous décrivons un nouvel algorithme, PhaseCut, qui résout numériquement un problème de reconstruction de phase générique. Comme l’algorithme similaire PhaseLift, PhaseCut utilise une relaxation convexe, qui se trouve en l’occurence être de la même forme que les relaxations du problème abondamment étudié MaxCut. Nous comparons les performances de PhaseCut et PhaseLift, en termes de précision et de rapidité. Dans les deux chapitres suivants, nous étudions le cas particulier de la reconstruction de phase pour la transformée en ondelettes. Nous montrons que toute fonction sans fréquence négative est uniquement déterminée (à une phase globale près) par le module de sa transformée en ondelettes, mais que la reconstruction à partir du module n’est pas stable au bruit, pour une définition forte de la stabilité. On démontre en revanche une propriété de stabilité locale. Nous présentons également un nouvel algorithme de reconstruction de phase, non-convexe, qui est spécifique à la transformée en ondelettes, et étudions numériquement ses performances. Enfin, dans les deux derniers chapitres, nous étudions une représentation plus sophistiquée, construite à partir du module de transformée en ondelettes : la transformée de scattering. Notre but est de comprendre quelles propriétés d’un signal sont caractérisées par sa transformée de scattering. On commence par démontrer un théorème majorant l’énergie des coefficients de scattering d’un signal, à un ordre donné, en fonction de l’énergie du signal initial, convolé par un filtre passe-haut qui dépend de l’ordre. On étudie ensuite une généralisation de la transformée de scattering, qui s’applique à des processus stationnaires. On montre qu’en dimension finie, cette transformée généralisée préserve la norme. En dimension un, on montre également que les coefficients de scattering généralisés d’un processus caractérisent la queue de distribution du processus. / Automatically understanding the content of a natural signal, like a sound or an image, is in general a difficult task. In their naive representation, signals are indeed complicated objects, belonging to high-dimensional spaces. With a different representation, they can however be easier to interpret. This thesis considers a representation commonly used in these cases, in particular for theanalysis of audio signals: the modulus of the wavelet transform. To better understand the behaviour of this operator, we study, from a theoretical as well as algorithmic point of view, the corresponding inverse problem: the reconstruction of a signal from the modulus of its wavelet transform. This problem belongs to a wider class of inverse problems: phase retrieval problems. In a first chapter, we describe a new algorithm, PhaseCut, which numerically solves a generic phase retrieval problem. Like the similar algorithm PhaseLift, PhaseCut relies on a convex relaxation of the phase retrieval problem, which happens to be of the same form as relaxations of the widely studied problem MaxCut. We compare the performances of PhaseCut and PhaseLift, in terms of precision and complexity. In the next two chapters, we study the specific case of phase retrieval for the wavelet transform. We show that any function with no negative frequencies is uniquely determined (up to a global phase) by the modulus of its wavelet transform, but that the reconstruction from the modulus is not stable to noise, for a strong notion of stability. However, we prove a local stability property. We also present a new non-convex phase retrieval algorithm, which is specific to the case of the wavelet transform, and we numerically study its performances. Finally, in the last two chapters, we study a more sophisticated representation, built from the modulus of the wavelet transform: the scattering transform. Our goal is to understand which properties of a signal are characterized by its scattering transform. We first prove that the energy of scattering coefficients of a signal, at a given order, is upper bounded by the energy of the signal itself, convolved with a high-pass filter that depends on the order. We then study a generalization of the scattering transform, for stationary processes. We show that, in finite dimension, this generalized transform preserves the norm. In dimension one, we also show that the generalized scattering coefficients of a process characterize the tail of its distribution.

A cornerstone in the industry's ongoing digital revolution, which is sometimes referred to as Industry 4.0, is the ability to trace products not only within the own production line but also throughout the remaining lifetime of the products. Traditionally, this is done by labeling products with, for instance, bar codes or radio-frequency identification (RFID) tags. In recent years, using the structure of the product itself as a unique identifier, a "fingerprint", has become a popular area of research. The purpose of this work was to develop software for an identification system using laser speckles as a unique identifier of steel components. Laser speckles, or simply speckles, are generated by illuminating a rough surface with coherent light, typically laser light. As the light is reflected, the granular pattern known as speckles can be seen by an observer. The complex nature of a speckle pattern together with its sensitivity to changes in the setup makes it robust against false-positive identifications and almost impossible to counterfeit. Because of this, speckles are suitable to be used as unique identifiers. In this work, three different identification algorithms have been tested in both simulations and experiments. The tested algorithms included one correlation-based, one method based on local feature extraction, and one method based on global feature extraction. The results showed that the correlation-based identification is most robust against speckle decorrelation, i.e changes in the speckle pattern, while being quite computationally expensive. The local feature-based method was shown to be unfit for this current application due to its sensitivity to speckle decorrelation and erroneous results. The global feature extraction method achieved high accuracy and fast computational speed when combined with a clustering method based on overlapping speckle patterns and a k-nearest neighbours (k-NN) search. In all the investigated methods, parallel calculations can be utilized to increase the computational speed.

We clear up two issues regarding the eigenvalue problem for the Manakov system; these problems relate directly to the existence of the soliton [sic] effect in fiber optic cables. The first issue is a bound on the eigenvalues of the Manakov system: if the parameter ξ is an eigenvalue, then it must lie in a certain region in the complex plane. The second issue has to do with a chirped Manakov system. We show that if a system is chirped too much, the soliton effect disappears. While this has been known for some time experimentally, there has not yet been a theoretical result along these lines for the Manakov system. / Ph. D.

