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 ...

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 ...

The development of a fully unsupervised algorithm to achieve image segmentation is the central theme of this dissertation. Existing literature falls short of such a goal providing many algorithms capable of solving a subset of this highly challenging problem. Unsupervised segmentation is the process of identifying and locating the constituent regions of an observed image, while having no prior knowledge of the number of regions. The problem can be formulated in a Bayesian framework and through the use of an assumed model unsupervised segmentation can be posed as a problem of optimisation. This is the approach pursued throughout this dissertation. Throughout the literature, the commonly adopted model is an hierarchical image model whose underlying components are various forms of Markov Random Fields Gaussian. Markov Random Field models are used to model the textural content of the observed images regions, while ...

The recent invasion of stereoscopic 3D television technologies is expected to be followed by autostereoscopic and holographic technologies. Glasses-free multiple stereoscopic pair displaying capabilities of these technologies will advance the 3D experience. The prospective 3D format to create the multiple views for such displays is Multiview Video plus Depth (MVD) format based on the Depth Image Based Rendering (DIBR) techniques. The depth modality of the MVD format is an active research area whose main objective is to develop DIBR friendly efficient compression methods. As a part this research, the thesis proposes novel 3D planar-based depth representations. The planar approximation of the stereo depth images is formulated as an energy-based co-segmentation problem by a Markov Random Field model. The energy terms of this problem are designed to mimic the rate-distortion tradeoff for a depth compression application. A heuristic algorithm is developed ...

The subject of the thesis is the emergence and analysis of visual texture microstructure for efficient modeling, descriptive feature extraction and image representation. Main objectives are the problems of image texture modeling and analysis in Computer Vision systems, with emphasis on the subproblems of texture detection, segmentation and separation in images. Advanced modeling and analysis methods are developed in parallel directions: a) Multiband models of narrowband components and spatial modulations, b) Energy methods for texture feature extraction, c) Variational techniques of image decomposition and texture separation. The proposed methods are applied on a database of digitized soilsection images to quantify and evaluate the biological quality of soils and in different types and collections of natural images. The developed model is the common ground to approach texture in its different forms and applications. In total, a complete system for texture processing ...

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 ...

In this thesis, we present a convex optimization approach to address three problems arising in multicomponent image recovery, supervised classification, and image forgery detection. The common thread among these problems is the presence of nonlinear convex constraints difficult to handle with state-of-the-art methods. Therefore, we present a novel splitting technique to simplify the management of such constraints. Relying on this approach, we also propose some contributions that are tailored to the aforementioned applications. The first part of the thesis presents the epigraphical splitting of nonlinear convex constraints. The principle is to decompose the sublevel set of a block-separable function into a collection of epigraphs. So doing, we reduce the complexity of optimization algorithms when the above constraint involves the sum of absolute values, distance functions to a convex set, Euclidean norms, infinity norms, or max functions. We demonstrate through numerical ...

Spatial hearing for human listeners is based on the interaural as well as on the monaural analysis of the signals arriving at both ears, enabling the listeners to assign certain spatial components to these signals. This spatial aspect gets lost when the signals are reproduced via headphones without considering the acoustical influence of the head and torso, i.e. head-related transfer function (HRTFs). A common procedure to take into account spatial aspects in a binaural reproduction is to use so-called artificial heads. Artificial heads are replicas of a human head and torso with average anthropometric geometries and built-in microphones in the ears. Although, the signals recorded with artificial heads contain relevant spatial aspects, binaural recordings using artificial heads often suffer from front-back confusions and the perception of the sound source being inside the head (internalization). These shortcomings can be attributed 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 ...

Gliomas represent about 80% of all malignant primary brain tumors. Despite recent advancements in glioma research, patient outcome remains poor. The 5 year survival rate of the most common and most malignant subtype, i.e. glioblastoma, is about 5%. Magnetic resonance imaging (MRI) has become the imaging modality of choice in the management of brain tumor patients. Conventional MRI (cMRI) provides excellent soft tissue contrast without exposing the patient to potentially harmful ionizing radiation. Over the past decade, advanced MRI modalities, such as perfusion-weighted imaging (PWI), diffusion-weighted imaging (DWI) and magnetic resonance spectroscopic imaging (MRSI) have gained interest in the clinical field, and their added value regarding brain tumor diagnosis, treatment planning and follow-up has been recognized. Tumor segmentation involves the imaging-based delineation of a tumor and its subcompartments. In gliomas, segmentation plays an important role in treatment planning as well ...

The present doctoral thesis aims towards the development of new long-term, multi-channel, audio-visual processing techniques for the analysis of bioacoustics phenomena. The effort is focused on the study of the physiology of the gastrointestinal system, aiming at the support of medical research for the discovery of gastrointestinal motility patterns and the diagnosis of functional disorders. The term "processing" in this case is quite broad, incorporating the procedures of signal processing, content description, manipulation and analysis, that are applied to all the recorded bioacoustics signals, the auxiliary audio-visual surveillance information (for the monitoring of experiments and the subjects' status), and the extracted audio-video sequences describing the abdominal sound-field alterations. The thesis outline is as follows. The main objective of the thesis, which is the technological support of medical research, is presented in the first chapter. A quick problem definition is initially ...

Strong academic and commercial interest in image compression has resulted in a number of sophisticated compression techniques. Some of these techniques have evolved into international standards such as JPEG. However, the widespread success of JPEG has slowed the rate of innovation in such standards. Even most recent techniques, such as those proposed in the JPEG2000 standard, do not show significantly improved compression performance; rather they increase the bitstream functionality. Nevertheless, the manifold of multimedia applications demands for further improvements in compression quality. The problem of stagnating compression quality can be overcome by exploiting the limitations of the human visual system (HVS) for compression purposes. To do so, commonly used distortion metrics such as mean-square error (MSE) are replaced by an HVS-model-based quality metric. Thus, the "visual" quality is optimized. Due to the tremendous complexity of the physiological structures involved in ...

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 ...

Inverse problems related to physical processes are of great importance in practically every field related to signal processing, such as tomography, acoustics, wireless communications, medical and radar imaging, to name only a few. At the same time, many of these problems are quite challenging due to their ill-posed nature. On the other hand, signals originating from physical phenomena are often governed by laws expressible through linear Partial Differential Equations (PDE), or equivalently, integral equations and the associated Green’s functions. In addition, these phenomena are usually induced by sparse singularities, appearing as sources or sinks of a vector field. In this thesis we primarily investigate the coupling of such physical laws with a prior assumption on the sparse origin of a physical process. This gives rise to a “dual” regularization concept, formulated either as sparse analysis (cosparse), yielded by a PDE ...

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. ...