As a three-dimensional viewing technique, holography provides successful three-dimensional perceptions. The technique is based on duplication of the information carrying optical waves which come from an object. Therefore, calculation of the diffraction field due to the object is an important process in digital holography. To have the exact reconstruction of the object, the exact diffraction field created by the object has to be calculated. In the literature, one of the commonly used approach in calculation of the diffraction field due to an object is to superpose the fields created by the elementary building blocks of the object; such procedures may be called as the ``source model" approach and such a computed field can be different from the exact field over the entire space. In this work, we propose four algorithms to calculate the exact diffraction field due to an object. ...

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 ...

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 ...

This thesis discusses approaches and techniques to convert Sparsely-Sampled Light Fields (SSLFs) into Densely-Sampled Light Fields (DSLFs), which can be used for visualization on 3DTV and Virtual Reality (VR) devices. Exemplarily, a movable 1D large-scale light field acquisition system for capturing SSLFs in real-world environments is evaluated. This system consists of 24 sparsely placed RGB cameras and two Kinect V2 sensors. The real-world SSLF data captured with this setup can be leveraged to reconstruct real-world DSLFs. To this end, three challenging problems require to be solved for this system: (i) how to estimate the rigid transformation from the coordinate system of a Kinect V2 to the coordinate system of an RGB camera; (ii) how to register the two Kinect V2 sensors with a large displacement; (iii) how to reconstruct a DSLF from a SSLF with moderate and large disparity ranges. ...

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 ...

Recent academic developments have initiated a paradigm shift in the way spatial sensor data can be acquired. Traditional localized and regularly arranged sensor arrays are replaced by sensor nodes that are randomly distributed over the entire spatial field, and which communicate with each other or with a master node through wireless communication links. Together, these nodes form a so-called ‘wireless sensor network’ (WSN). Each node of a WSN has a local sensor array and a signal processing unit to perform computations on the acquired data. The advantage of WSNs compared to traditional (wired) sensor arrays, is that many more sensors can be used that physically cover the full spatial field, which typically yields more variety (and thus more information) in the signals. It is likely that future data acquisition, control and physical monitoring, will heavily rely on this type of ...

Direction-of-Arrival (DOA) estimation from data collected at a sensor array in the presence of noise has been a fundamental and long-established research topic of interest in sensor array processing. The application of DOA estimation does not only restrict to radar but also spans multiple additional fields of research, including radio astronomy, biomedical imaging, seismic exploration, wireless communication, among others. Due to the wide applications of DOA estimation, various methods have been developed in the literature to increase the resolution capability, computational efficiency, and robustness of the algorithms. However, a trade-off between the estimation performance and the computational complexity is generally inevitable. This thesis addresses the challenge of developing low-complexity DOA estimators with the ability to resolve closely spaced source signals in the threshold region, i.e., low sample size or low Signal-to-Noise ratio. Motivated by various interpretations of the conventional DOA ...

Statistical robustness and collaborative inference in a distributed sensor network are two challenging requirements posed on many modern signal processing applications. This dissertation aims at solving these tasks jointly by providing generic algorithms that are applicable to a wide variety of real-world problems. The first part of the thesis is concerned with sequential detection---a branch of detection theory that is focused on decision-making based on as few measurements as possible. After reviewing some fundamental concepts of statistical hypothesis testing, a general formulation of the Consensus+Innovations Sequential Probability Ratio Test for sequential binary hypothesis testing in distributed networks is derived. In a next step, multiple robust versions of the algorithm based on two different robustification paradigms are developed. The functionality of the proposed detectors is verified in simulations, and their performance is examined under different network conditions and outlier concentrations. Subsequently, ...

