The main objective of $\gamma$ spectrometry is to characterize the radioactive elements of an unknown source by studying the energy of the emitted $\gamma$ photons. When a photon interacts with a detector, its photonic energy is converted into an electrical pulse, whose integral energy is measured. The histogram obtained by collecting the energies can be used to identify radionucleides and measure their activity. However, at high counting rates, perturbations which are due to the stochastic aspect of the temporal signal can cripple the identification of the radioactive elements. More specifically, since the detector has a finite resolution, close arrival times of photons which can be modeled as an homogeneous Poisson process cause pileups of individual pulses. This phenomenon distorts energy spectra by introducing multiple fake spikes and prolonging artificially the Compton continuum, which can mask spikes of low intensity. The ...

Computed tomography (CT) is a technique that uses computation to form an image of the inside of an object or person, by combining projections of that object or person. The word tomography is derived from the Greek word tomos, meaning slice. The basis for computed tomography was laid in 1917 by Johann Radon, an Austrian mathematician. Computed tomography has a broad range of applications, the best known being medical imaging (the CT scanner), where X-rays are used for making the projection images. The rst practical application of CT was, however, in astronomy, by Ronald Bracewell in 1956. He used CT to improve the resolution of radio-astronomical observations. The practical applications in this thesis are from electron tomography, where the images are made with an electron microscope, and from preclinical research, where the images are made with a CT scanner. There ...

Data acquisition is a necessary first step in digital signal processing applications such as radar, wireless communications and array processing. Traditionally, this process is performed by uniformly sampling signals at a frequency above the Nyquist rate and converting the resulting samples into digital numeric values through high-resolution amplitude quantization. While the traditional approach to data acquisition is straightforward and extremely well-proven, it may be either impractical or impossible in many modern applications due to the existing fundamental trade-off between sampling rate, amplitude quantization precision, implementation costs, and usage of physical resources, e.g. bandwidth and power consumption. Motivated by this fact, system designers have recently proposed exploiting sparse and few-bit quantized sampling instead of the traditional way of data acquisition in order to reduce implementation costs and usage of physical resources in such applications. However, before transition from the tradition data ...

Super-resolution (SR) is a filtering technique that combines a sequence of under-sampled and degraded low-resolution images to produce an image at a higher resolution. The reconstruction takes advantage of the additional spatio-temporal data available in the sequence of images portraying the same scene. The fundamental problem addressed in super-resolution is a typical example of an inverse problem, wherein multiple low-resolution (LR)images are used to solve for the original high-resolution (HR) image. Super-resolution has already proved useful in many practical cases where multiple frames of the same scene can be obtained, including medical applications, satellite imaging and astronomical observatories. The application of super resolution filtering in consumer cameras and mobile devices shall be possible in the future, especially that the computational and memory resources in these devices are increasing all the time. For that goal, several research problems need to be ...

Inverse scattering is relevant to a very large class of problems, where the unknown structure of a scattering object is estimated by measuring the scattered field produced by known probing waves. Therefore, for more than three decades, the promises of non-invasive imaging inspection by electromagnetic probing radiations have been justifying a research interest on these techniques. Several application areas are involved, such as civil and industrial engineering, non-destructive testing and medical imaging as well as subsurface inspection for oil exploration or unexploded devices. In spite of this relevance, most scattering tomography techniques are not reliable enough to solve practical problems. Indeed, the nonlinear relationship between the scattered field and the object function and the robustness of the inversion algorithms are still open issues. In particular, microwave tomography presents a number of specific difficulties that make it much more involved to ...

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 ...

Power reduction in digital communication systems can be achieved in many ways. Re- duction of the wordlengths used to represent data and control variables in the digital circuits comprising a communication system is an efective strategy, as register power consumption increases with wordlength. Another strategy is the reduction of the required data trans- mission rate, and hence speed of the digital circuits, by efficient source encoding. In this dissertation, applications of both of these power reduction strategies are investigated. The LMS adaptive filter, for which a myriad of applications exists in digital communi- cation systems, is optimized for performance with a power consumption constraint. This optimization is achieved by an analysis of the effects of wordlength reduction on both perfor- mance -transient and steady-state- as well as power consumption. Analytical formulas for the residual steady-state mean square error (MSE) due ...

Circumstellars environments observation is a key for the comprehension of planet formation. If the very large telescopes allow the resolution of these environments, their observation is difficult due to the high contrast between the environment and their host stars. In fact the host stars are 1000 to 10 000 times brighter than the environment, even 10 000 000 times brighter for exoplanets. When images of these circumstellar environnements are acquired in direct imaging, the signal of the environnements mixed to star light residuals. Yet, the light of the environment is partially linearly polarized while the light od the star is unpolarized. The instrument Infrared Dual-band Imaging and Spectroscopy (IRDIS) of the European Southern Observatory’s (ESO) Spectro-Polarimeter High-contrast Expolanet REsearch (SPHERE) instrument, installed at one of the four Very Large Telescopes (VLT) in Atacama in Chile, acquires datasets where the polarization ...

