Relevant bibliographies by topics / Inverse Problems in Imaging

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Inverse Problems in Imaging'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Inverse Problems in Imaging"

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Ribes, Alejandro, and Francis Schmitt. "Linear inverse problems in imaging." IEEE Signal Processing Magazine 25, no. 4 (July 2008): 84–99. http://dx.doi.org/10.1109/msp.2008.923099.

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Gilton, Davis, Gregory Ongie, and Rebecca Willett. "Model Adaptation for Inverse Problems in Imaging." IEEE Transactions on Computational Imaging 7 (2021): 661–74. http://dx.doi.org/10.1109/tci.2021.3094714.

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Oksanen, Lauri, and Mikko Salo. "Inverse problems in imaging and engineering science." Mathematics in Engineering 2, no. 2 (2020): 287–89. http://dx.doi.org/10.3934/mine.2020014.

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Abubakar, Aria, and Maokun Li. "Electromagnetic Inverse Problems for Sensing and Imaging." IEEE Antennas and Propagation Magazine 58, no. 2 (April 2016): 17. http://dx.doi.org/10.1109/map.2016.2520879.

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Kravchuk, Oleg, and Galyna Kriukova. "Regularization by Denoising for Inverse Problems in Imaging." Mohyla Mathematical Journal 5 (December 28, 2022): 57–61. http://dx.doi.org/10.18523/2617-70805202257-61.

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In this work, a generalized scheme of regularization of inverse problems is considered, where a priori knowledge about the smoothness of the solution is given by means of some self-adjoint operator in the solution space. The formulation of the problem is considered, namely, in addition to the main inverse problem, an additional problem is defined, in which the solution is the right-hand side of the equation. Thus, for the regularization of the main inverse problem, an additional inverse problem is used, which brings information about the smoothness of the solution to the initial problem. This formulation of the problem makes it possible to use operators of high complexity for regularization of inverse problems, which is an urgent need in modern machine learning problems, in particular, in image processing problems. The paper examines the approximation error of the solution of the initial problem using an additional problem.
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Gilton, Davis, Gregory Ongie, and Rebecca Willett. "Deep Equilibrium Architectures for Inverse Problems in Imaging." IEEE Transactions on Computational Imaging 7 (2021): 1123–33. http://dx.doi.org/10.1109/tci.2021.3118944.

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Bryan, Kurt, and Tanya Leise. "Impedance Imaging, Inverse Problems, and Harry Potter's Cloak." SIAM Review 52, no. 2 (January 2010): 359–77. http://dx.doi.org/10.1137/090757873.

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Gilton, Davis, Greg Ongie, and Rebecca Willett. "Neumann Networks for Linear Inverse Problems in Imaging." IEEE Transactions on Computational Imaging 6 (2020): 328–43. http://dx.doi.org/10.1109/tci.2019.2948732.

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Ongie, Gregory, Ajil Jalal, Christopher A. Metzler, Richard G. Baraniuk, Alexandros G. Dimakis, and Rebecca Willett. "Deep Learning Techniques for Inverse Problems in Imaging." IEEE Journal on Selected Areas in Information Theory 1, no. 1 (May 2020): 39–56. http://dx.doi.org/10.1109/jsait.2020.2991563.

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Velikhovskyi, G. O., V. B. Molodkin, V. V. Lizunov, T. P. Vladimirova, S. V. Lizunova, Ya V. Vasylyk, M. P. Kulish, O. P. Dmytrenko, O. L. Pavlenko, and Iu V. Davydova. "Solving of Direct and Inverse Scattering Problems for Heterogeneous Non-Crystalline Objects in Analyzer-Based Imaging." METALLOFIZIKA I NOVEISHIE TEKHNOLOGII 41, no. 3 (May 26, 2019): 375–88. http://dx.doi.org/10.15407/mfint.41.03.0375.

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Dissertations / Theses on the topic "Inverse Problems in Imaging"

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Leung, Wun Ying Valerie. "Inverse problems in astronomical and general imaging." Thesis, University of Canterbury. Electrical and Computer Engineering, 2002. http://hdl.handle.net/10092/7513.

