The sparse coding is approximation/representation of signals with the minimum number of coefficients using an overcomplete set of elementary functions. This kind of approximations/ representations has found numerous applications in source separation, denoising, coding and compressed sensing. The adaptation of the sparse approximation framework to the coding problem of signals is investigated in this thesis. Open problems are the selection of appropriate models and their orders, coefficient quantization and sparse approximation method. Some of these questions are addressed in this thesis and novel methods developed. Because almost all recent communication and storage systems are digital, an easy method to compute quantized sparse approximations is introduced in the first part. The model selection problem is investigated next. The linear model can be adapted to better fit a given signal class. It can also be designed based on some a priori information ...

Many signal and image processing applications have benefited remarkably from the theory of sparse representations. In its classical form this theory models signal as having a sparse representation under a given dictionary -- this is referred to as the "Synthesis Model". In this work we focus on greedy methods for the problem of recovering a signal from a set of deteriorated linear measurements. We consider four different sparsity frameworks that extend the aforementioned synthesis model: (i) The cosparse analysis model; (ii) the signal space paradigm; (iii) the transform domain strategy; and (iv) the sparse Poisson noise model. Our algorithms of interest in the first part of the work are the greedy-like schemes: CoSaMP, subspace pursuit (SP), iterative hard thresholding (IHT) and hard thresholding pursuit (HTP). It has been shown for the synthesis model that these can achieve a stable recovery ...

The sparse signal recovery, which appears not only in compressed sensing but also in other related problems such as sparse overcomplete representations, denoising, sparse learning, etc. has drawn a large attraction in the last decade. The literature contains a vast number of recovery methods, which have been analysed in theoretical and empirical aspects. This dissertation presents novel search-based sparse signal recovery methods. First, we discuss theoretical analysis of the orthogonal matching pursuit algorithm with more iterations than the number of nonzero elements of the underlying sparse signal. Second, best-fi rst tree search is incorporated for sparse recovery by a novel method, whose tractability follows from the properly de fined cost models and pruning techniques. The proposed method is evaluated by both theoretical and empirical analyses, which clearly emphasize the improvements in the recovery accuracy. Next, we introduce an iterative two ...

Over-complete transforms have recently become the focus of a wide wealth of research in signal processing, machine learning, statistics and related fields. Their great modelling flexibility allows to find sparse representations and approximations of data that in turn prove to be very efficient in a wide range of applications. Sparse models express signals as linear combinations of a few basis functions called atoms taken from a so-called dictionary. Finding the optimal dictionary from a set of training signals of a given class is the objective of dictionary learning and the main focus of this thesis. The experimental evidence presented here focuses on the processing of audio signals, and the role of sparse algorithms in audio applications is accordingly highlighted. The first main contribution of this thesis is the development of a pitch-synchronous transform where the frame-by-frame analysis of audio data ...

This thesis is based on nine papers, all concerned with parameter estimation. The thesis aims at solving problems related to real-world applications such as spectroscopy, DNA sequencing, and audio processing, using sparse modeling heuristics. For the problems considered in this thesis, one is not only concerned with finding the parameters in the signal model, but also to determine the number of signal components present in the measurements. In recent years, developments in sparse modeling have allowed for methods that jointly estimate the parameters in the model and the model order. Based on these achievements, the approach often taken in this thesis is as follows. First, a parametric model of the considered signal is derived, containing different parameters that capture the important characteristics of the signal. When the signal model has been determined, an optimization problem is formed aimed at finding ...

This thesis presents novel exemplar-based texture synthesis methods for image prediction (i.e., predictive coding) and image inpainting problems. The main contributions of this study can also be seen as extensions to simple template matching, however the texture synthesis problem here is well-formulated in an optimization framework with different constraints. The image prediction problem has first been put into sparse representations framework by approximating the template with a sparsity constraint. The proposed sparse prediction method with locally and adaptive dictionaries has been shown to give better performance when compared to static waveform (such as DCT) dictionaries, and also to the template matching method. The image prediction problem has later been placed into an online dictionary learning framework by adapting conventional dictionary learning approaches for image prediction. The experimental observations show a better performance when compared to H.264/AVC intra and sparse prediction. ...

Distributed signal or information processing using Internet of Things (IoT), facilitates real-time monitoring of signals, for example, environmental pollutants, health indicators, and electric energy consumption in a smart city. Despite the promising capabilities of IoTs, these distributed deployments often face the challenge of data privacy and communication rate constraints. In traditional machine learning, training data is moved to a data center, which requires massive data movement from distributed IoT devices to a third-party location, thus raising concerns over privacy and inefficient use of communication resources. Moreover, the growing network size, model size, and data volume combined lead to unusual complexity in the design of optimization algorithms beyond the compute capability of a single device. This necessitates novel system architectures to ensure stable and secure operations of such networks. Federated learning (FL) architecture, a novel distributed learning paradigm introduced by McMahan ...

