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A non-convex denoising model for impulse and Gaussian noise mixture removing using bi-level parameter identification Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-20 Lekbir Afraites, Aissam Hadri, Amine Laghrib, Mourad Nachaoui
We propose a new variational framework to remove a mixture of Gaussian and impulse noise from images. This framework is based on a non-convex PDE-constrained with a fractional-order operator. The non-convex norm is applied to the impulse component controlled by a weighted parameter \begin{document}$ \gamma $\end{document}, which depends on the level of the impulse noise and image feature. Furthermore
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Direct regularized reconstruction for the three-dimensional Calderón problem Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-20 Kim Knudsen, Aksel Kaastrup Rasmussen
Electrical Impedance Tomography gives rise to the severely ill-posed Calderón problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing equation. The uniqueness and stability questions for the three-dimensional problem were largely answered in the affirmative in the 1980's using complex geometrical
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Uniqueness of the partial travel time representation of a compact Riemannian manifold with strictly convex boundary Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Ella Pavlechko,Teemu Saksala
In this paper a compact Riemannian manifold with strictly convex boundary is reconstructed from its partial travel time data. This data assumes that an open measurement region on the boundary is given, and that for every point in the manifold, the respective distance function to the points on the measurement region is known. This geometric inverse problem has many connections to seismology, in particular
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Inverse source problem for a one-dimensional time-fractional diffusion equation and unique continuation for weak solutions Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Zhiyuan Li,Yikan Liu,Masahiro Yamamoto
In this paper, we obtain the sharp uniqueness for an inverse \begin{document}$ x $\end{document}-source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum possible lateral Cauchy data. The key ingredient is the unique continuation which holds for weak solutions.
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A spectral target signature for thin surfaces with higher order jump conditions Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Fioralba Cakoni,Heejin Lee,Peter Monk,Yangwen Zhang
In this paper we consider the inverse problem of determining structural properties of a thin anisotropic and dissipative inhomogeneity in \begin{document}$ {\mathbb R}^m $\end{document}, \begin{document}$ m = 2, 3 $\end{document} from scattering data. In the asymptotic limit as the thickness goes to zero, the thin inhomogeneity is modeled by an open \begin{document}$ m-1 $\end{document} dimensional
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Refined instability estimates for some inverse problems Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Pu-Zhao Kow,Jenn-Nan Wang
Many inverse problems are known to be ill-posed. The ill-posedness can be manifested by an instability estimate of exponential type, first derived by Mandache [29]. In this work, based on Mandache's idea, we refine the instability estimates for two inverse problems, including the inverse inclusion problem and the inverse scattering problem. Our aim is to derive explicitly the dependence of the instability
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Direct sampling methods for isotropic and anisotropic scatterers with point source measurements Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Isaac Harris,Dinh-Liem Nguyen,Thi-Phong Nguyen
In this paper, we consider the inverse scattering problem for recovering either an isotropic or anisotropic scatterer from the measured scattered field initiated by a point source. We propose two new imaging functionals for solving the inverse problem. The first one employs a 'far-field' transform to the data which we then use to derive and provide an explicit decay rate for the imaging functional
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Two single-measurement uniqueness results for inverse scattering problems within polyhedral geometries Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Xinlin Cao,Huaian Diao,Hongyu Liu,Jun Zou
We consider the unique determinations of impenetrable obstacles or diffraction grating profiles in \begin{document}$ \mathbb{R}^3 $\end{document} by a single far-field measurement within polyhedral geometries. We are particularly interested in the case that the scattering objects are of impedance type. We derive two new unique identifiability results by a single measurement for the inverse scattering
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Using the Navier-Cauchy equation for motion estimation in dynamic imaging Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Bernadette N. Hahn,Melina-Loren Kienle Garrido,Christian Klingenberg,Sandra Warnecke
Tomographic image reconstruction is well understood if the specimen being studied is stationary during data acquisition. However, if this specimen changes its position during the measuring process, standard reconstruction techniques can lead to severe motion artefacts in the computed images. Solving a dynamic reconstruction problem therefore requires to model and incorporate suitable information on
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Robust region-based active contour models via local statistical similarity and local similarity factor for intensity inhomogeneity and high noise image segmentation Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Ibrar Hussain,Haider Ali,Muhammad Shahkar Khan,Sijie Niu,Lavdie Rada
In this paper, we design a novel variational segmentation method for two types of segmentation problems, namely, global segmentation (all objects /features in a given image are aimed to be segmented) and selective/ interactive segmentation (an objects /feature of interest in a given image is aimed to be segmented) for inhomogeneous and severe additive noisy images. The proposed segmentation models
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A Carleman estimate and an energy method for a first-order symmetric hyperbolic system Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Giuseppe Floridia,Hiroshi Takase,Masahiro Yamamoto
For a symmetric hyperbolic system of the first order, we prove a Carleman estimate under some positivity condition concerning the coefficient matrices. Next, applying the Carleman estimate, we prove an observability \begin{document}$ L^2 $\end{document}-estimate for initial values by boundary data.