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The resolution and the quality of an imaged object are limited by four contributing factors. Firstly, the primary resolution limit of a system is imposed by the aperture of an instrument due to the effects of diffraction. Secondly, the finite sampling frequency, the finite measurement time and the mechanical limitations of the equipment also affect the resolution of the images captured. Thirdly, the images are corrupted by noise, a process inherent to all imaging systems. Finally, a turbulent imaging medium introduces random degradations to the signals before they are measured. In astronomical imaging, it is the atmosphere which distorts the wavefronts of the objects, severely limiting the resolution of the images captured by ground-based telescopes. These four factors affect all real imaging systems to varying degrees. All the limitations imposed on an imaging system result in the need to deduce or reconstruct the underlying object distribution from the distorted measured data. This class of problems is called inverse problems. The key to the success of solving an inverse problem is the correct modelling of the physical processes which give rise to the corresponding forward problem. However, the physical processes have an infinite amount of information, but only a finite number of parameters can be used in the model. Information loss is therefore inevitable. As a result, the solution to many inverse problems requires additional information or prior knowledge. The application of prior information to inverse problems is a recurrent theme throughout this thesis. An inverse problem that has been an active research area for many years is interpolation, and there exist numerous techniques for solving this problem. However, many of these techniques neither account for the sampling process of the instrument nor include prior information in the reconstruction. These factors are taken into account in the proposed optimal Bayesian interpolator. The process of interpolation is also examined from the point of view of superresolution, as these processes can be viewed as being complementary. Since the principal effect of atmospheric turbulence on an incoming wavefront is a phase distortion, most of the inverse problem techniques devised for this seek to either estimate or compensate for this phase component. These techniques are classified into computer post-processing methods, adaptive optics (AO) and hybrid techniques. Blind deconvolution is a post-processing technique which uses the speckle images to estimate both the object distribution and the point spread function (PSF), the latter of which is directly related to the phase. The most successful approaches are based on characterising the PSF as the aberrations over the aperture. Since the PSF is also dependent on the atmosphere, it is possible to constrain the solution using the statistics of the atmosphere. An investigation shows the feasibility of this approach. Bispectrum is also a post-processing method which reconstructs the spectrum of the object. The key component for phase preservation is the property of phase closure, and its application as prior information for blind deconvolution is examined. Blind deconvolution techniques utilise only information in the image channel to estimate the phase which is difficult. An alternative method for phase estimation is from a Shack-Hartmann (SH) wavefront sensing channel. However, since phase information is present in both the wavefront sensing and the image channels simultaneously, both of these approaches suffer from the problem that phase information from only one channel is used. An improved estimate of the phase is achieved by a combination of these methods, ensuring that the phase estimation is made jointly from the data in both the image and the wavefront sensing measurements. This formulation, posed as a blind deconvolution framework, is investigated in this thesis. An additional advantage of this approach is that since speckle images are imaged in a narrowband, while wavefront sensing images are captured by a charge-coupled device (CCD) camera at all wavelengths, the splitting of the light does not compromise the light level for either channel. This provides a further incentive for using simultaneous data sets. The effectiveness of using Shack-Hartmann wavefront sensing data for phase estimation relies on the accuracy of locating the data spots. The commonly used method which calculates the centre of gravity of the image is in fact prone to noise and is suboptimal. An improved method for spot location based on blind deconvolution is demonstrated. Ground-based adaptive optics (AO) technologies aim to correct for atmospheric turbulence in real time. Although much success has been achieved, the space- and time-varying nature of the atmosphere renders the accurate measurement of atmospheric properties difficult. It is therefore usual to perform additional post-processing on the AO data. As a result, some of the techniques developed in this thesis are applicable to adaptive optics. One of the methods which utilise elements of both adaptive optics and post-processing is the hybrid technique of deconvolution from wavefront sensing (DWFS). Here, both the speckle images and the SH wavefront sensing data are used. The original proposal of DWFS is simple to implement but suffers from the problem where the magnitude of the object spectrum cannot be reconstructed accurately. The solution proposed for overcoming this is to use an additional set of reference star measurements. This however does not completely remove the original problem; in addition it introduces other difficulties associated with reference star measurements such as anisoplanatism and reduction of valuable observing time. In this thesis a parameterised solution is examined which removes the need for a reference star, as well as offering a potential to overcome the problem of estimating the magnitude of the object.
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Szasz, Teodora. "Advanced beamforming techniques in ultrasound imaging and the associated inverse problems." Thesis, Toulouse 3, 2016. http://www.theses.fr/2016TOU30221/document.

