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Microwave time reversal for nondestructive testing of buried small damage in composite materials Inverse Probl. (IF 2.1) Pub Date : 2024-02-23 Kang An, Changyou Li, Guoqian Long, Jun Ding
Composite materials are widely applied in aerospace, civil engineering, and sports equipment. Various damages produced during fabrication and long-term use can destroy its original mechanical properties, which brings safety and structural healthy concerns. Microwave imaging based on time reversal (TR) is one of the most promising nondestructive testing methods for portable, low-cost, and accurate testing
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Geometric approach for determining stationary phase points in radar imaging Inverse Probl. (IF 2.1) Pub Date : 2024-02-23 Yixiang Luomei, Tiantian Yin, Kai Tan, Xudong Chen
This paper proposes a geometric approach to find out the stationary phase points in radar imaging, namely the coordinates of the transmitting and the receiving antennas that have the greatest contribution to a specified point in the wavenumber spectrum of the scattered field. The foundation of the proposed approach is that, the Green’s function can be approximated by a locally plane wave when the distance
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Adaptive anisotropic Bayesian meshing for inverse problems Inverse Probl. (IF 2.1) Pub Date : 2024-02-23 A Bocchinfuso, D Calvetti, E Somersalo
We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that errors arising from the discretization can be detrimental for ill-posed inverse problems, as discretization error behaves as correlated noise. While this problem can be avoided with
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A Bayesian approach for consistent reconstruction of inclusions Inverse Probl. (IF 2.1) Pub Date : 2024-02-23 B M Afkham, K Knudsen, A K Rasmussen, T Tarvainen
This paper considers a Bayesian approach for inclusion detection in nonlinear inverse problems using two known and popular push-forward prior distributions: the star-shaped and level set prior distributions. We analyze the convergence of the corresponding posterior distributions in a small measurement noise limit. The methodology is general; it works for priors arising from any Hölder continuous transformation
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Estimation of the Born data in inverse scattering of layered media Inverse Probl. (IF 2.1) Pub Date : 2024-02-23 Zekui Jia, Maokun Li, Fan Yang, Shenheng Xu
The first term in the Born series, as we call the Born data, is linear with the scatterers. Here we present a scheme to map the total field data to the Born data in layered media using only the single-input single-output (SISO) setup. This nonlinear mapping is based on the reduced order model (ROM) approach, which constructs ROMs of the original wave operator. Normally, the construction of ROMs requires
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Efficient kernel canonical correlation analysis using Nyström approximation Inverse Probl. (IF 2.1) Pub Date : 2024-02-23 Qin Fang, Lei Shi, Min Xu, Ding-Xuan Zhou
The main contribution of this paper is the derivation of non-asymptotic convergence rates for Nyström kernel canonical correlation analysis (CCA) in a setting of statistical learning. Our theoretical results reveal that, under certain conditions, Nyström kernel CCA can achieve a convergence rate comparable to that of the standard kernel CCA, while offering significant computational savings. This finding
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Increasing stability of a linearized inverse boundary value problem for a nonlinear Schrödinger equation on transversally anisotropic manifolds Inverse Probl. (IF 2.1) Pub Date : 2024-02-23 Shuai Lu, Jian Zhai
We consider the problem of recovering a nonlinear potential function in a nonlinear Schrödinger equation on transversally anisotropic manifolds from the linearized Dirichlet-to-Neumann map at a large wavenumber. By calibrating the complex geometric optics solutions according to the wavenumber, we prove the increasing stability of recovering the coefficient of a cubic term as the wavenumber becomes
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A deep learning enhanced inverse scattering framework for microwave imaging of piece-wise homogeneous targets Inverse Probl. (IF 2.1) Pub Date : 2024-02-21 Álvaro Yago Ruiz, Maria Nikolic Stevanovic, Marta Cavagnaro, Lorenzo Crocco
In this paper, we present a framework for the solution of inverse scattering problems that integrates traditional imaging methods and deep learning. The goal is to image piece-wise homogeneous targets and it is pursued in three steps. First, raw-data are processed via orthogonality sampling method to obtain a qualitative image of the targets. Then, such an image is fed into a U-Net. In order to take
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Imaging of nonlinear materials via the Monotonicity Principle Inverse Probl. (IF 2.1) Pub Date : 2024-02-13 Vincenzo Mottola, Antonio Corbo Esposito, Gianpaolo Piscitelli, Antonello Tamburrino