This thesis develops new mathematical theory and presents novel recovery algorithms for discrete linear dynamical systems (LDS) with sparsity constraints on either control inputs or initial state. The recovery problems in this framework manifest as the problem of reconstructing one or more sparse signals from a set of noisy underdetermined linear measurements. The goal of our work is to design algorithms for sparse signal recovery which can exploit the underlying structure in the measurement matrix and the unknown sparse vectors, and to analyze the impact of these structures on the efficacy of the recovery. We answer three fundamental and interconnected questions on sparse signal recovery problems that arise in the context of LDS. First, what are necessary and sufficient conditions for the existence of a sparse solution? Second, given that a sparse solution exists, what are good low-complexity algorithms that ...

Video signals are sequences of natural images, where images are often modeled as piecewise-smooth signals. Hence, video can be seen as a 3D piecewise-smooth signal made of piecewise-smooth regions that move through time. Based on the piecewise-smooth model and on related theoretical work on rate-distortion performance of wavelet and oracle based coding schemes, one can better analyze the appropriate coding strategies that adaptive video codecs need to implement in order to be efficient. Efficient video representations for coding purposes require the use of adaptive signal decompositions able to capture appropriately the structure and redundancy appearing in video signals. Adaptivity needs to be such that it allows for proper modeling of signals in order to represent these with the lowest possible coding cost. Video is a very structured signal with high geometric content. This includes temporal geometry (normally represented by motion ...

Magnetic Resonance Imaging (MRI) constitutes a non-invasive medical imaging technique that allows the exploration of the inner anatomy, tissues, and physiological processes of the body. Among the different MRI applications, functional Magnetic Resonance Imaging (fMRI) has slowly become an essential tool for investigating the brain behavior and, nowadays, it plays a fundamental role in clinical and neurophysiological research. Due to its particular nature, specialized signal processing techniques are required in order to analyze the fMRI data properly. Among the various related techniques that have been developed over the years, the General Linear Model (GLM) is one of the most widely used approaches, and it usually appears as a default in many specialized software toolboxes for fMRI. On the other end, Blind Source Separation (BSS) methods constitute the most common alternative to GLM, especially when no prior information regarding the brain ...

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 ...

In this thesis we investigate centralized and distributed variants of sparse Bayesian learning (SBL), an effective probabilistic regression method used in machine learning. Since inference in an SBL model is not tractable in closed form, approximations are needed. We focus on the variational Bayesian approximation, as opposed to others used in the literature, for three reasons: First, it is a flexible general framework for approximate Bayesian inference that estimates probability densities including point estimates as a special case. Second, it has guaranteed convergence properties. And third, it is a deterministic approximation concept that is even applicable for high dimensional problems where non-deterministic sampling methods may be prohibitive. We resolve some inconsistencies in the literature involved in other SBL approximation techniques with regard to a proper Bayesian treatment and the incorporation of a very desired property, namely scale invariance. More specifically, ...

Over the last decade there has been an increasing interest in solutions for the continuous monitoring of health status with wireless, and in particular, wearable devices that provide remote analysis of physiological data. The use of wireless technologies have introduced new problems such as the transmission of a huge amount of data within the constraint of limited battery life devices. The design of an accurate and energy efficient telemonitoring system can be achieved by reducing the amount of data that should be transmitted, which is still a challenging task on devices with both computational and energy constraints. Furthermore, it is not sufficient merely to collect and transmit data, and algorithms that provide real-time analysis are needed. In this thesis, we address the problems of compression and analysis of physiological data using the emerging frameworks of Compressive Sensing (CS) and sparse ...

Since the late 1990s, massive multiple-input multiple-output (MIMO) has been suggested to improve the achievable data rate in wireless communication systems. To overcome the high path losses in the high frequency bands, the use of massive MIMO will be a must rather than an option in future wireless communication systems. At the same time, due to the high cost and high energy consumption of the traditional fully digital beamforming architecture, a new beamforming architecture is required. Among the proposed solutions, the hybrid analog digital (HAD) beamforming architecture has received considerable attention. The promising massive MIMO gains heavily rely on the availability of accurate channel state information (CSI). This thesis considers a wideband massive MIMO orthogonal frequency division multiplexing (OFDM) system. We propose a channel estimation method called sequential alternating least squares approximation (SALSA) by exploiting a hidden tensor structure in ...

This thesis focuses on wearables for health status monitoring, covering applications aimed at emergency solutions to the COVID-19 pandemic and aging society. The methods of ambient assisted living (AAL) are presented for the neurodegenerative disease Parkinson’s disease (PD), facilitating ’aging in place’ thanks to machine learning and around wearables - solutions of mHealth. Furthermore, the approaches using machine learning and wearables are discussed for early-stage COVID-19 detection, with encouraging accuracy. Firstly, a publicly available dataset containing COVID-19, influenza, and healthy control data was reused for research purposes. The solution presented in this thesis is considering the classification problem and outperformed the state-of-the-art methods, whereas the original paper introduced just anomaly detection and not shown the specificity of the created models. The proposed model in the thesis for early detection of COVID-19 achieved 78 % for the k-NN classifier. Moreover, a ...