Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

Réduction d'interférence dans les systèmes de transmission sans fil

Wireless communications have known an exponential growth and a fast progress over the past few decades. Nowadays, wireless mobile communications have evolved over time starting with the first generation primarily developed for voice communications, and reaching the fourth generation referred to as long term evolution (LTE) that offers an increasing capacity and speed using a different radio interface together with core network improvements. Overall throughput and transmission reliability are among the essential measures of service quality in a wireless system. Such measures are mainly subjected to interference management constraint in a multi-user network. The interference management is at the heart of wireless regulation and is essential for maintaining a desirable throughput while avoiding the detrimental impact of interference at the undesired receivers. Our work is incorporated within the framework of interference network where each user is equipped with single or multiple antennas. The goal is to resolve the challenges that the communications face taking into account the achievable rate and the complexity cost. We propose several solutions for the precoding and decoding designs when transmitters have limited cooperation based on a technique called Interference Alignment. We also address the detection scheme in the absence of any precoding design and we introduce a low complexity detection scheme based on the sparse decomposition.Les communications mobiles sans fil ont connu un formidable essor au cours des dernières décennies. Tout a commencé avec les services vocaux offerts par les systèmes de la première génération en 1980, jusqu¿aux systèmes de la quatrième génération aujourd¿hui avec des services internet haut débit et un accroissement du nombre d¿utilisateurs. En effet, les caractéristiques essentielles qui définissent les services et la qualité de ces services dans les systèmes de communication sans fil sont: le débit, la fiabilité de transmission et le nombre d¿utilisateurs. Ces caractéristiques sont fortement liées entre elles et sont dépendantes de la gestion des interférences entre les différents utilisateurs. Les interférences entre-utilisateurs se produisent lorsque plusieurs émetteurs, dans une même zone, transmettent simultanément en utilisant la même bande de fréquence. Dans cette thèse, nous nous intéressons à la gestion d¿interférence entre utilisateurs par le biais de l¿approche d¿alignement d¿interférences où la coopération entre utilisateurs est réduite. Aussi, nous nous sommes intéressés au design d¿un récepteur où l¿alignement d¿interférences n¿est pas utilisé et où la gestion des interférences est réalisée par des techniques de décodage basées sur les décompositions parcimonieuses des signaux de communications. Ces approches ont conduit à des méthodes performantes et peu couteuses, exploitables dans les liens montant ou descendant

A unified approach to the analysis and design of digital line codes

In most areas of research the variety of possible approaches to analysis and design problems is very large. This is particularly true in the case of digital signal transmission where various conflicting requirements exist (e.g. minimum bandwidth for maximum information capacity and reliability). The lack of universally adopted analysis and evaluation methods is not due to any uncertainties or deficiencies in theoretical fundamentals, rather it is a problem of diversity of criteria and therefore modes of specification that apply. The work presented in the thesis is concerned with the creation and evaluation of a universal algorithm suitable for the assessment of digital codes together with a systematic approach to the comparative evaluation of essential structural and spectral features of coding schemes. The thesis begins with an overview of the basic theoretical principles of line coding as an essential part of the process of channel coding for reliable and efficient digital signal transmission. A general spectral analysis procedure is derived from the finite-state sequential machine model of fixed-length block coders, and is implemented in the form of a computer program. A technique for the conversion of coder rules, given in descriptive form into table and matrix form, suitable for the universal specification format used in the general spectral analysis procedure, is developed. A new method of general classification of codes into categories, according to their complexity levels, is proposed. A modification of the spectral analysis routine into a universal block-code generating scheme is then introduced. The virtually unlimited capabilities for the design and analysis of new code structures is demonstrated. Following from this, a new method for evaluation of the performance of block codes is suggested. It is based on the introduction of an integral parameter, the Information Capacity, which determines the degree of possible spectrum modification for a particular coder specification. Using this method, it is demonstrated how an optimal combination of a code structure, spectral features and information capacity can be achieved. The thesis concludes with a practical example of the application of the generalised analysis procedure, demonstrating the possibility to combine code multiplexing with modification of the spectrum of the line signal. A novel technique, based on the principles of spread spectrum for multichannel transmission, is proposed. It involves a Binary-Multiplexed Coding (BMC) scheme which is implemented in a generalised circuit, the performance of which is investigated and evaluated

