Convex and Nonconvex Optimization Geometries

As many machine learning and signal processing problems are fundamentally nonconvex and too expensive/difficult to be convexified, my research is focused on understanding the optimization landscapes of their fundamentally nonconvex formulations. After understanding their optimization landscapes, we can develop optimization algorithms to efficiently navigate these optimization landscapes and achieve the global optimality convergence. So, the main theme of this thesis would be optimization, with an emphasis on nonconvex optimization and algorithmic developments for these popular optimization problems. This thesis can be conceptually divided into four parts: Part 1: Convex Optimization. In the first part, we apply convex relaxations to several popular nonconvex problems in signal processing and machine learning (e.g. line spectral estimation problem and tensor decomposition problem) and prove that the solving the new convex relaxation problems is guaranteed to achieve the globally optimal solutions of their original nonconvex ...

Li, Qiuwei — Colorado School of Mines


Communication Rates for Fading Channels with Imperfect Channel-State Information

An important specificity of wireless communication channels are the rapid fluctuations of propagation coefficients. This effect is called fading and is caused by the motion of obstacles, scatterers and reflectors standing along the different paths of electromagnetic wave propagation between the transmitting and the receiving terminal. These changes in the geometry of the wireless channel prompt the attenuation coefficients and the relative phase shifts between the multiple propagation paths to vary. This suggests to model the channel coefficients (the transfer matrix) as random variables. The present thesis studies information rates for reliable transmission of information over fading channels under the realistic assumption that the receiver has only imperfect knowledge of the random fading state. While the over-idealized assumption of perfect channel-state information at the receiver (CSIR) gives rise to many simple expressions and is fairly well understood, the settings with ...

Pastore, Adriano — Universitat Politècnica de Catalunya


Antenna arrays in wireless communications

We investigate two aspects of multiple-antenna wireless communication systems in this thesis: 1) deployment of an adaptive beamformer array at the receiver; and 2) space-time coding for arrays at the transmitter and the receiver. In the first part of the thesis, we establish sufficient conditions for the convergence of a popular least mean squares (LMS) algorithm known as the sequential Partial Update LMS Algorithm for adaptive beamforming. Partial update LMS (PU-LMS) algorithms are reduced complexity versions of the full update LMS that update a subset of filter coefficients at each iteration. We introduce a new improved algorithm, called Stochastic PU-LMS, which selects the subsets at random at each iteration. We show that the new algorithm converges for a wider class of signals than the existing PU-LMS algorithms. The second part of this thesis deals with the multiple-input multiple-output (MIMO) Shannon ...

Godavarti, Mahesh — University of Michigan


Signal and Image Processing Algorithms Using Interval Convex Programming and Sparsity

In this thesis, signal and image processing algorithms based on sparsity and interval convex programming are developed for inverse problems. Inverse signal processing problems are solved by minimizing the ℓ1 norm or the Total Variation (TV) based cost functions in the literature. A modified entropy functional approximating the absolute value function is defined. This functional is also used to approximate the ℓ1 norm, which is the most widely used cost function in sparse signal processing problems. The modified entropy functional is continuously differentiable, and convex. As a result, it is possible to develop iterative, globally convergent algorithms for compressive sensing, denoising and restoration problems using the modified entropy functional. Iterative interval convex programming algorithms are constructed using Bregman’s D-Projection operator. In sparse signal processing, it is assumed that the signal can be represented using a sparse set of coefficients in ...

Kose, Kivanc — Bilkent University


Biometric Sample Quality and Its Application to Multimodal Authentication Systems

This Thesis is focused on the quality assessment of biometric signals and its application to multimodal biometric systems. Since the establishment of biometrics as an specific research area in late 90s, the biometric community has focused its efforts in the development of accurate recognition algorithms and nowadays, biometric recognition is a mature technology that is used in many applications. However, we can notice recent studies that demonstrate how performance of biometric systems is heavily affected by the quality of biometric signals. Quality measurement has emerged in the biometric community as an important concern after the poor performance observed in biometric systems on certain pathological samples. We first summarize the state-of-the-art in the biometric quality problem. We present the factors influencing biometric quality, which mainly have to do with four issues: the individual itself, the sensor used in the acquisition, the ...