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Reconstruction of singular and degenerate inclusions in Calderón's problem Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Henrik Garde,Nuutti Hyvönen
We consider the reconstruction of the support of an unknown perturbation to a known conductivity coefficient in Calderón's problem. In a previous result by the authors on monotonicity-based reconstruction, the perturbed coefficient is allowed to simultaneously take the values \begin{document}$ 0 $\end{document} and \begin{document}$ \infty $\end{document} in some parts of the domain and values bounded
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Microlocal analysis of borehole seismic data Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Raluca Felea,Romina Gaburro,Allan Greenleaf,Clifford Nolan
Borehole seismic data is obtained by receivers located in a well, with sources located on the surface or another well. Using microlocal analysis, we study possible approximate reconstruction, via linearized, filtered backprojection, of an isotropic sound speed in the subsurface for three types of data sets. The sources may form a dense array on the surface, or be located along a line on the surface
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Simultaneous uniqueness for multiple parameters identification in a fractional diffusion-wave equation Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Xiaohua Jing,Masahiro Yamamoto
We consider two kinds of inverse problems on determining multiple parameters simultaneously for one-dimensional time-fractional diffusion-wave equations with derivative order \begin{document}$ \alpha \in (0, 2) $\end{document}. Based on the analysis of the poles of Laplace transformed data and a transformation formula, we first prove the uniqueness in identifying multiple parameters, including the
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Bayesian neural network priors for edge-preserving inversion Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Chen Li,Matthew Dunlop,Georg Stadler
We consider Bayesian inverse problems wherein the unknown state is assumed to be a function with discontinuous structure a priori. A class of prior distributions based on the output of neural networks with heavy-tailed weights is introduced, motivated by existing results concerning the infinite-width limit of such networks. We show theoretically that samples from such priors have desirable discontinuous-like
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A direct imaging method for the exterior and interior inverse scattering problems Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Deyue Zhang,Yue Wu,Yinglin Wang,Yukun Guo
This paper is concerned with the inverse acoustic scattering problems by an obstacle or a cavity with a sound-soft or a sound-hard boundary. A direct imaging method relying on the boundary conditions is proposed for reconstructing the shape of the obstacle or cavity. First, the scattered fields are approximated by the Fourier-Bessel functions with the measurements on a closed curve. Then, the indicator
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Well-posedness of an inverse problem for two- and three-dimensional convective Brinkman-Forchheimer equations with the final overdetermination Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Pardeep Kumar,Manil T. Mohan
In this article, we study an inverse problem for the following convective Brinkman-Forchheimer (CBF) equations: \begin{document}$ \begin{align*} \boldsymbol{u}_t-\mu \Delta\boldsymbol{u}+(\boldsymbol{u}\cdot\nabla)\boldsymbol{u}+\alpha\boldsymbol{u}+\beta|\boldsymbol{u}|^{r-1}\boldsymbol{u}+\nabla p = \boldsymbol{F}: = \boldsymbol{f} g, \ \ \ \nabla\cdot\boldsymbol{u} = 0, \end{align*} $\end{document}
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Reconstruction of singularities in two-dimensional quasi-linear biharmonic operator Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Jaakko Kultima,Valery Serov
The inverse backscattering Born approximation for two-dimensional quasi-linear biharmonic operator is studied. We prove the precise formulae for the first nonlinear term of the Born sequence. We prove also that all other terms in this sequence are \begin{document}$ H^t- $\end{document}functions for any \begin{document}$ t<1 $\end{document}. These formulae and estimates allow us to conclude that all