Inverse problems, which are related to Maxwell’s equations, in the presence of nonlinear materials is a quite new topic in the literature. The lack of contributions in this area can be ascribed to the significant challenges that such problems pose. Retrieving the spatial behavior of some unknown physical property, from boundary measurements, is a nonlinear and highly ill-posed problem even in the presence
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A novel epidemiologically informed particle filter for assessing epidemic phenomena. Application to the monkeypox outbreak of 2022 Inverse Probl. (IF 2.1) Pub Date : 2024-02-09 Vasileios E Papageorgiou, Pavlos Kolias
Contagious diseases are constantly affecting more and more people every day, resulting in widespread health crises especially in developing nations. Previous studies have developed deterministic and stochastic mathematical models to investigate the spread of epidemics. In the present study, a hybrid particle filtering epidemiological model is proposed, which combines the elements of a deterministic
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Multilevel dimension-independent likelihood-informed MCMC for large-scale inverse problems Inverse Probl. (IF 2.1) Pub Date : 2024-02-05 Tiangang Cui, Gianluca Detommaso, Robert Scheichl
We present a non-trivial integration of dimension-independent likelihood-informed (DILI) MCMC (Cui et al 2016) and the multilevel MCMC (Dodwell et al 2015) to explore the hierarchy of posterior distributions. This integration offers several advantages: First, DILI-MCMC employs an intrinsic likelihood-informed subspace (LIS) (Cui et al 2014)—which involves a number of forward and adjoint model simulations—to
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Fourier series-based approximation of time-varying parameters in ordinary differential equations Inverse Probl. (IF 2.1) Pub Date : 2024-02-01 Anna Fitzpatrick, Molly Folino, Andrea Arnold
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some unobservable system parameters may vary with time without known evolution models. In this work, we propose a novel approximation method inspired by the Fourier series
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V-line 2-tensor tomography in the plane Inverse Probl. (IF 2.1) Pub Date : 2024-01-31 Gaik Ambartsoumian, Rohit Kumar Mishra, Indrani Zamindar
In this article, we introduce and study various V-line transforms (VLTs) defined on symmetric 2-tensor fields in R2 . The operators of interest include the longitudinal, transverse, and mixed VLTs, their integral moments, and the star transform. With the exception of the star transform, all these operators are natural generalizations to the broken-ray trajectories of the corresponding well-studied
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On inertial iterated Tikhonov methods for solving ill-posed problems Inverse Probl. (IF 2.1) Pub Date : 2024-01-29 J C Rabelo, A Leitão, A L Madureira
In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We establish convergence for exact data, and stability and semi-convergence for noisy data. Regarding numerical experiments we consider: (i) a 2D inverse potential
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Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging Inverse Probl. (IF 2.1) Pub Date : 2024-01-25 Marzieh Eini Keleshteri, Vladimir Okhmatovski, Ian Jeffrey, Martina Teresa Bevacqua, Joe LoVetri
This study explores the potential of implementing the focusing properties of a virtual ideal Veselago lens within a standard free-space microwave imaging scenario. To achieve this, the virtual lens is introduced as an inhomogeneous numerical background for the inverse source problem. This numerical Vesealgo lens is incorporated into the incident and scattered field decomposition, resulting in a new
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Deep unfolding as iterative regularization for imaging inverse problems Inverse Probl. (IF 2.1) Pub Date : 2024-01-19 Zhuo-Xu Cui, Qingyong Zhu, Jing Cheng, Bo Zhang, Dong Liang
Deep unfolding methods have gained significant popularity in the field of inverse problems as they have driven the design of deep neural networks (DNNs) using iterative algorithms. In contrast to general DNNs, unfolding methods offer improved interpretability and performance. However, their theoretical stability or regularity in solving inverse problems remains subject to certain limitations. To address
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Regularization of the inverse Laplace transform by mollification Inverse Probl. (IF 2.1) Pub Date : 2024-01-16 Pierre Maréchal, Faouzi Triki, Walter C Simo Tao Lee
In this paper we study the inverse Laplace transform. We first derive a new global logarithmic stability estimate that shows that the inversion is severely ill-posed. Then we propose a regularization method to compute the inverse Laplace transform using the concept of mollification. Taking into account the exponential instability we derive a criterion for selection of the regularization parameter.