Resistivity distribution estimation, widely known as Electrical Impedance Tomography (EIT), is a non linear ill-posed inverse problem. However, the partial derivative equation ruling this experiment yields no analytical solution for arbitrary conductivity distribution. Thus, solving the forward problem requires an approximation. The Finite Element Method (FEM) provides us with a computationally cheap forward model which preserves the non linear image-data relation and also reveals sufficiently accurate for the inversion. Within the Bayesian approach, Markovian priors on the log-conductivity distribution are introduced for regularization. The neighborhood system is directly derived from the FEM triangular mesh structure. We first propose a maximum a posteriori (MAP) estimation with a Huber-Markov prior which favours smooth distributions while preserving locally discontinuous features. The resulting criterion is minimized with the pseudo-conjugate gradient method. Simulation results reveal significant improvements in terms of robustness to noise, computation rapidity ...

Frequency Modulated Continuous Wave (FMCW) radar has emerged as a powerful sensing modality in both automotive and biomedical applications due to its ability to provide precise range, velocity, and Doppler measurements. This dissertation investigates novel methodologies to enhance FMCW radar's effectiveness in two critical domains: (1) forward-looking Synthetic Aperture Radar (SAR) imaging for automotive applications, and (2) biomedical monitoring for non-contact vital sign estimation and dehydration assessment. The proposed approaches leverage advanced signal processing, deep learning, and MIMO radar techniques to improve spatial resolution, classification accuracy, and robustness in real-world scenarios. In the automotive domain, the research focuses on improving the azimuthal resolution of forward-looking SAR imaging by incorporating MIMO radar and deep learning-based reconstruction methods. Two key methodologies are proposed to address the resolution limitations of conventional SAR imaging techniques. The first approach employs an unsupervised Deep Basis Pursuit ...

Compressed sensing (CS) is a recently introduced signal acquisition framework that goes against the traditional Nyquist sampling paradigm. CS demonstrates that a sparse, or compressible, signal can be acquired using a low rate acquisition process. Since noise is always present in practical data acquisition systems, sensing and reconstruction methods are developed assuming a Gaussian (light-tailed) model for the corrupting noise. However, when the underlying signal and/or the measurements are corrupted by impulsive noise, commonly employed linear sampling operators, coupled with Gaussian-derived reconstruction algorithms, fail to recover a close approximation of the signal. This dissertation develops robust sampling and reconstruction methods for sparse signals in the presence of impulsive noise. To achieve this objective, we make use of robust statistics theory to develop appropriate methods addressing the problem of impulsive noise in CS systems. We develop a generalized Cauchy distribution (GCD) ...

Frequency Modulated Continuous Wave (FMCW) radar has emerged as a powerful sensing modality in both automotive and biomedical applications due to its ability to provide precise range, velocity, and Doppler measurements. This dissertation investigates novel methodologies to enhance FMCW radar's effectiveness in two critical domains: (1) forward-looking Synthetic Aperture Radar (SAR) imaging for automotive applications, and (2) biomedical monitoring for non-contact vital sign estimation and dehydration assessment. The proposed approaches leverage advanced signal processing, deep learning, and MIMO radar techniques to improve spatial resolution, classification accuracy, and robustness in real-world scenarios. In the automotive domain, the research focuses on improving the azimuthal resolution of forward-looking SAR imaging by incorporating MIMO radar and deep learning-based reconstruction methods. Two key methodologies are proposed to address the resolution limitations of conventional SAR imaging techniques. The first approach employs an unsupervised Deep Basis Pursuit ...

This dissertation deals with the design of satellite-based navigation receivers. The term Global Navigation Satellite Systems (GNSS) refers to those navigation systems based on a constellation of satellites, which emit ranging signals useful for positioning. Although the american GPS is probably the most popular, the european contribution (Galileo) will be operative soon. Other global and regional systems exist, all with the same objective: aid user's positioning. Initially, the thesis provides the state-of-the-art in GNSS: navigation signals structure and receiver architecture. The design of a GNSS receiver consists of a number of functional blocks. From the antenna to the fi nal position calculation, the design poses challenges in many research areas. Although the Radio Frequency chain of the receiver is commented in the thesis, the main objective of the dissertation is on the signal processing algorithms applied after signal digitation. These ...

Digital video technology has been characterized by a steady growth in the last decade. New applications like video e-mail, third generation mobile phone video communications, videoconferencing, video streaming on the web continuously push for further evolution of research in digital video coding. In order to be sent over the internet or even wireless networks, video information clearly needs compression to meet bandwidth requirements. Compression is mainly realized by exploiting the redundancy present in the data. A sequence of images contains an intrinsic, intuitive and simple idea of redundancy: two successive images are very similar. This simple concept is called temporal redundancy. The research of a proper scheme to exploit the temporal redundancy completely changes the scenario between compression of still pictures and sequence of images. It also represents the key for very high performances in image sequence coding when compared ...

Digital image acquisition is an intricate process, which is subject to various errors. Some of these errors are signal-dependent, whereas others are signal-independent. In particular, photon emission and sensing are inherently random physical processes, which in turn substantially contribute to the randomness in the output of the imaging sensor. This signal-dependent noise can be approximated through a Poisson distribution. On the other hand, there are various signal-independent noise sources involved in the image capturing chain, arising from the physical properties and imperfections of the imaging hardware. The noise attributed to these sources is typically modelled collectively as additive white Gaussian noise. Hence, we have three common ways of modelling the noise present in a digital image: Gaussian, Poisson, or Poisson-Gaussian. Image denoising aims at removing or attenuating this noise from the captured image, in order to provide an estimate of ...