14 research outputs found

    Recent Techniques for Regularization in Partial Differential Equations and Imaging

    Get PDF
    abstract: Inverse problems model real world phenomena from data, where the data are often noisy and models contain errors. This leads to instabilities, multiple solution vectors and thus ill-posedness. To solve ill-posed inverse problems, regularization is typically used as a penalty function to induce stability and allow for the incorporation of a priori information about the desired solution. In this thesis, high order regularization techniques are developed for image and function reconstruction from noisy or misleading data. Specifically the incorporation of the Polynomial Annihilation operator allows for the accurate exploitation of the sparse representation of each function in the edge domain. This dissertation tackles three main problems through the development of novel reconstruction techniques: (i) reconstructing one and two dimensional functions from multiple measurement vectors using variance based joint sparsity when a subset of the measurements contain false and/or misleading information, (ii) approximating discontinuous solutions to hyperbolic partial differential equations by enhancing typical solvers with l1 regularization, and (iii) reducing model assumptions in synthetic aperture radar image formation, specifically for the purpose of speckle reduction and phase error correction. While the common thread tying these problems together is the use of high order regularization, the defining characteristics of each of these problems create unique challenges. Fast and robust numerical algorithms are also developed so that these problems can be solved efficiently without requiring fine tuning of parameters. Indeed, the numerical experiments presented in this dissertation strongly suggest that the new methodology provides more accurate and robust solutions to a variety of ill-posed inverse problems.Dissertation/ThesisDoctoral Dissertation Mathematics 201

    Synthetic Aperture Radar (SAR) Meets Deep Learning

    Get PDF
    This reprint focuses on the application of the combination of synthetic aperture radars and depth learning technology. It aims to further promote the development of SAR image intelligent interpretation technology. A synthetic aperture radar (SAR) is an important active microwave imaging sensor, whose all-day and all-weather working capacity give it an important place in the remote sensing community. Since the United States launched the first SAR satellite, SAR has received much attention in the remote sensing community, e.g., in geological exploration, topographic mapping, disaster forecast, and traffic monitoring. It is valuable and meaningful, therefore, to study SAR-based remote sensing applications. In recent years, deep learning represented by convolution neural networks has promoted significant progress in the computer vision community, e.g., in face recognition, the driverless field and Internet of things (IoT). Deep learning can enable computational models with multiple processing layers to learn data representations with multiple-level abstractions. This can greatly improve the performance of various applications. This reprint provides a platform for researchers to handle the above significant challenges and present their innovative and cutting-edge research results when applying deep learning to SAR in various manuscript types, e.g., articles, letters, reviews and technical reports

    Mixture of Latent Variable Models for Remotely Sensed Image Processing

    Get PDF
    The processing of remotely sensed data is innately an inverse problem where properties of spatial processes are inferred from the observations based on a generative model. Meaningful data inversion relies on well-defined generative models that capture key factors in the relationship between the underlying physical process and the measurements. Unfortunately, as two mainstream data processing techniques, both mixture models and latent variables models (LVM) are inadequate in describing the complex relationship between the spatial process and the remote sensing data. Consequently, mixture models, such as K-Means, Gaussian Mixture Model (GMM), Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA), characterize a class by statistics in the original space, ignoring the fact that a class can be better represented by discriminative signals in the hidden/latent feature space, while LVMs, such as Principal Component Analysis (PCA), Independent Component Analysis (ICA) and Sparse Representation (SR), seek representational signals in the whole image scene that involves multiple spatial processes, neglecting the fact that signal discovery for individual processes is more efficient. Although the combined use of mixture model and LVMs is required for remote sensing data analysis, there is still a lack of systematic exploration on this important topic in remote sensing literature. Driven by the above considerations, this thesis therefore introduces a mixture of LVM (MLVM) framework for combining the mixture models and LVMs, under which three models are developed in order to address different aspects of remote sensing data processing: (1) a mixture of probabilistic SR (MPSR) is proposed for supervised classification of hyperspectral remote sensing imagery, considering that SR is an emerging and powerful technique for feature extraction and data representation; (2) a mixture model of K “Purified” means (K-P-Means) is proposed for addressing the spectral endmember estimation, which is a fundamental issue in remote sensing data analysis; (3) and a clustering-based PCA model is introduced for SAR image denoising. Under a unified optimization scheme, all models are solved via Expectation and Maximization (EM) algorithm, by iteratively estimating the two groups of parameters, i.e., the labels of pixels and the latent variables. Experiments on simulated data and real remote sensing data demonstrate the advantages of the proposed models in the respective applications