Alonso-Fernandez, Fernando — Universidad Politecnica de Madrid


Stochastic Schemes for Dynamic Network Resource Allocation

Wireless networks and power distribution grids are experiencing increasing demands on their efficiency and reliability. Judicious methods for allocating scarce resources such as power and bandwidth are of paramount importance. As a result, nonlinear optimization and signal processing tools have been incorporated into the design of contemporary networks. This thesis develops schemes for efficient resource allocation (RA) in such dynamic networks, with an emphasis in stochasticity, which is accounted for in the problem formulation as well as in the algorithms and schemes to solve those problems. Stochastic optimization and decomposition techniques are investigated to develop low-complexity algorithms with specific applications in cross-layer design of wireless communications, cognitive radio (CR) networks and smart power distribution systems. The costs and constraints on the availability of network resources, together with diverse quality of service (QoS) requirements, render network design, management, and operation challenging ...

Lopez Ramos, Luis Miguel — King Juan Carlos University


Advances in graph signal processing: Graph filtering and network identification

To the surprise of most of us, complexity in nature spawns from simplicity. No matter how simple a basic unit is, when many of them work together, the interactions among these units lead to complexity. This complexity is present in the spreading of diseases, where slightly different policies, or conditions,might lead to very different results; or in biological systems where the interactions between elements maintain the delicate balance that keep life running. Fortunately, despite their complexity, current advances in technology have allowed us to have more than just a sneak-peak at these systems. With new views on how to observe such systems and gather data, we aimto understand the complexity within. One of these new views comes from the field of graph signal processing which provides models and tools to understand and process data coming from such complex systems. With ...

Coutino, Mario — Delft University of Technology


Antenna Arrays for Multipath and Interference Mitigation in GNSS Receivers

This thesis deals with the synchronization of one or several replicas of a known signal received in a scenario with multipath propagation and directional interference. A connecting theme along this work is the systematic application of the maximum likelihood (ML) principle together with a signal model in which the spatial signatures are unstructured and the noise term is Gaussian- distributed with an unknown correlation matrix. This last assumption is key in obtaining estimators that are capable of mitigating the disturbing signals that exhibit a certain structure, and this is achieved without resorting to the estimation of the parameters of those signals. On the other hand, the assumption of unstructured spatial signatures is interesting from a practical standpoint and facilitates the estimation problem since the estimates of these signatures can be obtained in closed form. This constitutes a first step towards ...

Seco-Granados, Gonzalo — Universitat Politecnica de Catalunya


Cooperative Techniques for Interference Management in Wireless Networks

In the last few years, wireless devices have evolved to unimaginable heights. Current forecasts suggest that, in the near future, every device that may take advantage of a wireless connection will have one. In addition, there is a gradual migration to smart devices and high-speed connections, and, as a consequence, the overall mobile traffic is expected to experience a tremendous growth in the next years. The multiuser interference will hence become the main limiting factor and the most critical point to address. As instrumental to efficiently manage interference between different systems, this thesis provides a thorough study on cooperative techniques. That is, users share information and exploit it to improve the overall performance. Since multiuser cooperation represents a very broad term, we will focus on algorithm design and transceiver optimization for three cooperative scenarios that capture some of the main ...

Lameiro, Christian — University of Cantabria


Robust Adaptive Machine Learning Algorithms for Distributed Signal Processing

Distributed networks comprising a large number of nodes, e.g., Wireless Sensor Networks, Personal Computers (PC’s), laptops, smart phones, etc., which cooperate with each other in order to reach a common goal, constitute a promising technology for several applications. Typical examples include: distributed environmental monitoring, acoustic source localization, power spectrum estimation, etc. Sophisticated cooperation mechanisms can significantly benefit the learning process, through which the nodes achieve their common objective. In this dissertation, the problem of adaptive learning in distributed networks is studied, focusing on the task of distributed estimation. A set of nodes sense information related to certain parameters and the estimation of these parameters constitutes the goal. Towards this direction, nodes exploit locally sensed measurements as well as information springing from interactions with other nodes of the network. Throughout this dissertation, the cooperation among the nodes follows the diffusion optimization ...