Orthogonal Time Frequency Space (OTFS) Modulation for Wireless Communications

The orthogonal time frequency space (OTFS) modulation is a recently proposed multi-carrier transmission scheme, which innovatively multiplexes the information symbols in the delay-Doppler (DD) domain instead of the conventional time-frequency (TF) domain. The DD domain symbol multiplexing gives rise to a direct interaction between the DD domain information symbols and DD domain channel responses, which are usually quasi-static, compact, separable, and potentially sparse. Therefore, OTFS modulation enjoys appealing advantages over the conventional orthogonal frequency-division multiplexing (OFDM) modulation for wireless communications. In this thesis, we investigate the related subjects of OTFS modulation for wireless communications, specifically focusing on its signal detection, performance analysis, and applications. In specific, we first offer a literature review on the OTFS modulation in Chapter~1. Furthermore, a summary of wireless channels is given in Chapter 2. In particular, we discuss the characteristics of wireless channels in different domains and compare their properties. In Chapter 3, we present a detailed derivation of the OTFS concept based on the theory of Zak transform (ZT) and discrete Zak transform (DZT). We unveil the connections between OTFS modulation and DZT, where the DD domain interpretations of key components for modulation, such as pulse shaping, and matched-filtering, are highlighted. The main research contributions of this thesis appear in Chapter 4 to Chapter 7. In Chapter 4, we introduce the hybrid maximum a posteriori (MAP) and parallel interference cancellation (PIC) detection. This detection approach exploits the power discrepancy among different resolvable paths and can obtain near-optimal error performance with a reduced complexity. In Chapter 5, we propose the cross domain iterative detection for OTFS modulation by leveraging the unitary transformations among different domains. After presenting the key concepts of the cross domain iterative detection, we study its performance via state evolution. We show that the cross domain iterative detection can approach the optimal error performance theoretically. Our numerical results agree with our theoretical analysis and demonstrate a significant performance improvement compared to conventional OTFS detection methods. In Chapter 6, we investigate the error performance for coded OTFS systems based on the pairwise-error probability (PEP) analysis. We show that there exists a fundamental trade-off between the coding gain and the diversity gain for coded OTFS systems. According to this trade-off, we further provide some rule-of-thumb guidelines for code design in OTFS systems. In Chapter 7, we study the potential of OTFS modulation in integrated sensing and communication (ISAC) transmissions. We propose the concept of spatial-spreading to facilitate the ISAC design, which is able to discretize the angular domain, resulting in simple and insightful input-output relationships for both radar sensing and communication. Based on spatial-spreading, we verify the effectiveness of OTFS modulation in ISAC transmissions and demonstrate the performance improvements in comparison to the OFDM counterpart. A summary of this thesis is presented in Chapter 8, where we also discuss some potential research directions on OTFS modulation. The concept of OTFS modulation and the elegant theory of DD domain communication may have opened a new gate for the development of wireless communications, which is worthy to be further explored