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Determining a parabolic system by boundary observation of its non-negative solutions with biological applications Inverse Probl. (IF 2.1) Pub Date : 2024-01-08 Hongyu Liu, Catharine W K Lo
In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions represent certain probability densities in different contexts. We innovate the successive linearisation method by further developing a high-order variation scheme which
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Numerical recovery of a time-dependent potential in subdiffusion * Inverse Probl. (IF 2.1) Pub Date : 2023-12-28 Bangti Jin, Kwancheol Shin, Zhi Zhou
In this work we investigate an inverse problem of recovering a time-dependent potential in a semilinear subdiffusion model from an integral measurement of the solution over the domain. The model involves the Djrbashian–Caputo fractional derivative in time. Theoretically, we prove a novel conditional Lipschitz stability result, and numerically, we develop an easy-to-implement fixed point iteration for
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Solution of the EEG inverse problem by random dipole sampling Inverse Probl. (IF 2.1) Pub Date : 2023-12-27 L Della Cioppa, M Tartaglione, A Pascarella, F Pitolli
Electroencephalography (EEG) source imaging aims to reconstruct brain activity maps from the neuroelectric potential difference measured on the skull. To obtain the brain activity map, we need to solve an ill-posed and ill-conditioned inverse problem that requires regularization techniques to make the solution viable. When dealing with real-time applications, dimensionality reduction techniques can
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Adaptive minimax optimality in statistical inverse problems via SOLIT—Sharp Optimal Lepskiĭ-Inspired Tuning Inverse Probl. (IF 2.1) Pub Date : 2023-12-27 Housen Li, Frank Werner
We consider statistical linear inverse problems in separable Hilbert spaces and filter-based reconstruction methods of the form fˆα=qαT∗TT∗Y , where Y is the available data, T the forward operator, qαα∈A an ordered filter, and α > 0 a regularization parameter. Whenever such a method is used in practice, α has to be appropriately chosen. Typically, the aim is to find or at least approximate the best
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Stochastic linear regularization methods: random discrepancy principle and applications Inverse Probl. (IF 2.1) Pub Date : 2023-12-27 Ye Zhang, Chuchu Chen
The a posteriori stopping rule plays a significant role in the design of efficient stochastic algorithms for various tasks in computational mathematics, such as inverse problems, optimization, and machine learning. Through the lens of classical regularization theory, this paper describes a novel analysis of Morozov’s discrepancy principle for the stochastic generalized Landweber iteration and its continuous
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Solving inverse scattering problems via reduced-order model embedding procedures Inverse Probl. (IF 2.1) Pub Date : 2023-12-22 Jörn Zimmerling, Vladimir Druskin, Murthy Guddati, Elena Cherkaev, Rob Remis
We present a reduced-order model (ROM) methodology for inverse scattering problems in which the ROMs are data-driven, i.e. they are constructed directly from data gathered by sensors. Moreover, the entries of the ROM contain localised information about the coefficients of the wave equation. We solve the inverse problem by embedding the ROM in physical space. Such an approach is also followed in the
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A Bayesian approach for CT reconstruction with defect detection for subsea pipelines Inverse Probl. (IF 2.1) Pub Date : 2023-12-22 Silja L Christensen, Nicolai A B Riis, Marcelo Pereyra, Jakob S Jørgensen
Subsea pipelines can be inspected via 2D cross-sectional x-ray computed tomography (CT). Traditional reconstruction methods produce an image of the pipe’s interior that can be post-processed for detection of possible defects. In this paper we propose a novel Bayesian CT reconstruction method with built-in defect detection. We decompose the reconstruction into a sum of two images; one containing the
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Chilled sampling for uncertainty quantification: a motivation from a meteorological inverse problem * Inverse Probl. (IF 2.1) Pub Date : 2023-12-22 P Héas, F Cérou, M Rousset
Atmospheric motion vectors (AMVs) extracted from satellite imagery are the only wind observations with good global coverage. They are important features for feeding numerical weather prediction (NWP) models. Several Bayesian models have been proposed to estimate AMVs. Although critical for correct assimilation into NWP models, very few methods provide a thorough characterization of the estimation errors
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Quantitative parameter reconstruction from optical coherence tomographic data Inverse Probl. (IF 2.1) Pub Date : 2023-12-19 Leopold Veselka, Peter Elbau, Leonidas Mindrinos, Lisa Krainz, Wolfgang Drexler
Quantitative tissue information, like the light scattering properties, is considered as a key player in the detection of cancerous cells in medical diagnosis. A promising method to obtain these data is optical coherence tomography (OCT). In this article, we will therefore discuss the refractive index reconstruction from OCT data, employing a Gaussian beam based forward model. We consider in particular
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3D tomographic phase retrieval and unwrapping Inverse Probl. (IF 2.1) Pub Date : 2023-12-14 Albert Fannjiang
