393 research outputs found
Low-rank and sparse reconstruction in dynamic magnetic resonance imaging via proximal splitting methods
Dynamic magnetic resonance imaging (MRI) consists of collecting multiple MR images in time, resulting in a spatio-temporal signal. However, MRI intrinsically suffers from long acquisition times due to various constraints. This limits the full potential of dynamic MR imaging, such as obtaining high spatial and temporal resolutions which are crucial to observe dynamic phenomena. This dissertation addresses the problem of the reconstruction of dynamic MR images from a limited amount of samples arising from a nuclear magnetic resonance experiment. The term limited can be explained by the approach taken in this thesis to speed up scan time, which is based on violating the Nyquist criterion by skipping measurements that would be normally acquired in a standard MRI procedure. The resulting problem can be classified in the general framework of linear ill-posed inverse problems. This thesis shows how low-dimensional signal models, specifically lowrank and sparsity, can help in the reconstruction of dynamic images from partial measurements. The use of these models are justified by significant developments in signal recovery techniques from partial data that have emerged in recent years in signal processing. The major contributions of this thesis are the development and characterisation of fast and efficient computational tools using convex low-rank and sparse constraints via proximal gradient methods, the development and characterisation of a novel joint reconstruction–separation method via the low-rank plus sparse matrix decomposition technique, and the development and characterisation of low-rank based recovery methods in the context of dynamic parallel MRI. Finally, an additional contribution of this thesis is to formulate the various MR image reconstruction problems in the context of convex optimisation to develop algorithms based on proximal splitting methods
Topics in image reconstruction for high resolution positron emission tomography
Les problèmes mal posés représentent un sujet d'intérêt interdisciplinaire qui surgires dans la télédétection et des applications d'imagerie. Cependant, il subsiste des questions cruciales pour l'application réussie de la théorie à une modalité d'imagerie. La tomographie d'émission par positron (TEP) est une technique d'imagerie non-invasive qui permet d'évaluer des processus biochimiques se déroulant à l'intérieur d'organismes in vivo. La TEP est un outil avantageux pour la recherche sur la physiologie normale chez l'humain ou l'animal, pour le diagnostic et le suivi thérapeutique du cancer, et l'étude des pathologies dans le coeur et dans le cerveau. La TEP partage plusieurs similarités avec d'autres modalités d'imagerie tomographiques, mais pour exploiter pleinement sa capacité à extraire le maximum d'information à partir des projections, la TEP doit utiliser des algorithmes de reconstruction d'images à la fois sophistiquée et pratiques. Plusieurs aspects de la reconstruction d'images TEP ont été explorés dans le présent travail. Les contributions suivantes sont d'objet de ce travail: Un modèle viable de la matrice de transition du système a été élaboré, utilisant la fonction de réponse analytique des détecteurs basée sur l'atténuation linéaire des rayons y dans un banc de détecteur. Nous avons aussi démontré que l'utilisation d'un modèle simplifié pour le calcul de la matrice du système conduit à des artefacts dans l'image. (IEEE Trans. Nucl. Sei., 2000) );> La modélisation analytique de la dépendance décrite à l'égard de la statistique des images a simplifié l'utilisation de la règle d'arrêt par contre-vérification (CV) et a permis d'accélérer la reconstruction statistique itérative. Cette règle peut être utilisée au lieu du procédé CV original pour des projections aux taux de comptage élevés, lorsque la règle CV produit des images raisonnablement précises. (IEEE Trans. Nucl. Sei., 2001) Nous avons proposé une méthodologie de régularisation utilisant la décomposition en valeur propre (DVP) de la matrice du système basée sur l'analyse de la résolution spatiale. L'analyse des caractéristiques du spectre de valeurs propres nous a permis d'identifier la relation qui existe entre le niveau optimal de troncation du spectre pour la reconstruction DVP et la résolution optimale dans l'image reconstruite. (IEEE Trans. Nucl. Sei., 2001) Nous avons proposé une nouvelle technique linéaire de reconstruction d'image événement-par-événement basée sur la matrice pseudo-inverse régularisée du système. L'algorithme représente une façon rapide de mettre à jour une image, potentiellement en temps réel, et permet, en principe, la visualisation instantanée de distribution de la radioactivité durant