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L'imagerie ultrasonore (US) permet de réaliser des examens médicaux non invasifs avec des méthodes d'acquisition rapides à des coûts modérés. L'imagerie cardiaque, abdominale, fœtale, ou mammaire sont quelques-unes des applications où elle est largement utilisée comme outil de diagnostic. En imagerie US classique, des ondes acoustiques sont transmises à une région d'intérêt du corps humain. Les signaux d'écho rétrodiffusés, sont ensuite formés pour créer des lignes radiofréquences. La formation de voies (FV) joue un rôle clé dans l'obtention des images US, car elle influence la résolution et le contraste de l'image finale. L'objectif de ce travail est de modéliser la formation de voies comme un problème inverse liant les données brutes aux signaux RF. Le modèle de formation de voies proposé ici améliore le contraste et la résolution spatiale des images échographiques par rapport aux techniques de FV existants. Dans un premier temps, nous nous sommes concentrés sur des méthodes de FV en imagerie US. Nous avons brièvement passé en revue les techniques de formation de voies les plus courantes, en commencent par la méthode par retard et somme standard puis en utilisant les techniques de formation de voies adaptatives. Ensuite, nous avons étudié l'utilisation de signaux qui exploitent une représentation parcimonieuse de l'image US dans le cadre de la formation de voies. Les approches proposées détectent les réflecteurs forts du milieu sur la base de critères bayésiens. Nous avons finalement développé une nouvelle façon d'aborder la formation de voies en imagerie US, en la formulant comme un problème inverse linéaire liant les échos réfléchis au signal final. L'intérêt majeur de notre approche est la flexibilité dans le choix des hypothèses statistiques sur le signal avant la formation de voies et sa robustesse dans à un nombre réduit d'émissions. Finalement, nous présentons une nouvelle méthode de formation de voies pour l'imagerie US basée sur l'utilisation de caractéristique statistique des signaux supposée alpha-stable
Ultrasound (US) allows non-invasive and ultra-high frame rate imaging procedures at reduced costs. Cardiac, abdominal, fetal, and breast imaging are some of the applications where it is extensively used as diagnostic tool. In a classical US scanning process, short acoustic pulses are transmitted through the region-of-interest of the human body. The backscattered echo signals are then beamformed for creating radiofrequency(RF) lines. Beamforming (BF) plays a key role in US image formation, influencing the resolution and the contrast of final image. The objective of this thesis is to model BF as an inverse problem, relating the raw channel data to the signals to be recovered. The proposed BF framework improves the contrast and the spatial resolution of the US images, compared with the existing BF methods. To begin with, we investigated the existing BF methods in medical US imaging. We briefly review the most common BF techniques, starting with the standard delay-and-sum BF method and emerging to the most known adaptive BF techniques, such as minimum variance BF. Afterwards, we investigated the use of sparse priors in creating original two-dimensional beamforming methods for ultrasound imaging. The proposed approaches detect the strong reflectors from the scanned medium based on the well-known Bayesian Information Criteria used in statistical modeling. Furthermore, we propose a new way of addressing the BF in US imaging, by formulating it as a linear inverse problem relating the reflected echoes to the signal to be recovered. Our approach offers flexibility in the choice of statistical assumptions on the signal to be beamformed and it is robust to a reduced number of pulse emissions. At the end of this research, we investigated the use of the non-Gaussianity properties of the RF signals in the BF process, by assuming alpha-stable statistics of US images
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Gregson, James. "Applications of inverse problems in fluids and imaging." Thesis, University of British Columbia, 2015. http://hdl.handle.net/2429/54081.

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Three applications of inverse problems relating to fluid imaging and image deblurring are presented. The first two, tomographic reconstruction of dye concentration fields from multi-view video and deblurring of photographs, are addressed by a stochastic optimization scheme that allows a wide variety of priors to be incorporated into the reconstruction process within a straightforward framework. The third, estimation of fluid velocities from volumetric dye concentration fields, highlights a previously unexplored connection between fluid simulation and proximal algorithms from convex optimization. This connection allows several classical imaging inverse problems to be investigated in the context of fluids, including optical flow, denoising and deconvolution. The connection also allows inverse problems to be incorporated into fluid simulation for the purposes of physically-based regularization of optical flow and for stylistic modifications of fluid captures. Through both methods and all three applications the importance of incorporating domain-specific priors into inverse problems for fluids and imaging is highlighted.
Science, Faculty of
Computer Science, Department of
Graduate
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Lecharlier, Loïc. "Blind inverse imaging with positivity constraints." Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209240.