This paper develops uniqueness theory for 3D phase retrieval with finite, discrete measurement data for strong phase objects and weak phase objects, including: (i) Unique determination of (phase) projections from diffraction patterns—General measurement schemes with coded and uncoded apertures are proposed and shown to ensure unique reduction of diffraction patterns to the phase projection for a strong
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Jointly determining the point sources and obstacle from Cauchy data Inverse Probl. (IF 2.1) Pub Date : 2023-12-12 Deyue Zhang, Yan Chang, Yukun Guo
A numerical method is developed for recovering both the source locations and the obstacle from the scattered Cauchy data of the time-harmonic acoustic field. First of all, the incident and scattered components are decomposed from the coupled Cauchy data by the representation of the single-layer potentials and the solution to the resulting linear integral system. As a consequence of this decomposition
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Optimal regularized hypothesis testing in statistical inverse problems Inverse Probl. (IF 2.1) Pub Date : 2023-12-11 Remo Kretschmann, Daniel Wachsmuth, Frank Werner
Testing of hypotheses is a well studied topic in mathematical statistics. Recently, this issue has also been addressed in the context of inverse problems, where the quantity of interest is not directly accessible but only after the inversion of a (potentially) ill-posed operator. In this study, we propose a regularized approach to hypothesis testing in inverse problems in the sense that the underlying
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Double-parameter regularization for solving the backward diffusion problem with parallel-in-time algorithm Inverse Probl. (IF 2.1) Pub Date : 2023-12-11 Jun-Liang Fu, Jijun Liu
We propose a double-parameter regularization scheme for dealing with the backward diffusion process. Considering the smoothing effect of Yosida approximation for PDE, we propose to regularize this ill-posed problem by modifying original governed system in terms of a pseudoparabolic equation together with a quasi-boundary condition simultaneously, which consequently contains two regularizing parameters
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Distributed parameter identification for the Navier–Stokes equations for obstacle detection Inverse Probl. (IF 2.1) Pub Date : 2023-12-11 Jorge Aguayo, Cristóbal Bertoglio, Axel Osses
We present a parameter identification problem for a scalar permeability field and the maximum velocity in an inflow, following a reference profile. We utilize a modified version of the Navier–Stokes equations, incorporating a permeability term described by the Brinkman’s Law into the momentum equation. This modification takes into account the presence of obstacles on some parts of the boundary. For
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Structured model selection via ℓ1−ℓ2 optimization Inverse Probl. (IF 2.1) Pub Date : 2023-12-11 Xiaofan Lu, Linan Zhang, Hongjin He
Automated model selection is an important application in science and engineering. In this work, we develop a learning approach for identifying structured dynamical systems from undersampled and noisy spatiotemporal data. The learning is performed by a sparse least-squares fitting over a large set of candidate functions via a nonconvex ℓ1−ℓ2 sparse optimization solved by the alternating direction method
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Inversion of generalized Radon transforms acting on 3D vector and symmetric tensor fields Inverse Probl. (IF 2.1) Pub Date : 2023-12-05 Ivan E Svetov, Anna P Polyakova
Currently, theory of the ray transforms of vector and tensor fields is well developed, but the generalized Radon transforms of such fields have not been fully studied. We consider the normal, longitudinal and mixed Radon transforms (with integration over planes) acting on three-dimensional vector and symmetric tensor fields. We prove that these operators are continuous. In case when values of all generalized
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Detection of scatterers using an XFEM-BEM level set solver based on the topological derivative Inverse Probl. (IF 2.1) Pub Date : 2023-12-01 Alfredo Canelas, Ana I Abreu, Jean R Roche
A numerical method is proposed for the solution of the inverse scattering problem. This problem consists of determining the location and shape of an unknown number of inclusions composed by a homogeneous material with known mechanical properties different that those of the surrounding medium. The information available to solve the inverse problem are measurements of the fundamental mechanical magnitude
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DRIP: deep regularizers for inverse problems Inverse Probl. (IF 2.1) Pub Date : 2023-12-01 Moshe Eliasof, Eldad Haber, Eran Treister
In this paper we consider inverse problems that are mathematically ill-posed. That is, given some (noisy) data, there is more than one solution that approximately fits the data. In recent years, deep neural techniques that find the most appropriate solution, in the sense that it contains a-priori information, were developed. However, they suffer from several shortcomings. First, most techniques cannot
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Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms * Inverse Probl. (IF 2.1) Pub Date : 2023-12-01 Wansheng Wang, Chengyu Jin, Yunqing Huang
The purpose of this study is to recover the diffuse interface width parameter for nonlinear Allen–Cahn equation by a continuous data assimilation algorithm proposed recently. We obtain the large-time error between the true solution of the Allen–Cahn equation and the data assimilated solution produced by implicit–explicit one-leg fully discrete finite element methods due to discrepancy between an approximate