l'acquisition des données tomographiques. L'image ainsi calculée est la solution minimisant les moindres carrés du problème inverse régularisé.Abstract: Ill-posed problems are a topic of an interdisciplinary interest arising in remote sensing and non-invasive imaging. However, there are issues crucial for successful application of the theory to a given imaging modality. Positron emission tomography (PET) is a non-invasive imaging technique that allows assessing biochemical processes taking place in an organism in vivo. PET is a valuable tool in investigation of normal human or animal physiology, diagnosing and staging cancer, heart and brain disorders. PET is similar to other tomographie imaging techniques in many ways, but to reach its full potential and to extract maximum information from projection data, PET has to use accurate, yet practical, image reconstruction algorithms. Several topics related to PET image reconstruction have been explored in the present dissertation. The following contributions have been made: (1) A system matrix model has been developed using an analytic detector response function based on linear attenuation of [gamma]-rays in a detector array. It has been demonstrated that the use of an oversimplified system model for the computation of a system matrix results in image artefacts. (IEEE Trans. Nucl. Sci., 2000); (2) The dependence on total counts modelled analytically was used to simplify utilisation of the cross-validation (CV) stopping rule and accelerate statistical iterative reconstruction. It can be utilised instead of the original CV procedure for high-count projection data, when the CV yields reasonably accurate images. (IEEE Trans. Nucl. Sci., 2001); (3) A regularisation methodology employing singular value decomposition (SVD) of the system matrix was proposed based on the spatial resolution analysis. A characteristic property of the singular value spectrum shape was found that revealed a relationship between the optimal truncation level to be used with the truncated SVD reconstruction and the optimal reconstructed image resolution. (IEEE Trans. Nucl. Sci., 2001); (4) A novel event-by-event linear image reconstruction technique based on a regularised pseudo-inverse of the system matrix was proposed. The algorithm provides a fast way to update an image potentially in real time and allows, in principle, for the instant visualisation of the radioactivity distribution while the object is still being scanned. The computed image estimate is the minimum-norm least-squares solution of the regularised inverse problem
Air Quality Prediction in Smart Cities Using Machine Learning Technologies Based on Sensor Data: A Review
The influence of machine learning technologies is rapidly increasing and penetrating almost in every field, and air pollution prediction is not being excluded from those fields. This paper covers the revision of the studies related to air pollution prediction using machine learning algorithms based on sensor data in the context of smart cities. Using the most popular databases and executing the corresponding filtration, the most relevant papers were selected. After thorough reviewing those papers, the main features were extracted, which served as a base to link and compare them to each other. As a result, we can conclude that: (1) instead of using simple machine learning techniques, currently, the authors apply advanced and sophisticated techniques, (2) China was the leading country in terms of a case study, (3) Particulate matter with diameter equal to 2.5 micrometers was the main prediction target, (4) in 41% of the publications the authors carried out the prediction for the next day, (5) 66% of the studies used data had an hourly rate, (6) 49% of the papers used open data and since 2016 it had a tendency to increase, and (7) for efficient air quality prediction it is important to consider the external factors such as weather conditions, spatial characteristics, and temporal features
Regularisation methods for imaging from electrical measurements
In Electrical Impedance Tomography the conductivity of an object is estimated from
boundary measurements. An array of electrodes is attached to the surface of the object
and current stimuli are applied via these electrodes. The resulting voltages are measured.
The process of estimating the conductivity as a function of space inside the object from
voltage measurements at the surface is called reconstruction. Mathematically the ElT
reconstruction is a non linear inverse problem, the stable solution of which requires regularisation
methods. Most common regularisation methods impose that the reconstructed image should
be smooth. Such methods confer stability to the reconstruction process, but limit the
capability of describing sharp variations in the sought parameter.