Empirical eigenfunctions: application in unsteady aerodynamics

Mención Internacional en el título de doctorThe main aim of modal decompositions is to obtain a set of functions which can describe in a compact way the variability contained in a set of observables/data. While this can be easily obtained by means of the eigenfunctions of the operator from which the observables depends, the empirical eigenfunctions allow to obtain a similar result from a set of data, without the knowledge of the problem operator. In Fluid Mechanics and related sciences one of the most prominent techniques to obtain empirical eigenfunctions is referred to as Proper Orthogonal Decomposition (POD). This thesis contains applications of the empirical eigenfunctions to (Experimental) Aerodynamics data. The mathematical framework of the POD is introduced following the bi-orthogonal approach by Aubry (1991). The mathematical derivation of the POD is given, wherever possible, in its most general formulation, without bounding it to the decomposition of a specific quantity. This choice of the author depends on the variety of POD applications which are included in this dissertation, ranging from signal processing problems to applications more strictly related with flow physics. The mathematical framework includes also one of the POD extensions, the Extended POD (EPOD), which allows to extract modes linearly correlated to the empirical eigenfunctions of a second quantity. The first two applications of the empirical eigenfunctions are strictly connected with the signal treatment in experimental techniques for Fluid Mechanics. In Chapter 3, the empirical eigenfunctions are identified as an optimal basis in which perform a "low-pass" spectral filter of experimental fluid data, such as velocity fields measured with Particle Image Velocimetry (PIV). This filtering is extremely beneficial to reduce the random errors contained in the PIV fields and obtain a more accurate estimate of derivative quantities (such as, for instance, vorticity), which are more affected by random errors. In Chapter 4 the POD is exploited for the pre-treatment of a sequence of PIV images. The aim is to remove background and reflections, which are sources of uncertainty in PIV measurements. In this case a "high-pass" spectral filtering is applied to the PIV image ensemble in order to remove the highly-coherent part of the signal corresponding to the background. In the third and fourth applications, the POD is applied to recover the underlying dynamics of a flow. More specifically, in Chapter 5 the POD is applied to the complex wake of a pair of cylinders in tandem arrangement with the additional perturbation of the wall proximity. Through this technique it is possible to track the changes in the oscillatory behaviour of the wake instabilities ascribed to different geometrical configurations of the cylinders. In Chapter 6 the POD and the EPOD are applied respectively to the flow fields around an airfoil in plunging and pitching motion and to the unsteady aerodynamic forces acting on the airfoil. The decomposition allows to extract a reduced set of modes of the flow field which are related to the force generation mechanism. These modes correspond to well-recognizable phenomena of the flow which can be identified for diverse airfoil kinematics. This flow-field driven force decomposition is analysed on the light of existing force models, enabling their reinterpretation and driving towards possible corrections. The final application is devoted to overcome the low temporal resolution of typical flow field measurements, such as PIV, by proposing a robust estimation of turbulent flows dynamics. The method employs a modified version of the EPOD to identify the correlation between a non-time-resolved field measurement and a time-resolved point measurement. The estimation of the time-resolved flow fields is obtained exploiting the correlation of the flow fields with the temporal information contained in the point measurements.El objetivo principal de las descomposiciones modales es obtener un conjunto de funciones que sean capaces de describir de una manera compacta la variabilidad contenida en un conjunto de observables/datos. Si bien este objetivo puede ser fácilmente realizado mediante el uso de las autofunciones del operador del cual los observables dependen, las autofunciones empíricas permiten obtener un resultado similar partiendo de un conjunto de datos sin la necesidad de conocer el operador del problema. En Mecánica de Fluidos y en ciencias relacionadas con esta disciplina, una de las técnicas más relevantes para obtener autofunciones empíricas es la conocida como Descomposición Modal Ortogonal (Proper Orthogonal Decomposition, POD). Esta tesis contiene diversas aplicaciones de las autofunciones empíricas en datos de Aerodinámica (Experimental). La base matemática de la POD es introducida siguiendo la aproximación biortogonal realizada por Aubry (1991). La formulación matemática de la POD es expresada siempre que es posible en el marco más general posible, sin condicionarla a la descomposición de una variable en concreto. La elección del autor dependerá de las diferentes aplicaciones de la POD, todas ellas descritas en la presente tesis, las cuales abarcan desde problemas de procesado de señales hasta aplicaciones más estrictamente relacionadas con el análisis de la física del flujo. La formulación matemática incluye también uno de las extensiones de la POD, la POD Extendida (EPOD), la cual permite extraer modos linealmente correlacionados con las autofunciones empíricas de una segunda variable. Las dos primeras aplicaciones de las autofunciones empíricas están estrictamente relacionadas con el tratamiento de señales en técnicas experimentales de Mecánica de Fluidos. En el Capítulo 3, las autofunciones empíricas son identificadas como una base optima, la cual se puede utilizar para realizar un filtro pasa bajos espectral para datos experimentales de flujos, tales como campos de velocidad obtenidos mediante la técnica de Velocimetría por Imágenes de Partículas, (Particle Image Velocimetry, PIV). Este tipo de filtro es muy beneficioso para reducir los errores de carácter aleatorio contenidos en los campos de PIV y por tanto obtener una estimación más precisa en las cantidades que precisan del uso de derivadas (por ejemplo, la vorticidad), ya que están más afectadas por este tipo de errores. En el Capítulo 4, la POD es utilizada para el pretratamiento de una secuencia de imágenes de PIV. El objetivo es reducir el fondo de la imagen y las reflexiones, ambas fuentes de incertidumbre en las medidas de PIV. En este caso, un filtro pasa altos espectral es aplicado al conjunto de imágenes de PIV para poder quitar la parte mayormente correlacionada de la señal, la cual corresponde con el fondo de la imagen. En la tercera y cuarta aplicación de la POD, está técnica es utilizada para reconstruir las dinámicas fundamentales de un flujo. Concretamente, en el Capítulo 5 la POD es utilizada para analizar la estela compleja que se produce en una pareja de cilindros en tándem con la perturbación adicional de una pared próxima a ellos. A través de esta técnica, es posible poder estudiar los cambios en el comportamiento oscilatorio de las inestabilidades de la estela, las cuales están relacionadas con las diferentes configuraciones geométricas de los cilindros. En el capítulo 6, la POD y la EPOD son aplicadas respectivamente a campos fluidos y fuerzas aerodinámicas producidos por un perfil aerodinámico en movimiento (de rotación y desplazamiento vertical) no estacionario. La técnica de descomposición permite extraer un conjunto reducido de modos del campo fluido que están relacionados con el mecanismo que genera las fuerzas aerodinámicas. Estos modos corresponden con fenómenos característicos del flujo que pueden ser identificados para diferentes cinemáticas de perfiles aerodinámicos. Estas dinámicas del flujo que están conectadas con las fuerzas aerodinámicas son analizadas teniendo en cuenta los modelos ya existentes en la literatura que describen las fuerzas aerodinámicas, permitiendo su reinterpretación e incluso pudiendo añadir posibles correcciones. La última aplicación propuesta está destinada a subsanar la baja resolución temporal típica de las medidas de campo fluido, como en aquellas realizadas utilizando PIV, mediante una estimación robusta de las dinámicas del flujo turbulento. El método propuesto emplea una versión modificada de la EPOD para identificar para correlación entre un campo fluido medido que no está resuelto en el tiempo y una medida puntual que sí que está resulta en el tiempo. La estimación del campo fluido resuelto en el tiempo es obtenida mediante la correlación de los campos de flujo con la información temporal contenida en la medida puntual.This work has been partially supported by the Grant TRA2013-41103-P of the Spanish Ministry of Economy and Competitiveness, which includes FEDER funding, and by the Grant DPI2016-79401-R, funded by the Spanish State Research Agency (SRA) and European Regional Development Fund (ERDF).Programa Oficial de Doctorado en Mecánica de FluidosPresidente: Bharathram Ganapathisubramani.- Secretario: Francisco Javier Rodríguez Rodríguez.- Vocal: Francisco J. Huera-Huart