    The University Defence Research Collaboration In Signal Processing

    Get PDF
    This chapter describes the development of algorithms for automatic detection of anomalies from multi-dimensional, undersampled and incomplete datasets. The challenge in this work is to identify and classify behaviours as normal or abnormal, safe or threatening, from an irregular and often heterogeneous sensor network. Many defence and civilian applications can be modelled as complex networks of interconnected nodes with unknown or uncertain spatio-temporal relations. The behavior of such heterogeneous networks can exhibit dynamic properties, reflecting evolution in both network structure (new nodes appearing and existing nodes disappearing), as well as inter-node relations. The UDRC work has addressed not only the detection of anomalies, but also the identification of their nature and their statistical characteristics. Normal patterns and changes in behavior have been incorporated to provide an acceptable balance between true positive rate, false positive rate, performance and computational cost. Data quality measures have been used to ensure the models of normality are not corrupted by unreliable and ambiguous data. The context for the activity of each node in complex networks offers an even more efficient anomaly detection mechanism. This has allowed the development of efficient approaches which not only detect anomalies but which also go on to classify their behaviour

    Fundamental and Harmonic Ultrasound Image Joint Restoration

    Get PDF
    L'imagerie ultrasonore conserve sa place parmi les principales modalitĂ©s d'imagerie en raison de ses capacitĂ©s Ă  rĂ©vĂ©ler l'anatomie et Ă  inspecter le mouvement des organes et le flux sanguin en temps rĂ©el, d'un maniĂšre non invasive et non ionisante, avec un faible coĂ»t, une facilitĂ© d'utilisation et une grande vitesse de reconstruction des images. NĂ©anmoins, l'imagerie ultrasonore prĂ©sente des limites intrinsĂšques en termes de rĂ©solution spatiale. L'amĂ©lioration de la rĂ©solution spatiale des images ultrasonores est un dĂ©fi actuel et de nombreux travaux ont longtemps portĂ© sur l'optimisation du dispositif d'acquisition. L'imagerie ultrasonore Ă  haute rĂ©solution atteint cet objectif grĂące Ă  l'utilisation de sondes spĂ©cialisĂ©es, mais se confronte aujourd'hui Ă  des limites physiques et technologiques. L'imagerie harmonique est la solution intuitive des spĂ©cialistes pour augmenter la rĂ©solution lors de l'acquisition. Cependant, elle souffre d'une attĂ©nuation en profondeur. Une solution alternative pour amĂ©liorer la rĂ©solution est de dĂ©velopper des techniques de post-traitement comme la restauration d'images ultrasonores. L'objectif de cette thĂšse est d'Ă©tudier la non-linĂ©aritĂ© des Ă©chos ultrasonores dans le processus de restauration et de prĂ©senter l'intĂ©rĂȘt d'incorporer des images US harmoniques dans ce processus. Par consĂ©quent, nous prĂ©sentons une nouvelle mĂ©thode de restauration d'images US qui utilise les composantes fondamentales et harmoniques de l'image observĂ©e. La plupart des mĂ©thodes existantes sont basĂ©es sur un modĂšle linĂ©aire de formation d'image. Sous l'approximation de Born du premier ordre, l'image RF est supposĂ©e ĂȘtre une convolution 2D entre la fonction de rĂ©flectivitĂ© et la rĂ©ponse impulsionelle du systĂšme. Par consĂ©quent, un problĂšme inverse rĂ©sultant est formĂ© et rĂ©solu en utilisant un algorithme de type ADMM. Plus prĂ©cisĂ©ment, nous proposons de rĂ©cupĂ©rer la fonction de reflectivitĂ© inconnue en minimisant une fonction composĂ©e de deux termes de fidĂ©litĂ© des donnĂ©es correspondant aux composantes linĂ©aires (fondamentale) et non linĂ©aires (premiĂšre harmonique) de l'image observĂ©e, et d'un terme de rĂ©gularisation basĂ© sur la parcimonie afin de stabiliser la solution. Pour tenir compte de l'attĂ©nuation en profondeur des images harmoniques, un terme d'attĂ©nuation dans le modĂšle direct de l'image harmonique est proposĂ© sur la base d'une analyse spectrale effectuĂ©e sur les signaux RF observĂ©s. La mĂ©thode proposĂ©e a d'abord Ă©tĂ© appliquĂ©e en deux Ă©tapes, en estimant d'abord la rĂ©ponse impulsionelle, suivi par la fonction de rĂ©flectivitĂ©. Dans un deuxiĂšme temps, une solution pour estimer simultanĂ©ment le rĂ©ponse impulsionelle et la fonction de rĂ©flectivitĂ© est proposĂ©e, et une autre solution pour prendre en compte la variabilitĂ© spatiale du la rĂ©ponse impulsionelle est prĂ©sentĂ©e. L'intĂ©rĂȘt de la mĂ©thode proposĂ©e est dĂ©montrĂ© par des rĂ©sultats synthĂ©tiques et in vivo et comparĂ© aux mĂ©thodes de restauration conventionnelles