Dans le cadre de la classification de sons,cette thèse construit des représentations du signal qui vérifient des propriétés d’invariance et de variabilité inter-classe. D’abord, nous étudions le scattering temps- fréquence, une représentation qui extrait des modulations spectrotemporelles à différentes échelles. Enclassification de sons urbains et environnementaux, nous obtenons de meilleurs résultats que les réseaux profonds à convolutions et les descripteurs à court terme. Ensuite, nous introduisons le scattering en spirale, une représentation qui combine des transformées en ondelettes selon le temps, selon les log-fréquences, et à travers les octaves. Le scattering en spirale suit la géométrie de la spirale de Shepard, qui fait un tour complet à chaque octave. Nous étudions les sons voisés avec un modèle source-filtre non stationnaire dans lequel la source et le filtre sont transposés au cours du temps, et montrons que le scattering en spirale sépare et linéarise ces transpositions. Le scattering en spirale améliore lesperformances de l’état de l’art en classification d’instruments de musique. Outre la classification de sons, le scattering temps-fréquence et le scattering en spirale peuvent être utilisés comme des descripteurspour la synthèse de textures audio. Contrairement au scattering temporel, le scattering temps-fréquence est capable de capturer la cohérence de motifs spectrotemporels en bioacoustique et en parole, jusqu’à une échelle d’intégration de 500 ms environ. À partir de ce cadre d’analyse-synthèse, une collaboration artscience avec le compositeur Florian Hecker / This dissertation addresses audio classification by designing signal representations which satisfy appropriate invariants while preserving inter-class variability. First, we study time-frequencyscattering, a representation which extract modulations at various scales and rates in a similar way to idealized models of spectrotemporal receptive fields in auditory neuroscience. We report state-of-the-artresults in the classification of urban and environmental sounds, thus outperforming short-term audio descriptors and deep convolutional networks. Secondly, we introduce spiral scattering, a representationwhich combines wavelet convolutions along time, along log-frequency, and across octaves. Spiral scattering follows the geometry of the Shepard pitch spiral, which makes a full turn at every octave. We study voiced sounds with a nonstationary sourcefilter model where both the source and the filter are transposed through time, and show that spiral scattering disentangles and linearizes these transpositions. Furthermore, spiral scattering reaches state-of-the-art results in musical instrument classification ofsolo recordings. Aside from audio classification, time-frequency scattering and spiral scattering can be used as summary statistics for audio texture synthesis. We find that, unlike the previously existing temporal scattering transform, time-frequency scattering is able to capture the coherence ofspectrotemporal patterns, such as those arising in bioacoustics or speech, up to anintegration scale of about 500 ms. Based on this analysis-synthesis framework, an artisticcollaboration with composer Florian Hecker has led to the creation of five computer music

Cardiovascular diseases are a leading cause of death globally. Early diagnosis and treatment is of prime importance to prevent or mitigate health complications. Electrocardiogram (ECG) is a standard test modality used for early diagnosis of arrhythmias. The standard ECG uses 12 leads (i.e., 12 different views of the electrical activity of the heart). However, it is not always possible to perform a standard 12-lead ECG, for instance, in certain emergency situations. Such devices used in emergency situations are able to measure only a subset of leads. Although it is a simpler way of recording ECG, it comes at the cost of losing some information. The project presented in this thesis applies three different models based on canonical correlation analysis (CCA) to perform transfer learning from 12-lead ECGs to improve performance when only a subset of leads is available. The models used were linear canonical correlation analysis, deep canonical correlation analysis (DCCA) and deep canonically correlated bidirectional long short-term memory networks (DCC-BiLSTMs). These models are compared to each other using different configurations to study their performance on ECG data. Linear canonical correlation analysis performed better than its more complex variants, DCCA and DCC-BiLSTMs. With this method, it was possible to improve performance on ECG classification when using two, three, four and six leads in a computationally efficient way. / Hjärt- och kärlsjukdomar är den främsta dödsorsaken i världen. Tidig diagnos och behandling är av största vikt för att förhindra ytterligare och allvarliga hälsoproblem. Elektrokardiogram (EKG) är den standardmetod som används för tidig diagnos av arytmier. Standardförfarandet inom EKG använder sig av 12 avledningar (dvs. 12 olika vyer av hjärtats elektriska aktivitet). Det är dock inte alltid möjligt att utföra ett standard-EKG med 12 ledningar, vilket t.ex. förekommer i vissa nödsituationer. I dessa fall kan utrustning som gör det möjligt att ta fram ett 12-ledars EKG inte vara tillgänglig av flera olika skäl, och därför används andra apparater som kan mäta endast en delmängd av ledningarna för tidig diagnostik. Även om det är ett enklare sätt att utföra ett EKG, innebär det att man förlorar en del information. I det projekt som presenteras i detta dokument används tre olika modeller baserade på kanonisk korrelationsanalys (CCA) för att utföra överföringsinlärning från 12-ledars EKG för att förbättra prestanda när endast en delmängd av avledningar används. De modeller som användes var linjär kanonisk korrelationsanalys, djup kanonisk korrelationsanalys (DCCA) och djupa kanoniskt korrelerade bidirektionella långtidsminnesnätverk (DCCBiLSTMs). Dessa modeller jämförs med varandra med hjälp av olika konfigurationer för att studera deras prestanda på EKG-data. Linjär kanonisk korrelationsanalys presterade bättre än dess mer komplexa varianter, DCCA och DCC-BiLSTMs. Med denna metod var det möjligt att förbättra prestandan för klassificering av EKG när man använder två, tre, fyra och sex ledningar på ett beräkningseffektivt sätt.