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Quasiconformal model with CNN features for large deformation image registration Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Ho Law,Gary P. T. Choi,Ka Chun Lam,Lok Ming Lui
Image registration has been widely studied over the past several decades, with numerous applications in science, engineering and medicine. Most of the conventional mathematical models for large deformation image registration rely on prescribed landmarks, which usually require tedious manual labeling. In recent years, there has been a surge of interest in the use of machine learning for image registration
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A uniqueness theorem for inverse problems in quasilinear anisotropic media Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Md. Ibrahim Kholil,Ziqi Sun
We study the question of whether one can uniquely determine a scalar quasilinear conductivity in an anisotropic medium by making voltage and current measurements at the boundary. This paper is dedicated to the memory of Professor Victor Isakov, who has made enormous contribution to the theory of inverse problem.
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An iterative scheme for imaging acoustic obstacle from phaseless total-field data Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Heping Dong,Deyue Zhang,Yingwei Chi
In this paper, we consider the inverse problem of determining the location and the shape of a sound-soft or sound-hard obstacle from the modulus of the total-field collected on a measured curve for an incident point source. We propose a system of nonlinear integral equations based iterative scheme to reconstruct both the location and the shape of the obstacle. Several validating numerical examples
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Variational source conditions for inverse Robin and flux problems by partial measurements Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 De-Han Chen,Daijun Jiang,Irwin Yousept,Jun Zou
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Recovering a bounded elastic body by electromagnetic far-field measurements Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Tielei Zhu,Jiaqing Yang,Bo Zhang
This paper is concerned with the scattering of a time-harmonic electromagnetic wave by a three-dimensional elastic body. The general transmission conditions are considered to model the interaction between the electromagnetic field and the elastic body on the interface by Voigt's model. The existence of a unique solution is first proved in an appropriate Sobolev space by employing the variational method
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Inverse boundary value problems for polyharmonic operators with non-smooth coefficients Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 R.M. Brown,L.D. Gauthier
We consider inverse boundary value problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a
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A new anisotropic fourth-order diffusion equation model based on image features for image denoising Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Ying Wen,Jiebao Sun,Zhichang Guo
Image denoising has always been a challenging task. For performing this task, one of the most effective methods is based on variational PDE. Inspired by the LLT model, we first propose a new adaptive LLT model by adding a weighted function, and then we propose a class of fourth-order diffusion equations based on the new functional. Owing to the adaptive function, the new functional is better than the
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A non-iterative sampling method for inverse elastic wave scattering by rough surfaces Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Tielei Zhu,Jiaqing Yang
Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-iterative sampling method is proposed for detecting the rough surface by taking elastic field measurements on a bounded line segment above the surface, based on reconstructing a modified near-field equation associated with a special surface, which generalized our previous
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Photoacoustic tomography in attenuating media with partial data Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Benjamin Palacios
The attenuation of ultrasound waves in photoacoustic and thermoacoustic imaging presents an important drawback in the applicability of these modalities. This issue has been addressed previously in the applied and theoretical literature, and some advances have been made on the topic. In particular, stability inequalities have been proposed for the inverse problem of initial source recovery with partial
