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Modified linear sampling method for inverse scattering by a partially coated dielectric J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2024-01-31 Jianli Xiang, Guozheng Yan
Consider time-harmonic electromagnetic wave scattering by an infinitely long, cylindrical, orthotropic dielectric partially coated with a very thin layer of a highly conductive material, which can be modeled by a transmission problem with mixed boundary conditions. Having established the well-posedness of the direct and interior transmission problem by the variational method under certain conditions
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Determination of the time-dependent effective ion collision frequency from an integral observation J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2024-01-31 Kai Cao, Daniel Lesnic
Identification of physical properties of materials is very important because they are in general unknown. Furthermore, their direct experimental measurement could be costly and inaccurate. In such a situation, a cheap and efficient alternative is to mathematically formulate an inverse, but difficult, problem that can be solved, in general, numerically; the challenge being that the problem is, in general
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On the mean field games system with lateral Cauchy data via Carleman estimates J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2024-01-31 Michael V. Klibanov, Jingzhi Li, Hongyu Liu
The second-order mean field games system (MFGS) in a bounded domain with the lateral Cauchy data are considered. This means that both Dirichlet and Neumann boundary data for the solution of the MFGS are given. Two Hölder stability estimates for two slightly different cases are derived. These estimates indicate how stable the solution of the MFGS is with respect to the possible noise in the lateral
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The high-order estimate of the entire function associated with inverse Sturm–Liouville problems J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2024-01-30 Zhaoying Wei, Guangsheng Wei, Yan Wang
The inverse Sturm–Liouville problem with smooth potentials is considered. The high-order estimate of the entire function associated with two Sturm–Liouville problems is established. Applying this estimate expression to inverse Sturm–Liouville problems, we proved that the conclusion in [L. Amour, J. Faupin and T. Raoux, Inverse spectral results for Schrödinger operators on the unit interval with partial
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CT image restoration method via total variation and L 0 smoothing filter J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2024-01-30 Hai Yin, Xianyun Li, Zhi Liu, Wei Peng, Chengxiang Wang, Wei Yu
In X-ray CT imaging, there are some cases where the obtained CT images have serious ring artifacts and noise, and these degraded CT images seriously affect the quality of clinical diagnosis. Thus, developing an effective method that can simultaneously suppress ring artifacts and noise is of great importance. Total variation (TV) is a famous prior regularization for image denoising in the image processing
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Inverting mechanical and variable-order parameters of the Euler–Bernoulli beam on viscoelastic foundation J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2024-01-30 Jin Cheng, Zhiwei Yang, Xiangcheng Zheng
We propose an inverse problem of determining the mechanical and variable-order parameters of the Euler–Bernoulli beam on viscoelastic foundation. For this goal, we develop a fully-discrete Hermite finite element scheme for this model and analyze the corresponding error estimates. The Levenberg–Marquardt method is then applied to determine the multiple parameters. Extensive numerical experiments are
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Acquiring elastic properties of thin composite structure from vibrational testing data J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2024-01-15 Vitalii Aksenov, Alexey Vasyukov, Katerina Beklemysheva
The paper is devoted to a problem of acquiring elastic properties of a composite material from the vibration testing data with a simplified experimental acquisition scheme. The specimen is considered to abide by the linear elasticity laws and subject to viscoelastic damping. The boundary value problem for transverse movement of such a specimen in the frequency domain is formulated and solved with finite-element
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Inverse problem for Sturm–Liouville operator with complex-valued weight and eigenparameter dependent boundary conditions J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2024-01-11 Gaofeng Du, Chenghua Gao
This paper is concerned with discontinuous inverse problem generated by complex-valued weight Sturm–Liouville differential operator with λ-dependent boundary conditions. We establish some properties of spectral characteristic and prove that the potential on the whole interval can be uniquely determined by the Weyl-type function or two spectra.