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Dans les problèmes inverses en imagerie, on suppose généralement connu l’opérateur ou matrice décrivant le système de formation de l’image. De façon équivalente pour un système linéaire, on suppose connue sa réponse impulsionnelle. Toutefois, ceci n’est pas une hypothèse réaliste pour de nombreuses applications pratiques pour lesquelles cet opérateur n’est en fait pas connu (ou n’est connu qu’approximativement). On a alors affaire à un problème d’inversion dite “aveugle”. Dans le cas de systèmes invariants par translation, on parle de “déconvolution aveugle” car à la fois l’image ou objet de départ et la réponse impulsionnelle doivent être estimées à partir de la seule image observée qui résulte d’une convolution et est affectée d’erreurs de mesure. Ce problème est notoirement difficile et pour pallier les ambiguïtés et les instabilités numériques inhérentes à ce type d’inversions, il faut recourir à des informations ou contraintes supplémentaires, telles que la positivité qui s’est avérée un levier de stabilisation puissant dans les problèmes d’imagerie non aveugle. La thèse propose de nouveaux algorithmes d’inversion aveugle dans un cadre discret ou discrétisé, en supposant que l’image inconnue, la matrice à inverser et les données sont positives. Le problème est formulé comme un problème d’optimisation (non convexe) où le terme d’attache aux données à minimiser, modélisant soit le cas de données de type Poisson (divergence de Kullback-Leibler) ou affectées de bruit gaussien (moindres carrés), est augmenté par des termes de pénalité sur les inconnues du problème. La stratégie d’optimisation consiste en des ajustements alternés de l’image à reconstruire et de la matrice à inverser qui sont de type multiplicatif et résultent de la minimisation de fonctions coût “surrogées” valables dans le cas positif. Le cadre assez général permet d’utiliser plusieurs types de pénalités, y compris sur la variation totale (lissée) de l’image. Une normalisation éventuelle de la réponse impulsionnelle ou de la matrice est également prévue à chaque itération. Des résultats de convergence pour ces algorithmes sont établis dans la thèse, tant en ce qui concerne la décroissance des fonctions coût que la convergence de la suite des itérés vers un point stationnaire. La méthodologie proposée est validée avec succès par des simulations numériques relatives à différentes applications telle que la déconvolution aveugle d'images en astronomie, la factorisation en matrices positives pour l’imagerie hyperspectrale et la déconvolution de densités en statistique.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Zhang, Wenlong. "Forward and Inverse Problems Under Uncertainty." Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLEE024/document.

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Cette thèse contient deux matières différentes. Dans la première partie, deux cas sont considérés. L'un est le modèle plus lisse de la plaque mince et l'autre est les équations des limites elliptiques avec des données limites incertaines. Dans cette partie, les convergences stochastiques des méthodes des éléments finis sont prouvées pour chaque problème.Dans la deuxième partie, nous fournissons une analyse mathématique du problème inverse linéarisé dans la tomographie d'impédance électrique multifréquence. Nous présentons un cadre mathématique et numérique pour une procédure d'imagerie du tenseur de conductivité électrique anisotrope en utilisant une nouvelle technique appelée Tentomètre de diffusion Magnéto-acoustographie et proposons une approche de contrôle optimale pour reconstruire le facteur de propriété intrinsèque reliant le tenseur de diffusion au tenseur de conductivité électrique anisotrope. Nous démontrons la convergence et la stabilité du type Lipschitz de l'algorithme et présente des exemples numériques pour illustrer sa précision. Le modèle cellulaire pour Electropermécanisme est démontré. Nous étudions les paramètres efficaces dans un modèle d'homogénéisation. Nous démontrons numériquement la sensibilité de ces paramètres efficaces aux paramètres microscopiques critiques régissant l'électropermécanisme
This thesis contains two different subjects. In first part, two cases are considered. One is the thin plate spline smoother model and the other one is the elliptic boundary equations with uncertain boundary data. In this part, stochastic convergences of the finite element methods are proved for each problem.In second part, we provide a mathematical analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We present a mathematical and numerical framework for a procedure of imaging anisotropic electrical conductivity tensor using a novel technique called Diffusion Tensor Magneto-acoustography and propose an optimal control approach for reconstructing the cross-property factor relating the diffusion tensor to the anisotropic electrical conductivity tensor. We prove convergence and Lipschitz type stability of the algorithm and present numerical examples to illustrate its accuracy. The cell model for Electropermeabilization is demonstrated. We study effective parameters in a homogenization model. We demonstrate numerically the sensitivity of these effective parameters to critical microscopic parameters governing electropermeabilization
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Zhu, Sha. "A Bayesian Approach for Inverse Problems in Synthetic Aperture Radar Imaging." Phd thesis, Université Paris Sud - Paris XI, 2012. http://tel.archives-ouvertes.fr/tel-00844748.