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A variational method for Abel inversion tomography with mixed Poisson-Laplace-Gaussian noise Inverse Probl. Imaging (IF 1.3) Pub Date : 2022-01-01 Linghai Kong,Suhua Wei
Abel inversion tomography plays an important role in dynamic experiments, while most known studies are started with a single Gaussian assumption. This paper proposes a mixed Poisson-Laplace-Gaussian distribution to characterize the noise in charge-coupled-device (CCD) sensed radiographic data, and develops a multi-convex optimization model to address the reconstruction problem. The proposed model is
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Ray transform on Sobolev spaces of symmetric tensor fields, I: Higher order Reshetnyak formulas Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-12-28 Venkateswaran P. Krishnan, Vladimir A. Sharafutdinov
For an integer \begin{document}$ r\ge0 $\end{document}, we prove the \begin{document}$ r^{\mathrm{th}} $\end{document} order Reshetnyak formula for the ray transform of rank \begin{document}$ m $\end{document} symmetric tensor fields on \begin{document}$ {{\mathbb R}}^n $\end{document}. Roughly speaking, for a tensor field \begin{document}$ f $\end{document}, the order \begin{document}$ r $\end{document}
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Analytical reconstruction formula with efficient implementation for a modality of Compton scattering tomography with translational geometry Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-12-28 Cécilia Tarpau, Javier Cebeiro, Geneviève Rollet, Maï K. Nguyen, Laurent Dumas
In this paper, we address an alternative formulation for the exact inverse formula of the Radon transform on circle arcs arising in a modality of Compton Scattering Tomography in translational geometry proposed by Webber and Miller (Inverse Problems (36)2, 025007, 2020). The original study proposes a first method of reconstruction, using the theory of Volterra integral equations. The numerical realization
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Euler equations and trace properties of minimizers of a functional for motion compensated inpainting Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-12-17 Riccardo March, Giuseppe Riey
We compute the Euler equations of a functional useful for simultaneous video inpainting and motion estimation, which was obtained in [17] as the relaxation of a modified version of the functional proposed in [16]. The functional is defined on vectorial functions of bounded variations, therefore we also get the Euler equations holding on the singular sets of minimizers, highlighting in particular the
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A wavelet frame constrained total generalized variation model for imaging conductivity distribution Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-12-17 Yanyan Shi, Zhiwei Tian, Meng Wang, Xiaolong Kong, Lei Li, Feng Fu
Electrical impedance tomography (EIT) is a sensing technique with which conductivity distribution can be reconstructed. It should be mentioned that the reconstruction is a highly ill-posed inverse problem. Currently, the regularization method has been an effective approach to deal with this problem. Especially, total variation regularization method is advantageous over Tikhonov method as the edge information
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A new approach to the inverse discrete transmission eigenvalue problem Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-12-17 Natalia P. Bondarenko, Vjacheslav A. Yurko
A discrete analog is considered for the inverse transmission eigenvalue problem, having applications in acoustics. We provide a well-posed inverse problem statement, develop a constructive procedure for solving this problem, prove uniqueness of solution, global solvability, local solvability, and stability. Our approach is based on the reduction of the discrete transmission eigenvalue problem to a
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The domain derivative for semilinear elliptic inverse obstacle problems Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-12-10 Frank Hettlich
We consider the recovering of the shape of a cavity from the Cauchy datum on an accessible boundary in case of semilinear boundary value problems. Existence and a characterization of the domain derivative of solutions of semilinear elliptic equations are proven. Furthermore, the result is applied to solve an inverse obstacle problem with an iterative regularization scheme. By some numerical examples