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A direct sampling-based deep learning approach for inverse medium scattering problems Inverse Probl. (IF 2.1) Pub Date : 2023-11-28 Jianfeng Ning, Fuqun Han, Jun Zou
In this work, we focus on the inverse medium scattering problem (IMSP), which aims to recover unknown scatterers based on measured scattered data. Motivated by the efficient direct sampling method (DSM) introduced in Ito et al (2012 Inverse Problems 28 025003), we propose a novel direct sampling-based deep learning approach (DSM-DL) for reconstructing inhomogeneous scatterers. In particular, we use
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The MLE is a reliable source: sharp performance guarantees for localization problems Inverse Probl. (IF 2.1) Pub Date : 2023-11-28 Nathanaël Munier, Emmanuel Soubies, Pierre Weiss
Single source localization from low-pass filtered measurements is ubiquitous in optics, wireless communications and sound processing. We analyze the performance of the maximum likelihood estimator (MLE) in this context with additive white Gaussian noise. We derive necessary conditions and sufficient conditions on the maximum admissible noise level to reach a given precision with high probability. The
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An image inpainting algorithm using exemplar matching and low-rank sparse prior Inverse Probl. (IF 2.1) Pub Date : 2023-11-27 Qiangwei Peng, Wen Huang
Image inpainting is a challenging problem with a wide range of applications such as object removal and old photo restoration. The methods based on low-rank sparse prior have been used for regular or nearly regular texture inpainting. However, since such inpainting results do not synthesize the original pixels, they are usually not sharp especially when the area to be recovered is large. One remedy
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3D refractive index reconstruction from phaseless coherent optical microscopy data using multiple scattering-based inverse solvers—a study Inverse Probl. (IF 2.1) Pub Date : 2023-11-27 Yingying Qin, Ankit Butola, Krishna Agarwal
Reconstructing 3D refractive index profile of scatterers using optical microscopy measurements presents several challenges over the conventional microwave and RF domain measurement scenario. These include phaseless and polarization-insensitive measurements, small numerical aperture, as well as a Green’s function where spatial frequencies are integrated in a weighted manner such that far-field angular
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Bilevel optimal parameter learning for a high-order nonlocal multiframe super-resolution problem Inverse Probl. (IF 2.1) Pub Date : 2023-11-27 Amine Laghrib, Fatim Zahra Ait Bella, Mourad Nachaoui, François Jauberteau
This work elaborated an improved method to multiframe super-resolution (SR), which involves a nonlocal first-order regularization combined with a nonlocal p-Laplacian term. The nonlocal TV term excels at edge preserving, whilst the nonlocal p-Laplacian is commonly used to perfectly reconstruct image textures. Firstly, we discuss the existence and uniqueness of a solution to our new model in a well
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The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition Inverse Probl. (IF 2.1) Pub Date : 2023-11-27 Leonie Fink, Frank Hettlich
In this paper an inverse obstacle scattering problem for the Helmholtz equation with nonlinear impedance boundary condition is considered. For a certain class of nonlinearities, well-posedness of the direct scattering problem is proven. Furthermore, differentiability of solutions with respect to the boundary is shown by the variational method. A characterization of the derivative allows for iterative
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Reply to Comment on ‘Revisiting the probe and enclosure methods’ Inverse Probl. (IF 2.1) Pub Date : 2023-11-17 Masaru Ikehata
What should you do when you re-read the paper you intended to cite and found an error in the proof? In section 4 of Ikehata (2022 Inverse Problems 38 075009) the author pointed out that the proof of lemma 3.5 in Sini and Yoshida (2012 Inverse Problems 28 055013; 2013 Inverse Problems 29 039501) does not work for a Lipschitz obstacle case, by applying their approach to an essentially same lemma (lemma
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Support condition identification of wind turbines based on a statistical time-domain damping parameter Inverse Probl. (IF 2.1) Pub Date : 2023-11-17 Yasen Liu, Jun Liang, Ying Wang
Owing to the harsh environment, the support conditions of wind turbines inevitably degrade/change over their lifetime, however, the evolution mechanism is not yet well understood. Although the damping parameters are sensitive to structural support and connection conditions, they are difficult to measure and quantify, which is a challenging inverse problem. This study aims to develop an approach to
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Comment on ‘Revisiting the probe and enclosure methods’ Inverse Probl. (IF 2.1) Pub Date : 2023-11-17 Mourad Sini
In the recent manuscript (Ikehata 2022 Inverse Problems 38 075009), the author made some comments on our previous work (Sini and Yoshida 2012 Inverse Problems 28 055013) saying that few arguments in the proof of lemma 3.5 might be incomplete for C0,1 -regular domains. In this note, we reply to his comments by showing that, for C 1-regular domains, those arguments are correct.