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Synthetic Aperture Radar (SAR) imaging is a well-known technique in the domain of remote sensing, aerospace surveillance, geography and mapping. To obtain images of high resolution under noise, taking into account of the characteristics of targets in the observed scene, the different uncertainties of measure and the modeling errors becomes very important.Conventional imaging methods are based on i) over-simplified scene models, ii) a simplified linear forward modeling (mathematical relations between the transmitted signals, the received signals and the targets) and iii) using a very simplified Inverse Fast Fourier Transform (IFFT) to do the inversion, resulting in low resolution and noisy images with unsuppressed speckles and high side lobe artifacts.In this thesis, we propose to use a Bayesian approach to SAR imaging, which overcomes many drawbacks of classical methods and brings high resolution, more stable images and more accurate parameter estimation for target recognition.The proposed unifying approach is used for inverse problems in Mono-, Bi- and Multi-static SAR imaging, as well as for micromotion target imaging. Appropriate priors for modeling different target scenes in terms of target features enhancement during imaging are proposed. Fast and effective estimation methods with simple and hierarchical priors are developed. The problem of hyperparameter estimation is also handled in this Bayesian approach framework. Results on synthetic, experimental and real data demonstrate the effectiveness of the proposed approach.
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Alfowzan, Mohammed Fowzan, and Mohammed Fowzan Alfowzan. "Solutions to Space-Time Inverse Problems." Diss., The University of Arizona, 2016. http://hdl.handle.net/10150/621791.

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Two inverse problems are investigated in this dissertation, taking into account both the spatial and temporal aspects. The first problem addresses the under determined image reconstruction problem for dynamic SPECT. The quality of the reconstructed image is often limited due to having fewer observations than the number of voxels. The proposed algorithms make use of the generalized α-divergence function to improve the estimation performance. The first algorithm is based on an alternating minimization framework to minimize a regularized α-divergence objective function. We demonstrate that selecting an adaptive α policy depending on the time evolution of the voxels gives better performance than a fixed α assignment. The second algorithm is based on Newton's method. A regularized approach has been taken to avoid stability issues. Newton's method is generally computationally demanding due to the complexity associated with inverting the Hessian matrix. A fast Newton-based method is proposed using majorization-minimization techniques that diagonalize the Hessian matrix. In dynamically evolving systems, the prediction matrix plays an important role in the estimation process. An estimation technique is proposed to estimate the prediction matrix using the α-divergence function. The simulation results show that our algorithms provide better performance than the techniques based on the Kullback-Leibler distance. The second problem is the recovery of data transmitted over free-space optical communication channels using orbital angular momentum (OAM). In the presence of atmospheric turbulence, crosstalk occurs among OAM optical modes resulting in an error floor at a relatively high bit error rate. The modulation format considered for the underlying problem is Q-ary pulse position modulation (PPM). We propose and evaluate three joint detection strategies to overcome the OAM crosstalk problem: i) maximum likelihood sequence estimation (MLSE). ii) Q-PPM factor graph detection. iii) branch-and-bound detection. We compare the complexity and the bit-error-rate performance of these strategies in realistic scenarios.
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Rückert, Nadja. "Studies on two specific inverse problems from imaging and finance." Doctoral thesis, Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-91587.