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Image fusion network for dual-modal restoration Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-10-29 Ying Zhang, Xuhua Ren, Bryan Alexander Clifford, Qian Wang, Xiaoqun Zhang
In recent years multi-modal data processing methods have gained considerable research interest as technological advancements in imaging, computing, and data storage have made the collection of redundant, multi-modal data more commonplace. In this work we present an image restoration method tailored for scenarios where pre-existing, high-quality images from different modalities or contrasts are available
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The interior inverse scattering problem for a two-layered cavity using the Bayesian method Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-11-09 Yunwen Yin, Weishi Yin, Pinchao Meng, Hongyu Liu
In this paper, the Bayesian method is proposed for the interior inverse scattering problem to reconstruct the interface of a two-layered cavity. The scattered field is measured by the point sources located on a closed curve inside the interior interface. The well-posedness of the posterior distribution in the Bayesian framework is proved. The Markov Chain Monte Carlo algorithm is employed to explore
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Automated filtering in the nonlinear Fourier domain of systematic artifacts in 2D electrical impedance tomography Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-11-02 Melody Alsaker, Benjamin Bladow, Scott E. Campbell, Emma M. Kar
For patients undergoing mechanical ventilation due to respiratory failure, 2D electrical impedance tomography (EIT) is emerging as a means to provide functional monitoring of pulmonary processes. In EIT, electrical current is applied to the body, and the internal conductivity distribution is reconstructed based on subsequent voltage measurements. However, EIT images are known to often suffer from large
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Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-11-02 Michael V. Klibanov, Thuy T. Le, Loc H. Nguyen, Anders Sullivan, Lam Nguyen
To compute the spatially distributed dielectric constant from the backscattering computationally simulated ane experimentally collected data, we study a coefficient inverse problem for a 1D hyperbolic equation. To solve this inverse problem, we establish a new version of the Carleman estimate and then employ this estimate to construct a cost functional, which is strictly convex on a convex bounded
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Nonconvex regularization for blurred images with Cauchy noise Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-11-02 Xiao Ai, Guoxi Ni, Tieyong Zeng
In this paper, we propose a nonconvex regularization model for images damaged by Cauchy noise and blur. This model is based on the method of the total variational proposed by Federica, Dong and Zeng [SIAM J. Imaging Sci.(2015)], where a variational approach for restoring blurred images with Cauchy noise is used. Here we consider the nonconvex regularization, namely a weighted difference of \begin{document}$
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Uniqueness and numerical reconstruction for inverse problems dealing with interval size search Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-10-27 Jone Apraiz, Jin Cheng, Anna Doubova, Enrique Fernández-Cara, Masahiro Yamamoto
We consider a heat equation and a wave equation in one spatial dimension. This article deals with the inverse problem of determining the size of the spatial interval from some extra boundary information on the solution. Under several different circumstances, we prove uniqueness, non-uniqueness and some size estimates. Moreover, we numerically solve the inverse problems and compute accurate approximations
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An inverse problem for a fractional diffusion equation with fractional power type nonlinearities Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-10-27 Li Li
We study the well-posedness of a semi-linear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map. Our arguments are based on a first order linearization as well as the parabolic Runge approximation property.
