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 ...

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 ...

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 ...

Image formation algorithms in a variety of applications have explicit or implicit dependence on a mathematical model of the observation process. Inaccuracies in the observation model may cause various degradations and artifacts in the reconstructed images. The application of interest in this thesis is synthetic aperture radar (SAR) imaging, which particularly suffers from motion-induced model errors. These types of errors result in phase errors in SAR data which cause defocusing of the reconstructed images. Particularly focusing on imaging of fields that admit a sparse representation, we propose a sparsity-driven method for joint SAR imaging and phase error correction. In this technique, phase error correction is performed during the image formation process. The problem is set up as an optimization problem in a nonquadratic regularization-based framework. The method involves an iterative algorithm each iteration of which consists of consecutive steps of ...

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 ...

During the last decades, information is being gathered and processed at an explosive rate. This fact gives rise to a very important issue, that is, how to effectively and precisely describe the information content of a given source signal or an ensemble of source signals, such that it can be stored, processed or transmitted by taking into consideration the limitations and capabilities of the several digital devices. One of the fundamental principles of signal processing for decades is the Nyquist-Shannon sampling theorem, which states that the minimum number of samples needed to reconstruct a signal without error is dictated by its bandwidth. However, there are many cases in our everyday life in which sampling at the Nyquist rate results in too many data and thus, demanding an increased processing power, as well as storage requirements. A mathematical theory that emerged ...

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 ...

Magnetic Resonance Imaging (MRI) is an important diagnostic tool for imaging soft tissue without the use of ionizing radiation. Moreover, through advanced signal processing, MRI can provide more than just anatomical information, such as estimates of tissue-specific physical properties. Signal processing lies at the very core of the MRI process, which involves input design, information encoding, image reconstruction, and advanced filtering. Based on signal modeling and estimation, it is possible to further improve the images, reduce artifacts, mitigate noise, and obtain quantitative tissue information. In quantitative MRI, different physical quantities are estimated from a set of collected images. The optimization problems solved are typically nonlinear, and require intelligent and application-specific algorithms to avoid suboptimal local minima. This thesis presents several methods for efficiently solving different parameter estimation problems in MRI, such as multi-component T2 relaxometry, temporal phase correction of complex-valued ...

In many hands-free speech communication applications such as teleconferencing or voice-controlled applications, the recorded microphone signals do not only contain the desired speech signal, but also attenuated and delayed copies of the desired speech signal due to reverberation as well as additive background noise. Reverberation and background noise cause a signal degradation which can impair speech intelligibility and decrease the performance for many signal processing techniques. Acoustic multi-channel equalization techniques, which aim at inverting or reshaping the measured or estimated room impulse responses between the speech source and the microphone array, comprise an attractive approach to speech dereverberation since in theory perfect dereverberation can be achieved. However in practice, such techniques suffer from several drawbacks, such as uncontrolled perceptual effects, sensitivity to perturbations in the measured or estimated room impulse responses, and background noise amplification. The aim of this thesis ...

Heavy demands on the development of medical imaging modalities for breast cancer detection have been witnessed in the last three decades in an attempt to reduce the mortality associated with the disease. Recently, Digital Breast Tomosynthesis (DBT) shows its promising in the early diagnosis when lesions are small. In particular, it offers potential benefits over X-ray mammography - the current modality of choice for breast screening - of increased sensitivity and specificity for comparable X-ray dose, speed, and cost. An important feature of DBT is that it provides a pseudo-3D image of the breast. This is of particular relevance for heterogeneous dense breasts of young women, which can inhibit detection of cancer using conventional mammography. In the same way that it is difficult to see a bird from the edge of the forest, detecting cancer in a conventional 2D mammogram ...

Standard signal processing techniques are implicitly based on the assumption that the signal lies on a regular, homogeneous domain. In practice, however, many signals lie on an irregular or inhomogeneous domain. An application area where data are naturally defined on an irregular or inhomogeneous domain is human brain neuroimaging. The goal in neuroimaging is to map the structure and function of the brain using imaging techniques. In particular, functional magnetic resonance imaging (fMRI) is a technique that is conventionally used in non-invasive probing of human brain function. This doctoral dissertation deals with the development of signal processing schemes that adapt to the domain of the signal. It consists of four papers that in different ways deal with exploiting knowledge of the signal domain to enhance the processing of signals. In each paper, special focus is given to the analysis of ...

This dissertation details two classes of cooperative localization methods for wireless networks in mixed line-of-sight and non-line-of-sight (LOS/NLOS) environments. The classes of methods depend on the amount of prior knowledge available. The methods used for both classes are based on the assumptions in practical localization environments that neither NLOS identification nor experimental campaigns are affordable. Two major contributions are, first, in methods that provide satisfactory localization accuracy whilst relaxing the requirement on statistical knowledge about the measurement model. Second, in methods that provide significantly improved localization performance without the requirement of good initialization. In the first half of the dissertation, cooperative localization using received signal strength (RSS) measurements in homogeneous mixed LOS/NLOS environments is considered for the case where the key model parameter, the path loss exponent, is unknown. The approach taken is to model the positions and the path ...

Understanding the cognitive processes that are going on in the human brain, requires the combination of several types of observations. For this reason, since several years, neuroscience research started to focus on multimodal approaches. One such multimodal approach is the combination of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI). The non-invasive character of these two modalities makes their combination not only harmless and painless, but also especially suited for widespread research in both clinical and experimental applications. Moreover, the complementarity between the high temporal resolution of the EEG and the high spatial resolution of the fMRI, allows obtaining a more complete picture of the processes under study. However, the combination of EEG and fMRI is challenging, not only on the level of the data acquisition, but also when it comes to extracting the activity of interest and interpreting the ...

Sparse signal recovery consists of algorithms that are able to recover undersampled high dimensional signals accurately. These algorithms require fewer measurements than traditional Shannon/Nyquist sampling theorem demands. Sparse signal recovery has found many applications including magnetic resonance imaging, electromagnetic inverse scattering, radar/sonar imaging, seismic data collection, sensor array processing and channel estimation. The focus of this thesis is on electromagentic inverse scattering problem and joint estimation of the frequency offset and the channel impulse response in OFDM. In the electromagnetic inverse scattering problem, the aim is to find the electromagnetic properties of unknown targets from measured scattered field. The reconstruction of closely placed point-like objects is investigated. The application of the greedy pursuit based sparse recovery methods, OMP and FTB-OMP, is proposed for increasing the reconstruction resolution. The performances of the proposed methods are compared against NESTA and MT-BCS methods. ...

A complex physical system like the human brain can only be comprehended by the use of a combination of various medical imaging techniques, each of which shed light on only a specific aspect of the neural processes that take place beneath the skull. Electroencephalography (EEG) and functional magnetic resonance (fMRI) are two such modalities, which enable the study of brain (dys)function. While the EEG is measured with a limited set of scalp electrodes which record rapid electrical changes resulting from neural activity, fMRI offers a superior spatial resolution at the expense of only picking up slow fluctuations of oxygen concentration that takes place near active brain cells. Hence, combining these very complementary modalities is an appealing, but complicated task due to their heterogeneous nature. In this thesis, we devise advanced signal processing techniques which integrate the multimodal data stemming from ...