This doctorate thesis focuses on sparse regression, a statistical modeling tool for selecting valuable predictors in underdetermined linear models. By imposing different constraints on the structure of the variable vector in the regression problem, one obtains estimates which have sparse supports, i.e., where only a few of the elements in the response variable have non-zero values. The thesis collects six papers which, to a varying extent, deals with the applications, implementations, modifications, translations, and other analysis of such problems. Sparse regression is often used to approximate additive models with intricate, non-linear, non-smooth or otherwise problematic functions, by creating an underdetermined model consisting of candidate values for these functions, and linear response variables which selects among the candidates. Sparse regression is therefore a widely used tool in applications such as, e.g., image processing, audio processing, seismological and biomedical modeling, but is ...

Reverberation consists of a complex acoustic phenomenon that occurs inside rooms. Many audio signal processing methods, addressing source localization, signal enhancement and other tasks, often assume absence of reverberation. Consequently, reverberant environments are considered challenging as state-ofthe-art methods can perform poorly. The acoustics of a room can be described using a variety of mathematical models, among which, physical models are the most complete and accurate. The use of physical models in audio signal processing methods is often non-trivial since it can lead to ill-posed inverse problems. These inverse problems require proper regularization to achieve meaningful results and involve the solution of computationally intensive large-scale optimization problems. Recently, however, sparse regularization has been applied successfully to inverse problems arising in different scientific areas. The increased computational power of modern computers and the development of new efficient optimization algorithms makes it possible ...

Multiple sclerosis is a progressive autoimmune disease that a˙ects young adults. Magnetic resonance (MR) imaging has become an integral part in monitoring multiple sclerosis disease. Conventional MR imaging sequences such as fluid attenuated inversion recovery imaging have high spatial resolution, and can visualise the presence of focal white matter brain lesions in multiple sclerosis disease. Manual delineation of these lesions on conventional MR images is time consuming and su˙ers from intra and inter-rater variability. Among the advanced MR imaging techniques, MR spectroscopic imaging can o˙er complementary information on lesion characterisation compared to conventional MR images. However, MR spectroscopic images have low spatial resolution. Therefore, the aim of this thesis is to automatically segment multiple sclerosis lesions on conventional MR images and use the information from high-resolution conventional MR images to enhance the resolution of MR spectroscopic images. Automatic single time ...

Modern research in environmental microbiology utilizes genomic data, especially sequencing of DNA, to describe microbial communities. The field studying all genetic material present in an environmental sample is referred to as metagenomics. This doctoral thesis deals with metagenomics from the perspective of bioinformatics that is unreplaceable during the data processing. In the theoretical part of this thesis, two different approaches of metagenomics are described including their main principles and weaknesses. The first approach, based on targeted sequencing, is a well-established field with a wide range of bioinformatics techniques. Yet, methods for comparison of samples from several environments can be highly improved. The approach introduced in this thesis uses unique transformation of data into a bipartite graph, where one partition is formed by taxa, while the other by samples or environments. Such a graph fully reflects qualitative as well as quantitative ...

Today’s society is characterized by an abundance of data that is generated at an unprecedented velocity. However, much of this data is immediately thrown away by compression or information extraction. In a compressed sensing (CS) setting the inherent sparsity in many datasets is exploited by avoiding the acquisition of superfluous data in the first place. We combine this technique with tensors, or multiway arrays of numerical values, which are higher-order generalizations of vectors and matrices. As the number of entries scales exponentially in the order, tensor problems are often large-scale. We show that the combination of simple, low-rank tensor decompositions with CS effectively alleviates or even breaks the so-called curse of dimensionality. After discussing the larger data fusion optimization framework for coupled and constrained tensor decompositions, we investigate three categories of CS type algorithms to deal with large-scale problems. First, ...

Wireless Sensor Networks (WSNs) aim for accurate data gathering and representation of one or multiple physical variables from the environment, by means of sensor reading and wireless data packets transmission to a Data Fusion Center (DFC). There is no comprehensive common set of requirements for all WSN, as they are application dependent. Moreover, due to specific node capabilities or energy consumption constraints several tradeoffs have to be considered during the design, and particularly, the price of the sensor nodes is a determining factor. The distinction between small and large scale WSNs does not only refers to the quantity of sensor nodes, but also establishes the main design challenges in each case. For example, the node organization is a key issue in large scale WSNs, where many inexpensive nodes have to properly work in a coordinated manner. Regarding the amount of ...

It takes more time to think of a silent scene, action or event than finding one that emanates sound. Not only speaking or playing music but almost everything that happens is accompanied with or results in one or more sounds mixed together. This makes acoustic event detection (AED) one of the most researched topics in audio signal processing nowadays and it will probably not see a decline anywhere in the near future. This is due to the thirst for understanding and digitally abstracting more and more events in life via the enormous amount of recorded audio through thousands of applications in our daily routine. But it is also a result of two intrinsic properties of audio: it doesn’t need a direct sight to be perceived and is less intrusive to record when compared to image or video. Many applications such ...