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On new surface-localized transmission eigenmodes Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-10-27 Youjun Deng, Yan Jiang, Hongyu Liu, Kai Zhang
Consider the transmission eigenvalue problem \begin{document}$ (\Delta+k^2\mathbf{n}^2) w = 0, \ \ (\Delta+k^2)v = 0\ \ \mbox{in}\ \ \Omega;\quad w = v, \ \ \partial_\nu w = \partial_\nu v\ \ \mbox{on} \ \partial\Omega. $\end{document} It is shown in [16] that there exists a sequence of eigenfunctions \begin{document}$ (w_m, v_m)_{m\in\mathbb{N}} $\end{document} associated with \begin{document}$ k_m\rightarrow
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Joint reconstruction and low-rank decomposition for dynamic inverse problems Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-10-27 Simon Arridge, Pascal Fernsel, Andreas Hauptmann
A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work, we consider the case, where the target can be represented by a decomposition of spatial and temporal basis functions and hence can be efficiently represented by a low-rank decomposition. We then propose a joint reconstruction and low-rank decomposition
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Generative imaging and image processing via generative encoder Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-10-27 Yong Zheng Ong, Haizhao Yang
This paper introduces a novel generative encoder (GE) framework for generative imaging and image processing tasks like image reconstruction, compression, denoising, inpainting, deblurring, and super-resolution. GE unifies the generative capacity of GANs and the stability of AEs in an optimization framework instead of stacking GANs and AEs into a single network or combining their loss functions as in
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A variational saturation-value model for image decomposition: Illumination and reflectance Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-10-27 Wei Wang, Caifei Li
In this paper, we study to decompose a color image into the illumination and reflectance components in saturation-value color space. By considering the spatial smoothness of the illumination component, the total variation regularization of the reflectance component, and the data-fitting in saturation-value color space, we develop a novel variational saturation-value model for image decomposition. The
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Counterexamples to inverse problems for the wave equation Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-10-09 Tony Liimatainen, Lauri Oksanen
We construct counterexamples to inverse problems for the wave operator on domains in $ \mathbb{R}^{n+1} $, $ n \ge 2 $, and on Lorentzian manifolds. We show that non-isometric Lorentzian metrics can lead to same partial data measurements, which are formulated in terms certain restrictions of the Dirichlet-to-Neumann map. The Lorentzian metrics giving counterexamples are time-dependent, but they are
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Weighted area constraints-based breast lesion segmentation in ultrasound image analysis Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-09-28 Qianting Ma, Tieyong Zeng, Dexing Kong, Jianwei Zhang
Breast ultrasound segmentation is a challenging task in practice due to speckle noise, low contrast and blurry boundaries. Although numerous methods have been developed to solve this problem, most of them can not produce a satisfying result due to uncertainty of the segmented region without specialized domain knowledge. In this paper, we propose a novel breast ultrasound image segmentation method that
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PCA reduced Gaussian mixture models with applications in superresolution Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-09-01 Johannes Hertrich, Dang-Phuong-Lan Nguyen, Jean-Francois Aujol, Dominique Bernard, Yannick Berthoumieu, Abdellatif Saadaldin, Gabriele Steidl
Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. The contribution of this paper to the topic is twofold. First, we propose a Gaussian mixture model in conjunction with a reduction of the dimensionality of the data in each component of the model by principal component analysis, which we call PCA-GMM. To learn
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A fuzzy edge detector driven telegraph total variation model for image despeckling Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-09-01 Sudeb Majee, Subit K. Jain, Rajendra K. Ray, Ananta K. Majee
Speckle noise suppression is a challenging and crucial pre-processing stage for higher-level image analysis. In this work, a new attempt has been made using telegraph total variation equation and fuzzy set theory for image despeckling. The intuitionistic fuzzy divergence function has been used to distinguish between edges and noise. To the best of the authors' knowledge, most of the studies on the
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An inverse source problem for the stochastic wave equation Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-09-01 Xiaoli Feng, Meixia Zhao, Peijun Li, Xu Wang
This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The inverse problem is to determine the statistical properties of the source from the expectation and covariance of the final-time data. For the direct problem, it is shown
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Small defects reconstruction in waveguides from multifrequency one-side scattering data Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-09-01 Éric Bonnetier, Angèle Niclas, Laurent Seppecher, Grégory Vial
Localization and reconstruction of small defects in acoustic or electromagnetic waveguides is of crucial interest in nondestructive evaluation of structures. The aim of this work is to present a new multi-frequency inversion method to reconstruct small defects in a 2D waveguide. Given one-side multi-frequency wave field measurements of propagating modes, we use a Born approximation to provide a $ \text{L}^2
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Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-07-16 Ru-Yu Lai, Laurel Ohm
We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown nonlinearities can be uniquely determined from exterior measurements under suitable settings.