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This thesis deals with regularization parameter selection methods in the context of Tikhonov-type regularization with Poisson distributed data, in particular the reconstruction of images, as well as with the identification of the volatility surface from observed option prices. In Part I we examine the choice of the regularization parameter when reconstructing an image, which is disturbed by Poisson noise, with Tikhonov-type regularization. This type of regularization is a generalization of the classical Tikhonov regularization in the Banach space setting and often called variational regularization. After a general consideration of Tikhonov-type regularization for data corrupted by Poisson noise, we examine the methods for choosing the regularization parameter numerically on the basis of two test images and real PET data. In Part II we consider the estimation of the volatility function from observed call option prices with the explicit formula which has been derived by Dupire using the Black-Scholes partial differential equation. The option prices are only available as discrete noisy observations so that the main difficulty is the ill-posedness of the numerical differentiation. Finite difference schemes, as regularization by discretization of the inverse and ill-posed problem, do not overcome these difficulties when they are used to evaluate the partial derivatives. Therefore we construct an alternative algorithm based on the weak formulation of the dual Black-Scholes partial differential equation and evaluate the performance of the finite difference schemes and the new algorithm for synthetic and real option prices.
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Som, Subhojit. "Topics in Sparse Inverse Problems and Electron Paramagnetic Resonance Imaging." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1282135281.

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Zamanian, Sam Ahmad. "Hierarchical Bayesian approaches to seismic imaging and other geophysical inverse problems." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/92970.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 189-196).
In many geophysical inverse problems, smoothness assumptions on the underlying geologic model are utilized to mitigate the effects of poor data coverage and observational noise and to improve the quality of the inferred model parameters. In the context of Bayesian inference, these smoothness assumptions take the form of a prior distribution on the model parameters. Conventionally, the regularization parameters defining these assumptions are fixed independently from the data or tuned in an ad hoc manner. However, it is often the case that the smoothness properties of the true earth model are not known a priori, and furthermore, these properties may vary spatially. In the seismic imaging problem, for example, where the objective is to estimate the earth's reflectivity, the reflectivity model is smooth along a particular reflector but exhibits a sharp contrast in the direction orthogonal to the reflector. In such cases, defining a prior using predefined smoothness assumptions may result in posterior estimates of the model that incorrectly smooth out these sharp contrasts. In this thesis, we explore the application of Bayesian inference to different geophysical inverse problems and seek to address issues related to smoothing by appealing to the hierarchical Bayesian framework. We capture the smoothness properties of the prior distribution on the model by defining a Markov random field (MRF) on the set of model parameters and assigning weights to the edges of the underlying graph; we refer to these parameters as the edge strengths of the MRF. We investigate two cases where the smoothing is specified a priori and introduce a method for estimating the edge strengths of the MRF. In the first part of this thesis, we apply a Bayesian inference framework (where the edge strengths of the MRF are predetermined) to the problem of characterizing the fractured nature of a reservoir from seismic data. Our methodology combines different features of the seismic data, particularly P-wave reflection amplitudes and scattering attributes, to allow for estimation of fracture properties under a larger physical regime than would be attainable using only one of these data types. Through this application, we demonstrate the capability of our parameterization of the prior distribution with edge strengths to both enforce smoothness in the estimates of the fracture properties and capture a priori information about geological features in the model (such as a discontinuity that may arise in the presence of a fault). We solve the inference problem via loopy belief propagation to approximate the posterior marginal distributions of the fracture properties, as well as their maximum a posteriori (MAP) and Bayes least squares estimates. In the second part of the thesis, we investigate how the parameters defining the prior distribution are connected to the model covariance and address the question of how to optimize these parameters in the context of the seismic imaging problem. We formulate the seismic imaging problem within the hierarchical Bayesian setting, where the edge strengths are treated as random variables to be inferred from the data, and provide a framework for computing the marginal MAP estimate of the edge strengths by application of the expectation-maximization (E-M) algorithm. We validate our methodology on synthetic datasets arising from 2-D models. The images we obtain after inferring the edge strengths exhibit the desired spatially-varying smoothness properties and yield sharper, more coherent reflectors. In the final part of the thesis, we shift our focus and consider the problem of timelapse seismic processing, where the objective is to detect changes in the subsurface over a period of time using repeated seismic surveys. We focus on the realistic case where the surveys are taken with differing acquisition geometries. In such situations, conventional methods for processing time-lapse data involve inverting surveys separately and subtracting the inversion models to estimate the change in model parameters; however, such methods often perform poorly as they do not correctly account for differing model uncertainty between surveys due to differences in illumination and observational noise. Applying the machinery explored in the previous chapters, we formulate the time-lapse processing problem within the hierarchical Bayesian setting and present a framework for computing the marginal MAP estimate of the time-lapse change model using the E-M algorithm. The results of our inference framework are validated on synthetic data from a 2-D time-lapse seismic imaging example, where the hierarchical Bayesian estimates significantly outperform conventional time-lapse inversion results.
by Sam Ahmad Zamanian.
Ph. D.
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Books on the topic "Inverse Problems in Imaging"

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Carpio, Ana, Oliver Dorn, Miguel Moscoso, Frank Natterer, George C. Papanicolaou, Maria Luisa Rapún, and Alessandro Teta. Inverse Problems and Imaging. Edited by Luis L. Bonilla. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78547-7.