This dissertation details three approaches for direction-of-arrival (DOA) estimation or beamforming in array signal processing from the perspective of sparsity. In the first part of this dissertation, we consider sparse array beamformer design based on the alternating direction method of multipliers (ADMM); in the second part of this dissertation, the problem of joint DOA estimation and distorted sensor detection is investigated; and off-grid DOA estimation is studied in the last part of this dissertation. In the first part of this thesis, we devise a sparse array design algorithm for adaptive beamforming. Our strategy is based on finding a sparse beamformer weight to maximize the output signal-to-interference-plus-noise ratio (SINR). The proposed method utilizes ADMM, and admits closed-form solutions at each ADMM iteration. The algorithm convergence properties are analyzed by showing the monotonicity and boundedness of the augmented Lagrangian function. In addition, ...

In this thesis, advanced techniques for antenna array processing are addressed. The problem of autocalibration is considered and a novel method for a two-dimensional array is developed. Moreover, practicable methods for high-resolution direction-of-arrival (DOA) estimation and detection in automotive radar are proposed. A precise model of the array response is required to maintain the performance of DOA estimation. When the sensor environment is time-varying, this can only be achieved with autocalibration. The fundamental problem of autocalibration of an unknown phase response for uniform rectangular arrays is considered. For the case with a single source, a simple and robust least squares algorithm for joint two-dimensional DOA estimation and phase calibration is developed. An identification problem is determined and a suitable constraint is proposed. Simulation results show that the performance of the proposed estimator is close to the approximate CRB for both ...

The field of Life Science Engineering (LSE) is rapidly expanding and predicted to grow strongly in the next decades. It covers areas of food and medical research, plant and pests’ research, and environmental research. In each research area, engineers try to find equations that model a certain life science problem. Once found, they research different numerical techniques to solve for the unknown variables of these equations. Afterwards, solution improvement is examined by adopting more accurate conventional techniques, or developing novel algorithms. In particular, signal and image processing techniques are widely used to solve those LSE problems require pattern recognition. However, due to the continuous evolution of the life science problems and their natures, these solution techniques can not cover all aspects, and therefore demanding further enhancement and improvement. The thesis presents numerical algorithms of digital signal and image processing to ...

Due to a variety of potential barriers to sample acquisition, many of the datasets encountered in important classification applications, ranging from tumor identification to facial recognition, are characterized by small samples of high-dimensional data. In such situations, linear classifiers are popular as they have less risk of overfitting while being faster and more interpretable than non-linear classifiers. They are also easier to understand and implement for the inexperienced practitioner. In this dissertation, several gaps in the literature regarding the analysis and design of linear classifiers for high-dimensional data are addressed using tools from the field of asymptotic Random Matrix Theory (RMT) which facilitate the derivation of limits of relevant quantities or distributions, such as the probability of misclassification of a particular classifier or the asymptotic distribution of its discriminant, in the RMT regime where both the sample size and dimensionality ...

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 ...

Chapter 2 contains a short introduction to the fundamentals of compressed sensing theory, which is the larger context of this thesis. We start with introducing the key concepts of sparsity and sparse representations of signals. We discuss the central problem of compressed sensing, i.e. how to adequately recover sparse signals from a small number of measurements, as well as the multiple formulations of the reconstruction problem. A large part of the chapter is devoted to some of the most important conditions necessary and/or sufficient to guarantee accurate recovery. The aim is to introduce the reader to the basic results, without the burden of detailed proofs. In addition, we also present a few of the popular reconstruction and optimization algorithms that we use throughout the thesis. Chapter 3 presents an alternative sparsity model known as analysis sparsity, that offers similar recovery ...

Mapping stationary objects and tracking moving targets are essential for many autonomous functions in vehicles. In order to compute the map and track estimates, sensor measurements from radar, laser and camera are used together with the standard proprioceptive sensors present in a car. By fusing information from different types of sensors, the accuracy and robustness of the estimates can be increased. Different types of maps are discussed and compared in the thesis. In particular, road maps make use of the fact that roads are highly structured, which allows relatively simple and powerful models to be employed. It is shown how the information of the lane markings, obtained by a front looking camera, can be fused with inertial measurement of the vehicle motion and radar measurements of vehicles ahead to compute a more accurate and robust road geometry estimate. Further, it ...