    The University Defence Research Collaboration In Signal Processing: 2013-2018

    Get PDF
    Signal processing is an enabling technology crucial to all areas of defence and security. It is called for whenever humans and autonomous systems are required to interpret data (i.e. the signal) output from sensors. This leads to the production of the intelligence on which military outcomes depend. Signal processing should be timely, accurate and suited to the decisions to be made. When performed well it is critical, battle-winning and probably the most important weapon which you’ve never heard of. With the plethora of sensors and data sources that are emerging in the future network-enabled battlespace, sensing is becoming ubiquitous. This makes signal processing more complicated but also brings great opportunities. The second phase of the University Defence Research Collaboration in Signal Processing was set up to meet these complex problems head-on while taking advantage of the opportunities. Its unique structure combines two multi-disciplinary academic consortia, in which many researchers can approach different aspects of a problem, with baked-in industrial collaboration enabling early commercial exploitation. This phase of the UDRC will have been running for 5 years by the time it completes in March 2018, with remarkable results. This book aims to present those accomplishments and advances in a style accessible to stakeholders, collaborators and exploiters

    Interferometric Synthetic Aperture RADAR and Radargrammetry towards the Categorization of Building Changes

    Get PDF
    The purpose of this work is the investigation of SAR techniques relying on multi image acquisition for fully automatic and rapid change detection analysis at building level. In particular, the benefits and limitations of a complementary use of two specific SAR techniques, InSAR and radargrammetry, in an emergency context are examined in term of quickness, globality and accuracy. The analysis is performed using spaceborne SAR data

    Comparative study of the diachronic evolution of the geological and volcanological environments of the earth with the saturnian satellites Titan and Enceladus.

    Get PDF
    This thesis presents on the study of the environment of Titan and Enceladus, Saturn’s satellites observed by the Cassini-Huygens mission. Various aspects of the geology of Titan are presented focusing on the characteristics of the surface geological features and processes,the internal structure and the correlation with the atmosphere. The morphotectonic features are presented on the basis of terrestrial models. Moreover, Titan areas probably correlated with the interior are tested against a geophysical model of tidal distortion and found to conform with localisation and internal dynamics. We then study the surface albedo and composition of specific Titan areas (Hotei Regio, Tui Regio, Sotra Patera) –determined by the PCA method- based on data from Cassini/VIMS (0.4–5 ÎŒm) on which a radiative transfer code is applied with the most updated spectroscopic parameters. Monitoring of these areas showed surface albedo changes in the course of 1-3.5 yrs, implying dynamic exogenic-endogenic processes that affect the surface and compatible with cryovolcanism in the case of Sotra Patera. Processes that form the surface of Enceladus are also discussed. In addition, the analogies with the Earth's surface and possible internal processes on the icy satellites are being explored. The astrobiological implications of this work are discussed within the framework of the quest for habitable environments in our outer Solar system. These studies are related to the preparation of future space missions to the systems of Jupiter and Saturn and payload capability. Finally, public awareness and perspectives of this research are discussed
    corecore