Contributions to signal analysis and processing using compressed sensing techniques

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 ...

Cleju, Nicolae — "Gheorghe Asachi" Technical University of Iasi


Matrix Designs and Methods for Secure and Efficient Compressed Sensing

The idea of balancing the resources spent in the acquisition and encoding of natural signals strictly to their intrinsic information content has interested nearly a decade of research under the name of compressed sensing. In this doctoral dissertation we develop some extensions and improvements upon this technique’s foundations, by modifying the random sensing matrices on which the signals of interest are projected to achieve different objectives. Firstly, we propose two methods for the adaptation of sensing matrix ensembles to the second-order moments of natural signals. These techniques leverage the maximisation of different proxies for the quantity of information acquired by compressed sensing, and are efficiently applied in the encoding of natural signals with minimum complexity digital hardware. Secondly, we focus on the possibility of using compressed sensing as a method to provide a partial, yet cryptanalysis-resistant form of encryption. In ...

Cambareri, Valerio — University of Bologna


Constrained Non-negative Matrix Factorization for Vocabulary Acquisition from Continuous Speech

One desideratum in designing cognitive robots is autonomous learning of communication skills, just like humans. The primary step towards this goal is vocabulary acquisition. Being different from the training procedures of the state-of-the-art automatic speech recognition (ASR) systems, vocabulary acquisition cannot rely on prior knowledge of language in the same way. Like what infants do, the acquisition process should be data-driven with multi-level abstraction and coupled with multi-modal inputs. To avoid lengthy training efforts in a word-by-word interactive learning process, a clever learning agent should be able to acquire vocabularies from continuous speech automatically. The work presented in this thesis is entitled \emph{Constrained Non-negative Matrix Factorization for Vocabulary Acquisition from Continuous Speech}. Enlightened by the extensively studied techniques in ASR, we design computational models to discover and represent vocabularies from continuous speech with little prior knowledge of the language to ...

Sun, Meng — Katholieke Universiteit Leuven


Three Dimensional Human Face Acquisition for Recognition

Machine identification and recognition of human faces is a rapidly growing research area in both the academic and commercial world. Most of the research to date has concentrated on the use of two dimensional information, acquired from video cameras or photographs. The use of a three dimensional system is hoped to remove many of the problems affecting the two dimensional systems such as disruption caused by changes in the face’s orientation or changes in the ambient lighting. A three dimensional system will obviously not be influenced by orientation changes and the lighting is irrelevant, as it is the shape not the shading of the face that is important. For this system to be of practical use it is important that the process of acquiring the necessary information to generate the three dimensional surface model should not require any complex or ...

Tibbalds, Adam D. — University of Cambridge


Digital Processing Based Solutions for Life Science Engineering Recognition Problems

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 ...

Hussein, Walid — Technische Universität München


Adaptive Nonlocal Signal Restoration and Enhancement Techniques for High-Dimensional Data

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 ...

Maggioni, Matteo — Tampere University of Technology


Bayesian Compressed Sensing using Alpha-Stable Distributions

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 ...

Tzagkarakis, George — University of Crete


Robust Methods for Sensing and Reconstructing Sparse Signals

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) ...

Carrillo, Rafael — University of Delaware


Tradeoffs and limitations in statistically based image reconstruction problems

Advanced nuclear medical imaging systems collect multiple attributes of a large number of photon events, resulting in extremely large datasets which present challenges to image reconstruction and assessment. This dissertation addresses several of these challenges. The image formation process in nuclear medical imaging can be posed as a parametric estimation problem where the image pixels are the parameters of interest. Since nuclear medical imaging applications are often ill-posed inverse problems, unbiased estimators result in very noisy, high-variance images. Typically, smoothness constraints and a priori information are used to reduce variance in medical imaging applications at the cost of biasing the estimator. For such problems, there exists an inherent tradeoff between the recovered spatial resolution of an estimator, overall bias, and its statistical variance; lower variance can only be bought at the price of decreased spatial resolution and/or increased overall bias. ...

Kragh, Tom — University of Michigan


Bayesian Fusion of Multi-band Images: A Powerful Tool for Super-resolution

Hyperspectral (HS) imaging, which consists of acquiring a same scene in several hundreds of contiguous spectral bands (a three dimensional data cube), has opened a new range of relevant applications, such as target detection [MS02], classification [C.-03] and spectral unmixing [BDPD+12]. However, while HS sensors provide abundant spectral information, their spatial resolution is generally more limited. Thus, fusing the HS image with other highly resolved images of the same scene, such as multispectral (MS) or panchromatic (PAN) images is an interesting problem. The problem of fusing a high spectral and low spatial resolution image with an auxiliary image of higher spatial but lower spectral resolution, also known as multi-resolution image fusion, has been explored for many years [AMV+11]. From an application point of view, this problem is also important as motivated by recent national programs, e.g., the Japanese next-generation space-borne ...

