Accurate Non-Iterative Modelling and Inference of Longitudinal Neuroimaging Data

In recent years, increasing efforts have been made to collect longitudinal neuroimaging data in order to study how brains change over time. However, the popular methods used to analyse such kind of data may not always be appropriate (e.g., overly sensitive to model misspecifications, difficult to specify adequately or prohibitively slow to compute) and may sometimes lead to erroneous conclusions. Motivated by these shortcomings, in this dissertation, we have proposed and studied the use of an alternative method, referred to as “the Sandwich Estimator method”, and have demonstrated that it is a fast, easy-to-specify and accurate option to analyse longitudinal or repeated-measures neuroimaging data

Accurate Non-Iterative Modelling and Inference of Longitudinal Neuroimaging Data

Despite the growing importance of longitudinal data in neuroimaging, the standard analysis methods make restrictive or unrealistic assumptions. For example, the widely used SPM software package assumes spatially homogeneous longitudinal correlations while the FSL software package assumes Compound Symmetry, the state of all equal variances and equal correlations. While some new methods have been recently pro- posed to more accurately account for such data, these methods can be difficult to specify and are based on iterative algorithms that are generally slow and failure- prone. In this thesis, we propose and investigate the use of the Sandwich Estimator method which first estimates the parameters of interest with a (non-iterative) Ordinary Least Square model and, second, estimates variances/covariances with the “so-called” Sandwich Estimator (SwE) which accounts for the within-subject covariance structure existing in longitudinal data. We introduce the SwE method in its classic form, and review existing and propose new adjustments to improve its behaviour, specifically in small samples. We compare the SwE method to other popular methods, isolating the combination of SwE adjustments that provides valid and powerful inferences. While this result provides p-values at each voxel, it does not provide spatial inferences, e.g. voxel- or cluster-wise family-wise error-corrected p-values. For this, we investigate the use of the non-parametric inference approach called Wild Bootstrap. We again identify the set of procedures and adjustments that provide valid inferences. Finally, in the third and fourth projects, we investigate two ideas to improve the statistical power of the SwE method, by using a shrinkage estimator or a covariance spatial smoothing, respectively. For all the projects, in order to assess the methods, we use intensive Monte Carlo simulations in settings important for longitudinal neuroimaging studies and, for the first two projects, we also illustrate the methods by analysing a highly unbalanced longitudinal dataset obtained from the Alzheimer’s Disease Neuroimaging Initiative

Unit Circle Roots Based Sensor Array Signal Processing

As technology continues to rapidly evolve, the presence of sensor arrays and the algorithms processing the data they generate take an ever-increasing role in modern human life. From remote sensing to wireless communications, the importance of sensor signal processing cannot be understated. Capon\u27s pioneering work on minimum variance distortionless response (MVDR) beamforming forms the basis of many modern sensor array signal processing (SASP) algorithms. In 2004, Steinhardt and Guerci proved that the roots of the polynomial corresponding to the optimal MVDR beamformer must lie on the unit circle, but this result was limited to only the MVDR. This dissertation contains a new proof of the unit circle roots property which generalizes to other SASP algorithms. Motivated by this result, a unit circle roots constrained (UCRC) framework for SASP is established and includes MVDR as well as single-input single-output (SISO) and distributed multiple-input multiple-output (MIMO) radar moving target detection. Through extensive simulation examples, it will be shown that the UCRC-based SASP algorithms achieve higher output gains and detection probabilities than their non-UCRC counterparts. Additional robustness to signal contamination and limited secondary data will be shown for the UCRC-based beamforming and target detection applications, respectively

High-resolution Direction-of-Arrival estimation

Direction of Arrival (DOA) estimation is considered one of the most crucial problems in array signal processing, with considerable research efforts for developing efficient and effective direction-finding algorithms, especially in the transportation industry, where the demand for an effective, real-time, and accurate DOA algorithm is increasing. However, challenges must be addressed before real-world deployment can be realised. Firstly, there is the requirement for fast computational time for real-time detection. Secondly, there is a demand for high-resolution and accurate DOA estimation. In this thesis, two state-of-the-art DOA estimation algorithms are proposed and evaluated to address the challenges. Firstly, a novel covariance matrix reconstruction approach for single snapshot DOA estimation (CbSS) was proposed. CbSS was developed by exploiting the relationship between the theoretical and sample covariance matrices to reduce estimation error for a single snapshot scenario. CbSS can resolve accurate DOAs without requiring lengthy peak searching computational time by computationally changing the received sample covariance matrix. Simulation results have verified that the CbSS technique yields the highest DOA estimation accuracy by up to 25.5% compared to existing methods such as root-MUSIC and the Partial Relaxation approach. Furthermore, CbSS presents negligible bias when compared to the existing techniques in a wide range of scenarios, such as in multiple uncorrelated and coherent signal source environments. Secondly, an adaptive diagonal-loading technique was proposed to improve DOA estimation accuracy without requiring a high computational load by integrating a modified novel and adaptive diagonal-loading method (DLT-DOA) to further improve estimation accuracy. An in-depth simulation performance analysis was conducted to address the challenges, with a comparison against existing state-of-the-art DOA estimation techniques such as EPUMA and MODEX. Simulation results verify that the DLT-DOA technique performs up to 8.5% higher DOA estimation performance in terms of estimation accuracy compared to existing methods with significantly lower computational time. On this basis, the two novel DOA estimation techniques are recommended for usage in real-world scenarios where fast computational time and high estimation accuracy are expected. Further research is needed to identify other factors that could further optimize the algorithms to meet different demands

Atomic Norm decomposition for sparse model reconstruction applied to positioning and wireless communications

This thesis explores the recovery of sparse signals, arising in the wireless communication and radar system fields, via atomic norm decomposition. Particularly, we focus on compressed sensing gridless methodologies, which avoid the always existing error due to the discretization of a continuous space in on-grid methods. We define the sparse signal by means of a linear combination of so called atoms defined in a continuous parametrical atom set with infinite cardinality. Those atoms are fully characterized by a multi-dimensional parameter containing very relevant information about the application scenario itself. Also, the number of composite atoms is much lower than the dimension of the problem, which yields sparsity. We address a gridless optimization solution enforcing sparsity via atomic norm minimization to extract the parameters that characterize the atom from an observed measurement of the model, which enables model recovery. We also study a machine learning approach to estimate the number of composite atoms that construct the model, given that in certain scenarios this number is unknown. The applications studied in the thesis lay on the field of wireless communications, particularly on MIMO mmWave channels, which due to their natural properties can be modeled as sparse. We apply the proposed methods to positioning in automotive pulse radar working in the mmWave range, where we extract relevant information such as angle of arrival (AoA), distance and velocity from the received echoes of objects or targets. Next we study the design of a hybrid precoder for mmWave channels which allows the reduction of hardware cost in the system by minimizing as much as possible the number of required RF chains. Last, we explore full channel estimation by finding the angular parameters that model the channel. For all the applications we provide a numerical analysis where we compare our proposed method with state-of-the-art techniques, showing that our proposal outperforms the alternative methods.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Juan José Murillo Fuentes.- Secretario: Pablo Martínez Olmos.- Vocal: David Luengo Garcí