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F, Roach G., ed. Inverse problems and imaging. Harlow, Essex, England: Longman Scientific & Technical, 1991.

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Seo, Jin Keun, and Eung Je Woo. Nonlinear Inverse Problems in Imaging. Chichester, UK: John Wiley & Sons, Ltd, 2013. http://dx.doi.org/10.1002/9781118478141.

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Patrizia, Boccacci, ed. Introduction to inverse problems in imaging. Bristol, UK: Institute of Physics Pub., 1998.

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Nashed, M. Zuhair, and Otmar Scherzer, eds. Inverse Problems, Image Analysis, and Medical Imaging. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/conm/313.

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Donatelli, Marco, and Stefano Serra-Capizzano, eds. Computational Methods for Inverse Problems in Imaging. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-32882-5.

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Chalmond, Bernard. Modeling and Inverse Problems in Imaging Analysis. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/978-0-387-21662-1.

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Chalmond, Bernard. Modeling and Inverse Problems in Imaging Analysis. New York, NY: Springer New York, 2003.

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Chalmond, Bernard. Modeling and inverse problems in imaging analysis. New York: Springer, 2003.

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Engl, Heinz W., Alfred K. Louis, and William Rundell, eds. Inverse Problems in Medical Imaging and Nondestructive Testing. Vienna: Springer Vienna, 1997. http://dx.doi.org/10.1007/978-3-7091-6521-8.

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Book chapters on the topic "Inverse Problems in Imaging"

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Groetsch, Charles. "Linear Inverse Problems." In Handbook of Mathematical Methods in Imaging, 3–41. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-0-387-92920-0_1.

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Groetsch, Charles. "Linear Inverse Problems." In Handbook of Mathematical Methods in Imaging, 3–46. New York, NY: Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-0790-8_1.

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Moscoso, Miguel. "Polarization-Based Optical Imaging." In Inverse Problems and Imaging, 67–83. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78547-7_4.

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Moscoso, Miguel. "Introduction to Image Reconstruction." In Inverse Problems and Imaging, 1–16. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78547-7_1.

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Natterer, Frank. "X-ray Tomography." In Inverse Problems and Imaging, 17–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78547-7_2.

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Dorn, Oliver, Hugo Bertete-Aguirre, and George C. Papanicolaou. "Adjoint Fields and Sensitivities for 3D Electromagnetic Imaging in Isotropic and Anisotropic Media." In Inverse Problems and Imaging, 35–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78547-7_3.

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Carpio, Ana, and Maria Luisa Rapún. "Topological Derivatives for Shape Reconstruction." In Inverse Problems and Imaging, 85–133. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78547-7_5.

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Dorn, Oliver. "Time-Reversal and the Adjoint Imaging Method with an Application in Telecommunication." In Inverse Problems and Imaging, 135–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78547-7_6.

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Dell'Antonio, Gianfausto, Rodolfo Figari, and Alessandro Teta. "A Brief Review on Point Interactions." In Inverse Problems and Imaging, 171–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78547-7_7.

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Beilina, Larisa, and Michael V. Klibanov. "Approximate Global Convergence in Imaging of Land Mines from Backscattered Data." In Applied Inverse Problems, 15–36. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7816-4_2.

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Conference papers on the topic "Inverse Problems in Imaging"

1

Bala, Raja. "Inverse problems in color device characterization." In Electronic Imaging 2003, edited by Charles A. Bouman and Robert L. Stevenson. SPIE, 2003. http://dx.doi.org/10.1117/12.488617.

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Oberai, Assad A. "Inverse problems biomechanical imaging (Conference Presentation)." In Optical Elastography and Tissue Biomechanics III, edited by Kirill V. Larin and David D. Sampson. SPIE, 2016. http://dx.doi.org/10.1117/12.2216702.