In this thesis two new methods of regularisation are proposed. The first method, Gallssian
anisotropic regularisation, enhances the reconstruction of sharp conductivity changes
occurring at the interface between a contrasting object and the background. As such
changes are step changes, reconstruction with traditional smoothing regularisation techniques
is unsatisfactory. The Gaussian anisotropic filtering works by incorporating prior
structural information. The approximate knowledge of the shapes of contrasts allows us
to relax the smoothness in the direction normal to the expected boundary. The construction
of Gaussian regularisation filters that express such directional properties on the basis
of the structural information is discussed, and the results of numerical experiments are
analysed. The method gives good results when the actual conductivity distribution is in
accordance with the prior information. When the conductivity distribution violates the
prior information the method is still capable of properly locating the regions of contrast.
The second part of the thesis is concerned with regularisation via the total variation
functional. This functional allows the reconstruction of discontinuous parameters. The
properties of the functional are briefly introduced, and an application in inverse problems
in image denoising is shown. As the functional is non-differentiable, numerical difficulties
are encountered in its use. The aim is therefore to propose an efficient numerical implementation
for application in ElT. Several well known optimisation methods arc analysed,
as possible candidates, by theoretical considerations and by numerical experiments. Such
methods are shown to be inefficient. The application of recent optimisation methods
called primal- dual interior point methods is analysed be theoretical considerations and
by numerical experiments, and an efficient and stable algorithm is developed. Numerical
experiments demonstrate the capability of the algorithm in reconstructing sharp conductivity profiles
Proximal Markov chain Monte Carlo algorithms
This paper presents a new Metropolis-adjusted Langevin algorithm (MALA) that uses convex analysis to simulate efficiently from high-dimensional densities that are log-concave, a class of probability distributions that is widely used in modern high-dimensional statistics and data analysis. The method is based on a new first-order approximation for Langevin diffusions that exploits log-concavity to construct Markov chains with favourable convergence properties. This approximation is closely related to Moreau--Yoshida regularisations for convex functions and uses proximity mappings instead of gradient mappings to approximate the continuous-time process. The proposed method complements existing MALA methods in two ways. First, the method is shown to have very robust stability properties and to converge geometrically for many target densities for which other MALA are not geometric, or only if the step size is sufficiently small. Second, the method can be applied to high-dimensional target densities that are not continuously differentiable, a class of distributions that is increasingly used in image processing and machine learning and that is beyond the scope of existing MALA and HMC algorithms. To use this method it is necessary to compute or to approximate efficiently the proximity mappings of the logarithm of the target density. For several popular models, including many Bayesian models used in modern signal and image processing and machine learning, this can be achieved with convex optimisation algorithms and with approximations based on proximal splitting techniques, which can be implemented in parallel. The proposed method is demonstrated on two challenging high-dimensional and non-differentiable models related to image resolution enhancement and low-rank matrix estimation that are not well addressed by existing MCMC methodology
Multilinear methods for disentangling variations with applications to facial analysis
Several factors contribute to the appearance of an object in a visual scene, including pose,
illumination, and deformation, among others. Each factor accounts for a source of variability
in the data. It is assumed that the multiplicative interactions of these factors emulate the
entangled variability, giving rise to the rich structure of visual object appearance. Disentangling
such unobserved factors from visual data is a challenging task, especially when the data have
been captured in uncontrolled recording conditions (also referred to as “in-the-wild”) and label
information is not available. The work presented in this thesis focuses on disentangling the
variations contained in visual data, in particular applied to 2D and 3D faces. The motivation
behind this work lies in recent developments in the field, such as (i) the creation of large, visual
databases for face analysis, with (ii) the need of extracting information without the use of labels
and (iii) the need to deploy systems under demanding, real-world conditions.