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Bayesian design of measurements for magnetorelaxometry imaging * Inverse Probl. (IF 2.1) Pub Date : 2023-11-17 T Helin, N Hyvönen, J Maaninen, J-P Puska
The aim of magnetorelaxometry imaging is to determine the distribution of magnetic nanoparticles inside a subject by measuring the relaxation of the superposition magnetic field generated by the nanoparticles after they have first been aligned using an external activation magnetic field that has subsequently been switched off. This work applies techniques of Bayesian optimal experimental design to
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Linearly convergent adjoint free solution of least squares problems by random descent Inverse Probl. (IF 2.1) Pub Date : 2023-11-16 Dirk A Lorenz, Felix Schneppe, Lionel Tondji
We consider the problem of solving linear least squares problems in a framework where only evaluations of the linear map are possible. We derive randomized methods that do not need any other matrix operations than forward evaluations, especially no evaluation of the adjoint map is needed. Our method is motivated by the simple observation that one can get an unbiased estimate of the application of the
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Invertible residual networks in the context of regularization theory for linear inverse problems Inverse Probl. (IF 2.1) Pub Date : 2023-11-13 Clemens Arndt, Alexander Denker, Sören Dittmer, Nick Heilenkötter, Meira Iske, Tobias Kluth, Peter Maass, Judith Nickel
Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step procedure. First, one trains the often neural network-based reconstruction scheme via a dataset. Second, one applies the scheme to new measurements to obtain reconstructions. We follow these steps but parameterize the reconstruction
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Optimal design of strain sensor placement for distributed static load determination Inverse Probl. (IF 2.1) Pub Date : 2023-11-13 Benjamin K Morris, R Benjamin Davis
In many applications it is desirable to inverse-calculate the distributed loading on a structure using a limited number of sensors. Yet, the calculated loads can be extremely sensitive to the placement of these sensors. In the case of predicting point loading applied at a known location, best results are typically achieved when one sensor is collocated with the force. However, the extension of this
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Multipoint formulas in inverse problems and their numerical implementation Inverse Probl. (IF 2.1) Pub Date : 2023-11-08 Roman G Novikov, Vladimir N Sivkin, Grigory V Sabinin
We present the first numerical study of multipoint formulas for finding leading coefficients in asymptotic expansions arising in potential and scattering theories. In particular, we implement different formulas for finding the Fourier transform of potential from the scattering amplitude at several high energies. We show that the aforementioned approach can be used for essential numerical improvements
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Relaxation approach for learning neural network regularizers for a class of identification problems Inverse Probl. (IF 2.1) Pub Date : 2023-11-07 Sébastien Court
The present paper deals with the data-driven design of regularizers in the form of artificial neural networks, for solving certain inverse problems formulated as optimal control problems. These regularizers aim at improving accuracy, wellposedness or compensating uncertainties for a given class of optimal control problems (inner-problems). Parameterized as neural networks, their weights are chosen
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Component-wise iterative ensemble Kalman inversion for static Bayesian models with unknown measurement error covariance Inverse Probl. (IF 2.1) Pub Date : 2023-11-07 Imke Botha, Matthew P Adams, David Frazier, Dang Khuong Tran, Frederick R Bennett, Christopher Drovandi
The ensemble Kalman filter (EnKF) is a Monte Carlo approximation of the Kalman filter for high dimensional linear Gaussian state space models. EnKF methods have also been developed for parameter inference of static Bayesian models with a Gaussian likelihood, in a way that is analogous to likelihood tempering sequential Monte Carlo (SMC). These methods are commonly referred to as ensemble Kalman inversion