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Fourier method for reconstructing elastic body force from the coupled-wave field Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-07-16 Xianchao Wang, Jiaqi Zhu, Minghui Song, Wei Wu
This paper is concerned with the inverse source problem of the time-harmonic elastic waves. A novel non-iterative reconstruction scheme is proposed for determining the elastic body force by using the multi-frequency Fourier expansion. The key ingredient of the approach is to choose appropriate admissible frequencies and establish an relationship between the Fourier coefficients and the coupled-wave
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Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-07-16 María Ángeles García-Ferrero, Angkana Rüland, Wiktoria Zatoń
In this article, we discuss quantitative Runge approximation properties for the acoustic Helmholtz equation and prove stability improvement results in the high frequency limit for an associated partial data inverse problem modelled on [3,35]. The results rely on quantitative unique continuation estimates in suitable function spaces with explicit frequency dependence. We contrast the frequency dependence
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A mathematical perspective on radar interferometry Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-07-07 Mikhail Gilman, Semyon Tsynkov
Radar interferometry is an advanced remote sensing technology that utilizes complex phases of two or more radar images of the same target taken at slightly different imaging conditions and/or different times. Its goal is to derive additional information about the target, such as elevation. While this kind of task requires centimeter-level accuracy, the interaction of radar signals with the target,
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Smoothing Newton method for \begin{document}$ \ell^0 $\end{document}-\begin{document}$ \ell^2 $\end{document} regularized linear inverse problem Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-07-07 Peili Li, Xiliang Lu, Yunhai Xiao
Sparse regression plays a very important role in statistics, machine learning, image and signal processing. In this paper, we consider a high-dimensional linear inverse problem with $ \ell^0 $-$ \ell^2 $ penalty to stably reconstruct the sparse signals. Based on the sufficient and necessary condition of the coordinate-wise minimizers, we design a smoothing Newton method with continuation strategy on
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Learning to scan: A deep reinforcement learning approach for personalized scanning in CT imaging Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-07-07 Ziju Shen, Yufei Wang, Dufan Wu, Xu Yang, Bin Dong
. Computed Tomography (CT) takes X-ray measurements on the subjects to reconstruct tomographic images. As X-ray is radioactive, it is desirable to control the total amount of dose of X-ray for safety concerns. Therefore, we can only select a limited number of measurement angles and assign each of them limited amount of dose. Traditional methods such as compressed sensing usually randomly select the
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Identification and stability of small-sized dislocations using a direct algorithm Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-07-07 Batoul Abdelaziz, Abdellatif El Badia, Ahmad El Hajj
This paper considers the problem of identifying dislocation lines of curvilinear form in three-dimensional materials from boundary measurements, when the areas surrounded by the dislocation lines are assumed to be small-sized. The objective of this inverse problem is to reconstruct the number, the initial position and certain characteristics of these dislocations and establish, using certain test functions
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Partial inversion of the 2D attenuated \begin{document}$ X $\end{document}-ray transform with data on an arc Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-07-07 Hiroshi Fujiwara, Kamran Sadiq, Alexandru Tamasan
In two dimensions, we consider the problem of inversion of the attenuated $ X $-ray transform of a compactly supported function from data restricted to lines leaning on a given arc. We provide a method to reconstruct the function on the convex hull of this arc. The attenuation is assumed known. The method of proof uses the Hilbert transform associated with $ A $-analytic functions in the sense of Bukhgeim
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Refined stability estimates in electrical impedance tomography with multi-layer structure Inverse Probl. Imaging (IF 1.3) Pub Date : 2021-07-07 Haigang Li, Jenn-Nan Wang, Ling Wang
In this paper we study the inverse problem of determining an electrical inclusion in a multi-layer composite from boundary measurements in 2D. We assume the conductivities in different layers are different and derive a stability estimate for the linearized map with explicit formulae on the conductivity and the thickness of each layer. Intuitively, if an inclusion is surrounded by a highly conductive