The recent announcement by the LIGO and Virgo Collaborations of the direct detection of gravitational waves started the era of gravitational wave astrophysics. Up to now there have been five confirmed detections (GW150914, GW151226, GW170104, GW170814 and GW170817). Each of the GW events detected so far, shed light on multiple aspects of gravity. The first four events were due to the coalescence of a binary black hole system. August 17th 2017 marked the beginning of the so-called Multi-Messenger astronomy: the binary neutron star merger GW170817 has been observed almost simultaneously by LIGO and Virgo interferometers and several telescopes in space and on Earth, which detected the electromagnetic counterpart of this event (first as a short gamma-ray burst, GRB 170817A, and then in the visible, infra-red and X-ray bands). These last two years of great scientific discoveries would not have been ...

Learning parameters from voluminous data can be prohibitive in terms of memory and computational requirements. Furthermore, new challenges arise from modern database architectures, such as the requirements for learning methods to be amenable to streaming, parallel and distributed computing. In this context, an increasingly popular approach is to first compress the database into a representation called a linear sketch, that satisfies all the mentioned requirements, then learn the desired information using only this sketch, which can be significantly faster than using the full data if the sketch is small. In this thesis, we introduce a generic methodology to fit a mixture of probability distributions on the data, using only a sketch of the database. The sketch is defined by combining two notions from the reproducing kernel literature, namely kernel mean embedding and Random Features expansions. It is seen to correspond ...

The large number of practical applications involving digital images has motivated a significant interest towards restoration solutions that improve the visual quality of the data under the presence of various acquisition and compression artifacts. Digital images are the results of an acquisition process based on the measurement of a physical quantity of interest incident upon an imaging sensor over a specified period of time. The quantity of interest depends on the targeted imaging application. Common imaging sensors measure the number of photons impinging over a dense grid of photodetectors in order to produce an image similar to what is perceived by the human visual system. Different applications focus on the part of the electromagnetic spectrum not visible by the human visual system, and thus require different sensing technologies to form the image. In all cases, even with the advance of ...

In this thesis, we presented a detailed study of the face verification problem on the mobile device, covering every component of the system. The study includes face detection, registration, normalization, and verification. Furthermore, the information fusion problem is studied to verify face sequences, and to fuse different modalities. Although the work is application-specific, the thesis is not limited to the application, but more extensive. In every step, we have justified the methods we choose both from the theoretical and the practical point of view. In the review part of each chapter, we discussed principles and methodologies on a higher level, for a better understanding of the problems in general. In our solutions, on the other hand, we have taken care of the application requirements, and put much emphasis on the efficiency and simplicity of the methods. The system has dealt ...

Multimedia consumer electronics are nowadays everywhere from teleconferencing, hands-free communications, in-car communications to smart TV applications and more. We are living in a world of telecommunication where ideal scenarios for implementing these applications are hard to find. Instead, practical implementations typically bring many problems associated to each real-life scenario. This thesis mainly focuses on two of these problems, namely, acoustic echo and acoustic feedback. On the one hand, acoustic echo cancellation (AEC) is widely used in mobile and hands-free telephony where the existence of echoes degrades the intelligibility and listening comfort. On the other hand, acoustic feedback limits the maximum amplification that can be applied in, e.g., in-car communications or in conferencing systems, before howling due to instability, appears. Even though AEC and acoustic feedback cancellation (AFC) are functional in many applications, there are still open issues. This means that ...

In this thesis, advanced robust estimation methodologies for signal processing are developed and analyzed. The developed methodologies solve problems concerning multi-sensor data, robust model selection as well as robustness for dependent data. The work has been applied to solve practical signal processing problems in different areas of biomedical and array signal processing. In particular, for univariate independent data, a robust criterion is presented to select the model order with an application to corneal-height data modeling. The proposed criterion overcomes some limitations of existing robust criteria. For real-world data, it selects the radial model order of the Zernike polynomial of the corneal topography map in accordance with clinical expectations, even if the measurement conditions for the videokeratoscopy, which is the state-of-the-art method to collect corneal-height data, are poor. For multi-sensor data, robust model order selection selection criteria are proposed and applied ...

Developing realistic channel models is one of the greatest challenges for describing wireless communications. Their quality is crucial for accurately predicting the performance of a wireless system. While on the one hand, channel models have to be accurate in describing the physical properties of wave propagation, on the other hand, they have to be as least complex as possible. With the recent emergence of antennas with a massive amount of elements as a promising technology for a further enhancement of spectral efficiency, new channel models that characterize the propagation environment in both azimuth and elevation become necessary. While standardization bodies such as 3rd Generation Partnership Project (3GPP) and International Telecommunications Unit (ITU) have introduced a 3-dimensional (3D) geometry-based stochastic channel model, a system-level modeling has been missing to serve the purpose of further analysis and evaluations. Furthermore, with such a ...

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 ...