The first part of this dissertation considers distributed learning problems over networked agents. The general objective of distributed adaptation and learning is the solution of global, stochastic optimization problems through localized interactions and without information about the statistical properties of the data. Regularization is a useful technique to encourage or enforce structural properties on the resulting solution, such as sparsity or constraints. A substantial number of regularizers are inherently non-smooth, while many cost functions are differentiable. We propose distributed and adaptive strategies that are able to minimize aggregate sums of objectives. In doing so, we exploit the structure of the individual objectives as sums of differentiable costs and non-differentiable regularizers. The resulting algorithms are adaptive in nature and able to continuously track drifts in the problem; their recursions, however, are subject to persistent perturbations arising from the stochastic nature of ...

High dimensional time series data are observed in many complex systems. In networked data, some of the time series are influenced by other time series. Identifying these relations encoded in a graph structure or topology among the time series is of paramount interest in certain applications since the identifi ed structure can provide insights about the underlying system and can assist in inference tasks. In practice, the underlying topology is usually sparse, that is, not all the participating time series influence each other. The goal of this dissertation pertains to study the problem of sparse topology identi fication under various settings. Topology identi fication from time series is a challenging task. The first major challenge in topology identi fication is that the assumption of static topology does not hold always in practice since most of the practical systems are evolving ...

Ill-posed inverse problems appear in many signal and image processing applications, such as deblurring, super-resolution and compressed sensing. The common approach to address them is to design a specific algorithm, or recently, a specific deep neural network, for each problem. Both signal processing and machine learning tactics have drawbacks: traditional reconstruction strategies exhibit limited performance for complex signals, such as natural images, due to the hardness of their mathematical modeling; while modern works that circumvent signal modeling by training deep convolutional neural networks (CNNs) suffer from a huge performance drop when the observation model used in training is inexact. In this work, we develop and analyze reconstruction algorithms that are not restricted to a specific signal model and are able to handle different observation models. Our main contributions include: (a) We generalize the popular sparsity-based CoSaMP algorithm to any signal ...

In many fields, such as linear algebra, computational geometry, combinatorial optimization, analytical chemistry and geoscience, nonnegativity of the solution is required, which is either due to the fact that the data is physically nonnegative, or that the mathematical modeling of the problem requires nonnegativity. Image and audio processing are two examples for which the data are physically nonnegative. Probability and graph theory are examples for which the mathematical modeling requires nonnegativity. This thesis is about the nonnegative factorization of matrices and tensors: namely nonnegative matrix factorization (NMF) and nonnegative tensor factorization (NTF). NMF problems arise in a wide range of scenarios such as the aforementioned fields, and NTF problems arise as a generalization of NMF. As the title suggests, the contributions of this thesis are centered on NMF and NTF over three aspects: modeling, algorithms and applications. On the modeling ...

The spectral signatures of the materials contained in hyperspectral images, also called endmembers (EMs), can be significantly affected by variations in atmospheric, illumination or environmental conditions typically occurring within an image. Traditional spectral unmixing (SU) algorithms neglect the spectral variability of the endmembers, what propagates significant mismodeling errors throughout the whole unmixing process and compromises the quality of the estimated abundances. Therefore, significant effort have been recently dedicated to mitigate the effects of spectral variability in SU. However, many challenges still remain in how to best explore a priori information about the problem in order to improve the quality, the robustness and the efficiency of SU algorithms that account for spectral variability. In this thesis, new strategies are developed to address spectral variability in SU. First, an (over)-segmentation-based multiscale regularization strategy is proposed to explore spatial information about the abundance ...

The aim of this thesis is to introduce a variety of signal processing methodologies specifically designed to model, interpret, and learn from data structured within topological spaces. These spaces are loosely characterized as a collection of points together with a neighborhood notion among points. The methodologies and tools discussed herein hold particular relevance and utility when applied to signals defined over combinatorial topological spaces, such as cell complexes, or within metric spaces that exhibit non-trivial properties, such as Riemann manifolds with non-flat metrics. One of the primary motivations behind this research is to address and surmount the constraints encountered with traditional graph-based representations when they are employed to depict intricate systems. This thesis emphasizes the necessity to account for sophisticated, multiway, and geometry-sensitive interactions that are not adequately captured by conventional graph models. The contributions of this work include but ...

Extending the concepts of classical signal processing to graphs, a wide array of methods have come to the fore, including filtering, reconstruction, classification, and sampling. Existing approaches in graph signal processing consider a known and static topology, i.e., fixed number of nodes and a fixed edge support. Two types of tasks stand out, namely, topology inference, where the edge support along with their weights are estimated from signals; and data processing, where existing data and the known topology are used to perform different tasks. However, such tasks become quite challenging when the network size and support changes over time. Particularly, these challenges involve adapting to the changing topology, data distributions and dealing with unknown topological information. The latter manifests for example, when new nodes are available to attach to the graph but their connectivity is uncertain as is the case ...