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Multiscale hierarchical decomposition methods for ill-posed problems Inverse Probl. (IF 2.1) Pub Date : 2023-11-07 Stefan Kindermann, Elena Resmerita, Tobias Wolf
The multiscale hierarchical decomposition method (MHDM) was introduced in Tadmor et al (2004 Multiscale Model. Simul. 2 554–79; 2008 Commun. Math. Sci. 6 281–307) as an iterative method for total variation (TV) regularization, with the aim of recovering details at various scales from images corrupted by additive or multiplicative noise. Given its success beyond image restoration, we extend the MHDM
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Born and inverse Born series for scattering problems with Kerr nonlinearities Inverse Probl. (IF 2.1) Pub Date : 2023-11-07 Nicholas DeFilippis, Shari Moskow, John C Schotland
We consider the Born and inverse Born series for scalar waves with a cubic nonlinearity of Kerr type. We find a recursive formula for the operators in the Born series and prove their boundedness. This result gives conditions which guarantee convergence of the Born series, and subsequently yields conditions which guarantee convergence of the inverse Born series. We also use fixed point theory to give
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Strong maximum a posteriori estimation in Banach spaces with Gaussian priors Inverse Probl. (IF 2.1) Pub Date : 2023-11-07 Hefin Lambley
This article shows that a large class of posterior measures that are absolutely continuous with respect to a Gaussian prior have strong maximum a posteriori estimators in the sense of Dashti et al (2013 Inverse Problems 29 095017). This result holds in any separable Banach space and applies in particular to nonparametric Bayesian inverse problems with additive noise. When applied to Bayesian inverse
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Determining the viscosity of the Navier–Stokes equations from observations of finitely many modes Inverse Probl. (IF 2.1) Pub Date : 2023-11-07 Animikh Biswas, Joshua Hudson
In this work, we ask and answer the question: when is the viscosity of a fluid uniquely determined from spatially sparse measurements of its velocity field? We pose the question mathematically as an optimization problem using the determining map (the mapping of data to an approximation made via a nudging algorithm) to define a loss functional, the minimization of which solves the inverse problem of
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Stability estimates for an inverse problem for Schrödinger operators at high frequencies from arbitrary partial boundary measurements Inverse Probl. (IF 2.1) Pub Date : 2023-11-03 Xiaomeng Zhao, Ganghua Yuan
In this paper, we study the partial data inverse boundary value problem for the Schrödinger operator at a high frequency k⩾1 in a bounded domain with smooth boundary in Rn , n⩾3 . Assuming that the potential is known in a neighborhood of the boundary, we obtain the logarithmic stability when both Dirichlet data and Neumann data are taken on arbitrary open subsets of the boundary where the two sets
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Stability estimates for the expected utility in Bayesian optimal experimental design Inverse Probl. (IF 2.1) Pub Date : 2023-11-02 Duc-Lam Duong, Tapio Helin, Jose Rodrigo Rojo-Garcia
We study stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in a non-parametric setting and prove a convergence rate of the expected utility with respect to a likelihood perturbation. This rate is uniform over the design space and its sharpness in the general setting is demonstrated by proving a lower bound in a special
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Adaptive Spectral Inversion for inverse medium problems Inverse Probl. (IF 2.1) Pub Date : 2023-10-31 Yannik G Gleichmann, Marcus J Grote
A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown control variables resulting from standard grid-based representations, the misfit is instead minimized in a small subspace spanned by the first few eigenfunctions of a judicious elliptic operator, which itself depends on the previous
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Phase recovery from phaseless scattering data for discrete Schrödinger operators Inverse Probl. (IF 2.1) Pub Date : 2023-10-30 Roman Novikov, Basant Lal Sharma
We consider scattering for the discrete Schrödinger operator on the square lattice Zd , d⩾1 , with compactly supported potential. We give formulas for finding the phased scattering amplitude from phaseless near-field scattering data.