Wei, Qi — University of Toulouse


GNSS Array-based Acquisition: Theory and Implementation

This Dissertation addresses the signal acquisition problem using antenna arrays in the general framework of Global Navigation Satellite Systems (GNSS) receivers. GNSSs provide the necessary infrastructures for a myriad of applications and services that demand a robust and accurate positioning service. GNSS ranging signals are received with very low signal-to-noise ratio. Despite that the GNSS CDMA modulation offers limited protection against Radio Frequency Interferences (RFI), an interference that exceeds the processing gain can easily degrade receivers' performance or even deny completely the GNSS service. A growing concern of this problem has appeared in recent times. A single-antenna receiver can make use of time and frequency diversity to mitigate interferences, even though the performance of these techniques is compromised in the presence of wideband interferences. Antenna arrays receivers can benefit from spatial-domain processing, and thus mitigate the effects of interfering signals. ...

Arribas, Javier — Universitat Politecnica de Catalunya


Unsupervised Models for White Matter Fiber-Bundles Analysis in Multiple Sclerosis

Diffusion Magnetic Resonance Imaging (dMRI) is a meaningful technique for white matter (WM) fiber-tracking and microstructural characterization of axonal/neuronal integrity and connectivity. By measuring water molecules motion in the three directions of space, numerous parametric maps can be reconstructed. Among these, fractional anisotropy (FA), mean diffusivity (MD), and axial (λa) and radial (λr) diffusivities have extensively been used to investigate brain diseases. Overall, these findings demonstrated that WM and grey matter (GM) tissues are subjected to numerous microstructural alterations in multiple sclerosis (MS). However, it remains unclear whether these tissue alterations result from global processes, such as inflammatory cascades and/or neurodegenerative mechanisms, or local inflammatory and/or demyelinating lesions. Furthermore, these pathological events may occur along afferent or afferent WM fiber pathways, leading to antero- or retrograde degeneration. Thus, for a better understanding of MS pathological processes like its spatial and ...

Stamile, Claudio — Université Claude Bernard Lyon 1, KU Leuven


Bayesian methods for sparse and low-rank matrix problems

Many scientific and engineering problems require us to process measurements and data in order to extract information. Since we base decisions on information, it is important to design accurate and efficient processing algorithms. This is often done by modeling the signal of interest and the noise in the problem. One type of modeling is Compressed Sensing, where the signal has a sparse or low-rank representation. In this thesis we study different approaches to designing algorithms for sparse and low-rank problems. Greedy methods are fast methods for sparse problems which iteratively detects and estimates the non-zero components. By modeling the detection problem as an array processing problem and a Bayesian filtering problem, we improve the detection accuracy. Bayesian methods approximate the sparsity by probability distributions which are iteratively modified. We show one approach to making the Bayesian method the Relevance Vector ...

Sundin, Martin — Department of Signal Processing, Royal Institute of Technology KTH


Image quality in context

An analysis of the ergonomic quality of the current standards for the visual display quality leads to a number of recommendations for the development of new international standards: - Separation for different types of users, esp. display designers, purchasers, and end users, -Independence of display technology to allow comparison, -Modular construction with several quality grades to allow benchmarking for different types of applications, -A test method for the end user standard that can be performed at the place of work, to take into account the effects of wear and drift of components and to be able to correct suboptimal configurations. The separate parameters that exert influence on the image quality of a broad category of images in the context of use, and their mutual coherence within the cycle of evaluation and adaptation of image quality are presented in the "Image ...

Besuijen, Jacobus — Delft University of Technology


Distributed Compressed Representation of Correlated Image Sets

Vision sensor networks and video cameras find widespread usage in several applications that rely on effective representation of scenes or analysis of 3D information. These systems usually acquire multiple images of the same 3D scene from different viewpoints or at different time instants. Therefore, these images are generally correlated through displacement of scene objects. Efficient compression techniques have to exploit this correlation in order to efficiently communicate the 3D scene information. Instead of joint encoding that requires communication between the cameras, in this thesis we concentrate on distributed representation, where the captured images are encoded independently, but decoded jointly to exploit the correlation between images. One of the most important and challenging tasks relies in estimation of the underlying correlation from the compressed correlated images for effective reconstruction or analysis in the joint decoder. This thesis focuses on developing efficient ...

Thirumalai, Vijayaraghavan — EPFL, Switzerland

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