Chouvardas, Symeon — National and Kapodistrian University of Athens


Distributed Localization and Tracking of Acoustic Sources

Localization, separation and tracking of acoustic sources are ancient challenges that lots of animals and human beings are doing intuitively and sometimes with an impressive accuracy. Artificial methods have been developed for various applications and conditions. The majority of those methods are centralized, meaning that all signals are processed together to produce the estimation results. The concept of distributed sensor networks is becoming more realistic as technology advances in the fields of nano-technology, micro electro-mechanic systems (MEMS) and communication. A distributed sensor network comprises scattered nodes which are autonomous, self-powered modules consisting of sensors, actuators and communication capabilities. A variety of layout and connectivity graphs are usually used. Distributed sensor networks have a broad range of applications, which can be categorized in ecology, military, environment monitoring, medical, security and surveillance. In this dissertation we develop algorithms for distributed sensor networks ...

Dorfan, Yuval — Bar Ilan University


Estimation of Nonlinear Dynamic Systems: Theory and Applications

This thesis deals with estimation of states and parameters in nonlinear and non-Gaussian dynamic systems. Sequential Monte Carlo methods are mainly used to this end. These methods rely on models of the underlying system, motivating some developments of the model concept. One of the main reasons for the interest in nonlinear estimation is that problems of this kind arise naturally in many important applications. Several applications of nonlinear estimation are studied. The models most commonly used for estimation are based on stochastic difference equations, referred to as state-space models. This thesis is mainly concerned with models of this kind. However, there will be a brief digression from this, in the treatment of the mathematically more intricate differential-algebraic equations. Here, the purpose is to write these equations in a form suitable for statistical signal processing. The nonlinear state estimation problem is ...

Schon, Thomas — Linkopings Universitet


Facial Soft Biometrics: Methods, Applications and Solutions

This dissertation studies soft biometrics traits, their applicability in different security and commercial scenarios, as well as related usability aspects. We place the emphasis on human facial soft biometric traits which constitute the set of physical, adhered or behavioral human characteristics that can partially differentiate, classify and identify humans. Such traits, which include characteristics like age, gender, skin and eye color, the presence of glasses, moustache or beard, inherit several advantages such as ease of acquisition, as well as a natural compatibility with how humans perceive their surroundings. Specifically, soft biometric traits are compatible with the human process of classifying and recalling our environment, a process which involves constructions of hierarchical structures of different refined traits. This thesis explores these traits, and their application in soft biometric systems (SBSs), and specifically focuses on how such systems can achieve different goals ...

Dantcheva, Antitza — EURECOM / Telecom ParisTech


Decentralized Estimation Under Communication Constraints

In this thesis, we consider the problem of decentralized estimation under communication constraints in the context of Collaborative Signal and Information Processing. Motivated by sensor network applications, a high volume of data collected at distinct locations and possibly in diverse modalities together with the spatially distributed nature and the resource limitations of the underlying system are of concern. Designing processing schemes which match the constraints imposed by the system while providing a reasonable accuracy has been a major challenge in which we are particularly interested in the tradeoff between the estimation performance and the utilization of communications subject to energy and bandwidth constraints. One remarkable approach for decentralized inference in sensor networks is to exploit graphical models together with message passing algorithms. In this framework, after the so-called information graph of the problem is constructed, it is mapped onto the ...

Uney, Murat — Middle East Technical University


Prediction and Optimization of Speech Intelligibility in Adverse Conditions

In digital speech-communication systems like mobile phones, public address systems and hearing aids, conveying the message is one of the most important goals. This can be challenging since the intelligibility of the speech may be harmed at various stages before, during and after the transmission process from sender to receiver. Causes which create such adverse conditions include background noise, an unreliable internet connection during a Skype conversation or a hearing impairment of the receiver. To overcome this, many speech-communication systems include speech processing algorithms to compensate for these signal degradations like noise reduction. To determine the effect on speech intelligibility of these signal processing based solutions, the speech signal has to be evaluated by means of a listening test with human listeners. However, such tests are costly and time consuming. As an alternative, reliable and fast machine-driven intelligibility predictors are ...

Taal, Cees — Delft University of Technology

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