When listening to music, some humans can easily recognize which instruments play at what time or when a new musical segment starts, but cannot describe exactly how they do this. To automatically describe particular aspects of a music piece – be it for an academic interest in emulating human perception, or for practical applications –, we can thus not directly replicate the steps taken by a human. We can, however, exploit that humans can easily annotate examples, and optimize a generic function to reproduce these annotations. In this thesis, I explore solving different music perception tasks with deep learning, a recent branch of machine learning that optimizes functions of many stacked nonlinear operations – referred to as deep neural networks – and promises to obtain better results or require less domain knowledge than more traditional techniques. In particular, I employ ...

Hyperspectral (HS) imaging, which consists of acquiring a same scene in several hundreds of contiguous spectral bands (a three dimensional data cube), has opened a new range of relevant applications, such as target detection [MS02], classification [C.-03] and spectral unmixing [BDPD+12]. However, while HS sensors provide abundant spectral information, their spatial resolution is generally more limited. Thus, fusing the HS image with other highly resolved images of the same scene, such as multispectral (MS) or panchromatic (PAN) images is an interesting problem. The problem of fusing a high spectral and low spatial resolution image with an auxiliary image of higher spatial but lower spectral resolution, also known as multi-resolution image fusion, has been explored for many years [AMV+11]. From an application point of view, this problem is also important as motivated by recent national programs, e.g., the Japanese next-generation space-borne ...

The field of Life Science Engineering (LSE) is rapidly expanding and predicted to grow strongly in the next decades. It covers areas of food and medical research, plant and pests’ research, and environmental research. In each research area, engineers try to find equations that model a certain life science problem. Once found, they research different numerical techniques to solve for the unknown variables of these equations. Afterwards, solution improvement is examined by adopting more accurate conventional techniques, or developing novel algorithms. In particular, signal and image processing techniques are widely used to solve those LSE problems require pattern recognition. However, due to the continuous evolution of the life science problems and their natures, these solution techniques can not cover all aspects, and therefore demanding further enhancement and improvement. The thesis presents numerical algorithms of digital signal and image processing to ...

Single-channel source separation for radio-frequency (RF) systems is a challenging problem relevant to key applications, including wireless communications, radar, and spectrum monitoring. This thesis addresses the challenge by focusing on data-driven approaches for source separation, leveraging datasets of sample realizations when source models are not explicitly provided. To this end, deep learning techniques are employed as function approximations for source separation, with models trained using available data. Two problem abstractions are studied as benchmarks for our proposed deep-learning approaches. Through a simplified problem involving Orthogonal Frequency Division Multiplexing (OFDM), we reveal the limitations of existing deep learning solutions and suggest modifications that account for the signal modality for improved performance. Further, we study the impact of time shifts on the formulation of an optimal estimator for cyclostationary Gaussian time series, serving as a performance lower bound for evaluating data-driven methods. ...

Inference and data analysis over networks have become significant areas of research due to the increasing prevalence of interconnected systems and the growing volume of data they produce. Many of these systems generate data in the form of multivariate time series, which are collections of time series data that are observed simultaneously across multiple variables. For example, EEG measurements of the brain produce multivariate time series data that record the electrical activity of different brain regions over time. Cyber-physical systems generate multivariate time series that capture the behaviour of physical systems in response to cybernetic inputs. Similarly, financial time series reflect the dynamics of multiple financial instruments or market indices over time. Through the analysis of these time series, one can uncover important details about the behavior of the system, detect patterns, and make predictions. Therefore, designing effective methods for ...

Recent years have witnessed a significant interest in interpretable machine learning (IML) research that develops techniques to analyse machine learning (ML) models. Understanding ML models is essential to gain trust in their predictions and to improve datasets, model architectures and training techniques. The majority of effort in IML research has been in analysing models that classify images or structured data and comparatively less work exists that analyses models for other domains. This research focuses on developing novel IML methods and on extending existing methods to understand machine listening models that analyse audio. In particular, this thesis reports the results of three studies that apply three different IML methods to analyse five singing voice detection (SVD) models that predict singing voice activity in musical audio excerpts. The first study introduces SoundLIME (SLIME), a method to generate temporal, spectral or time-frequency explanations ...

This thesis contributes to motion characterization through inertial and physiological signals captured by wearable devices and analyzed using signal processing and deep learning techniques. This research leverages the possibilities of motion analysis for three main applications: to know what physical activity a person is performing (Human Activity Recognition), to identify who is performing that motion (user identification) or know how the movement is being performed (motor anomaly detection). Most previous research has addressed human motion modeling using invasive sensors in contact with the user or intrusive sensors that modify the user’s behavior while performing an action (cameras or microphones). In this sense, wearable devices such as smartphones and smartwatches can collect motion signals from users during their daily lives in a less invasive or intrusive way. Recently, there has been an exponential increase in research focused on inertial-signal processing to ...

This work is concerned with two image-processing problems, image deconvolution with incomplete observations and data fusion of spectral images, and with some of the algorithms that are used to solve these and related problems. In image-deconvolution problems, the diagonalization of the blurring operator by means of the discrete Fourier transform usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard deconvolution techniques normally involve non-diagonalizable operators, resulting in rather slow methods, or, otherwise, use inexact convolution models, resulting in the occurrence of artifacts in the enhanced images. We propose a new deconvolution framework for images with incomplete observations that allows one to work with diagonalizable convolution operators, and therefore is very fast. The framework is also an efficient, high-quality alternative to existing methods of dealing with the image boundaries, such as edge ...