In the first part of this thesis, we present a method to synthesise plausible 3D expressions
that preserve the identity of a target subject. This method is supervised as the model uses
labels, in this case 3D facial meshes of people performing a defined set of facial expressions, to
learn. The ability to synthesise an entire facial rig from a single neutral expression has a large
range of applications both in computer graphics and computer vision, ranging from the ecient
and cost-e↵ective creation of CG characters to scalable data generation for machine learning
purposes. Unlike previous methods based on multilinear models, the proposed approach is
capable to extrapolate well outside the sample pool, which allows it to accurately reproduce
the identity of the target subject and create artefact-free expression shapes while requiring
only a small input dataset. We introduce global-local multilinear models that leverage the
strengths of expression-specific and identity-specific local models combined with coarse motion
estimations from a global model. The expression-specific and identity-specific local models
are built from di↵erent slices of the patch-wise local multilinear model. Experimental results
show that we achieve high-quality, identity-preserving facial expression synthesis results that
outperform existing methods both quantitatively and qualitatively.
In the second part of this thesis, we investigate how the modes of variations from visual data
can be extracted. Our assumption is that visual data has an underlying structure consisting of
factors of variation and their interactions. Finding this structure and the factors is important
as it would not only help us to better understand visual data but once obtained we can edit the factors for use in various applications. Shape from Shading and expression transfer are just two
of the potential applications. To extract the factors of variation, several supervised methods
have been proposed but they require both labels regarding the modes of variations and the same
number of samples under all modes of variations. Therefore, their applicability is limited to
well-organised data, usually captured in well-controlled conditions. We propose a novel general
multilinear matrix decomposition method that discovers the multilinear structure of possibly
incomplete sets of visual data in unsupervised setting. We demonstrate the applicability of the
proposed method in several computer vision tasks, including Shape from Shading (SfS) (in the
wild and with occlusion removal), expression transfer, and estimation of surface normals from
images captured in the wild.
Finally, leveraging the unsupervised multilinear method proposed as well as recent advances in
deep learning, we propose a weakly supervised deep learning method for disentangling multiple
latent factors of variation in face images captured in-the-wild. To this end, we propose a deep
latent variable model, where we model the multiplicative interactions of multiple latent factors
of variation explicitly as a multilinear structure. We demonstrate that the proposed approach
indeed learns disentangled representations of facial expressions and pose, which can be used in
various applications, including face editing, as well as 3D face reconstruction and classification
of facial expression, identity and pose.Open Acces
Development of electrical resistivity imaging methods for geological and archaeological prospecting
Not availabl
(An overview of) Synergistic reconstruction for multimodality/multichannel imaging methods
Imaging is omnipresent in modern society with imaging devices based on a zoo of physical principles, probing a specimen across different wavelengths, energies and time. Recent years have seen a change in the imaging landscape with more and more imaging devices combining that which previously was used separately. Motivated by these hardware developments, an ever increasing set of mathematical ideas is appearing regarding how data from different imaging modalities or channels can be synergistically combined in the image reconstruction process, exploiting structural and/or functional correlations between the multiple images. Here we review these developments, give pointers to important challenges and provide an outlook as to how the field may develop in the forthcoming years. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'
Data-scarce surrogate modeling of shock-induced pore collapse process
Understanding the mechanisms of shock-induced pore collapse is of great
interest in various disciplines in sciences and engineering, including
materials science, biological sciences, and geophysics. However, numerical
modeling of the complex pore collapse processes can be costly. To this end, a
strong need exists to develop surrogate models for generating economic
predictions of pore collapse processes. In this work, we study the use of a
data-driven reduced order model, namely dynamic mode decomposition, and a deep
generative model, namely conditional generative adversarial networks, to
resemble the numerical simulations of the pore collapse process at
representative training shock pressures. Since the simulations are expensive,
the training data are scarce, which makes training an accurate surrogate model
challenging. To overcome the difficulties posed by the complex physics
phenomena, we make several crucial treatments to the plain original form of the
methods to increase the capability of approximating and predicting the
dynamics. In particular, physics information is used as indicators or
conditional inputs to guide the prediction. In realizing these methods, the
training of each dynamic mode composition model takes only around 30 seconds on
CPU. In contrast, training a generative adversarial network model takes 8 hours
on GPU. Moreover, using dynamic mode decomposition, the final-time relative
error is around 0.3% in the reproductive cases. We also demonstrate the
predictive power of the methods at unseen testing shock pressures, where the
error ranges from 1.3% to 5% in the interpolatory cases and 8% to 9% in
extrapolatory cases
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