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Weiss, Pierre. "The geometry of convex regularized inverse problems." In Mathematics in Imaging. Washington, D.C.: OSA, 2018. http://dx.doi.org/10.1364/math.2018.mw2d.5.

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Oh, Seungseok, Adam B. Milstein, Charles A. Bouman, and Kevin J. Webb. "Multigrid algorithms for optimization and inverse problems." In Electronic Imaging 2003, edited by Charles A. Bouman and Robert L. Stevenson. SPIE, 2003. http://dx.doi.org/10.1117/12.484805.

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Marais, Willem, Robert Holz, Yu Hen Hu, and Rebecca Willett. "Atmospheric lidar imaging and poisson inverse problems." In 2016 IEEE International Conference on Image Processing (ICIP). IEEE, 2016. http://dx.doi.org/10.1109/icip.2016.7532504.

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Liu, Jiaming, Yu Sun, Weijie Gan, Xiaojian Xu, Brendt Wohlberg, and Ulugbek S. Kamilov. "Stochastic Deep Unfolding for Imaging Inverse Problems." In ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2021. http://dx.doi.org/10.1109/icassp39728.2021.9414332.

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"Deep Learning for Inverse Problems in Imaging." In 2019 Ninth International Conference on Image Processing Theory, Tools and Applications (IPTA). IEEE, 2019. http://dx.doi.org/10.1109/ipta.2019.8936102.

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Sinha, Ayan T., Justin Lee, Shuai Li, and George Barbastathis. "Solving inverse problems using residual neural networks." In Digital Holography and Three-Dimensional Imaging. Washington, D.C.: OSA, 2016. http://dx.doi.org/10.1364/dh.2017.w1a.3.

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McCormick, N. J. "Source Estimation in Inverse Radiative Transfer Problems." In Advances in Optical Imaging and Photon Migration. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/aoipm.1994.ncpdir.207.

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Oliveri, Giacomo, and Toshifumi Moriyama. "Compressive Sensing Methods Applied to Inverse Imaging Problems." In Computational Optical Sensing and Imaging. Washington, D.C.: OSA, 2014. http://dx.doi.org/10.1364/cosi.2014.cw2c.3.

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Reports on the topic "Inverse Problems in Imaging"

1

Schotland, John C. Inverse Problems and Optical Imaging with Nanoscale Resolution. Fort Belvoir, VA: Defense Technical Information Center, March 2010. http://dx.doi.org/10.21236/ada565342.

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Prasad, S. Post Detection Processing and Inverse Problems in Ground Based Imaging. Fort Belvoir, VA: Defense Technical Information Center, November 2002. http://dx.doi.org/10.21236/ada409722.

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Fowler, Michael James. Generalized Uncertainty Quantification for Linear Inverse Problems in X-ray Imaging. Office of Scientific and Technical Information (OSTI), April 2014. http://dx.doi.org/10.2172/1179471.

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Santosa, Fadil. Inverse Problems in Nondestructive Evaluations. Fort Belvoir, VA: Defense Technical Information Center, August 1992. http://dx.doi.org/10.21236/ada261370.

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Friedman, Avner. Inverse Problems in Wave Propagation. Fort Belvoir, VA: Defense Technical Information Center, November 1995. http://dx.doi.org/10.21236/ada302229.

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Barhen, J., J. G. Berryman, L. Borcea, J. Dennis, C. de Groot-Hedlin, F. Gilbert, P. Gill, et al. Optimization and geophysical inverse problems. Office of Scientific and Technical Information (OSTI), October 2000. http://dx.doi.org/10.2172/939130.

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Angell, T. S., and R. E. Kleinman. Inverse and Control Problems in Electromagnetics. Fort Belvoir, VA: Defense Technical Information Center, June 1994. http://dx.doi.org/10.21236/ada292993.

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Gordon, Howard R. Inverse Problems in Hydrologic Radiative Transfer. Fort Belvoir, VA: Defense Technical Information Center, September 1999. http://dx.doi.org/10.21236/ada629879.

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Colton, David, and Peter Monk. Inverse Scattering Problems for Electromagnetic Waves. Fort Belvoir, VA: Defense Technical Information Center, January 1998. http://dx.doi.org/10.21236/ada337286.

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Michalski, Anatoli I. Inverse problems in demography and biodemography. Rostock: Max Planck Institute for Demographic Research, November 2006. http://dx.doi.org/10.4054/mpidr-wp-2006-041.

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