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Right and left inverse scattering problems formulations for the Zakharov–Shabat system J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2024-01-10 Alexander E. Chernyavsky, Leonid L. Frumin, Andrey A. Gelash
We consider right and left formulations of the inverse scattering problem for the Zakharov–Shabat system and the corresponding integral Gelfand–Levitan–Marchenko equations. Both formulations are helpful for numerical solving of the inverse scattering problem, which we perform using the previously developed Toeplitz Inner Bordering (TIB) algorithm. First, we establish general relations between the right
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A discretizing Tikhonov regularization method via modified parameter choice rules J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2024-01-05 Rong Zhang, Feiping Xie, Xingjun Luo
In this paper, we propose two parameter choice rules for the discretizing Tikhonov regularization via multiscale Galerkin projection for solving linear ill-posed integral equations. In contrast to previous theoretical analyses, we introduce a new concept called the projection noise level to obtain error estimates for the approximate solutions. This concept allows us to assess how noise levels change
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A comparative study of variational autoencoders, normalizing flows, and score-based diffusion models for electrical impedance tomography J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2024-01-01 Huihui Wang, Guixian Xu, Qingping Zhou
Electrical Impedance Tomography (EIT) is a widely employed imaging technique in industrial inspection, geophysical prospecting, and medical imaging. However, the inherent nonlinearity and ill-posedness of EIT image reconstruction present challenges for classical regularization techniques, such as the critical selection of regularization terms and the lack of prior knowledge. Deep generative models
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Analytical solution of Stefan-type problems J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2024-01-01 Samat A. Kassabek, Targyn A. Nauryz, Amankeldy Toleukhanov
In this paper, free surface problems of Stefan type for the parabolic heat equation are considered. The analytical solutions of the problems are based on the method of heat polynomials and integral error function in the form of series. Convergence of the series solution is considered and proved. Both one-and two-phase Stefan-type problems are investigated. Numerical results for one-phase inverse Stefan
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Generalized Abel equations and applications to translation invariant Radon transforms J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-11-29 James W. Webber
Generalized Abel equations have been employed in the recent literature to invert Radon transforms which arise in a number of important imaging applications, including Compton Scatter Tomography (CST), Ultrasound Reflection Tomography (URT), and X-ray CT. In this paper, we present novel injectivity results and inversion methods for generalized Abel operators. We apply our theory to a new Radon transform
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Determination of unknown shear force in transverse dynamic force microscopy from measured final data J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-11-20 Onur Baysal, Alemdar Hasanov, Sakthivel Kumarasamy
In this paper, we present a new methodology, based on the inverse problem approach, for the determination of an unknown shear force acting on the inaccessible tip of the microcantilever, which is a key component of transverse dynamic force microscopy (TDFM). The mathematical modelling of this phenomenon leads to the inverse problem of determining the shear force g ( t ) {g(t)} acting on the inaccessible
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A layer potential approach to inverse problems in brain imaging J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-11-10 Paul Asensio, Jean-Michel Badier, Juliette Leblond, Jean-Paul Marmorat, Masimba Nemaire
We study the inverse source localisation problem using the electric potential measured point-wise inside the head with stereo-ElectroEncephaloGraphy (sEEG), the electric potential measured point-wise on the scalp with ElectroEncephaloGraphy (EEG) or the magnetic flux density measured point-wise outside the head with MagnetoEncephaloGraphy (MEG). We present a method that works on a wide range of models
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Complex turbulent exchange coefficient in Akerblom–Ekman model J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-11-02 Philipp L. Bykov, Vladimir A. Gordin
The turbulent exchange in boundary layer models is usually characterized by a scalar eddy viscosity coefficient assumed to be a positive function of the vertical variable. We introduce a more general form for the turbulence exchange description, which includes two functions that describe the turbulence without any assumption about their positivity. We construct a model of the Akerblom–Ekman type, but
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Simplified REGINN-IT method in Banach spaces for nonlinear ill-posed operator equations J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-10-27 Pallavi Mahale, Farheen M. Shaikh
In 2021, Z. Fu, Y. Chen and B. Han introduced an inexact Newton regularization (REGINN-IT) using an idea involving the non-stationary iterated Tikhonov regularization scheme for solving nonlinear ill-posed operator equations. In this paper, we suggest a simplified version of the REGINN-IT scheme by using the Bregman distance, duality mapping and a suitable parameter choice strategy to produce an approximate
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Inverse nodal problem for singular Sturm–Liouville operator on a star graph J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-10-26 Rauf Amirov, Merve Arslantaş, Sevim Durak
In this study, singular Sturm–Liouville operators on a star graph with edges are investigated. First, the behavior of sufficiently large eigenvalues is learned. Then the solution of the inverse problem is given to determine the potential functions and parameters of the boundary condition on the star graph with the help of a dense set of nodal points. Lastly, a constructive solution to the inverse problems
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Extract the information via multiple repeated observations under randomly distributed noise J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-10-26 Min Zhong, Xinyan Li, Xiaoman Liu
Extracting the useful information has been used almost everywhere in many fields of mathematics and applied mathematics. It is a classical ill-posed problem due to the unstable dependence of approximations on small perturbation of the data. The traditional regularization methods depend on the choice of the regularization parameter, which are closely related to an available accurate upper bound of noise
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Direct numerical algorithm for calculating the heat flux at an inaccessible boundary J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-10-26 Sergey B. Sorokin
A fast numerical algorithm for solving the Cauchy problem for elliptic equations with variable coefficients in standard calculation domains (rectangles, circles, or rings) is proposed. The algorithm is designed to calculate the heat flux at the inaccessible boundary. It is based on the separation of variables method. This approach employs a finite difference approximation and allows obtaining a solution
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Fast iterative regularization by reusing data J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-10-26 Cristian Vega, Cesare Molinari, Lorenzo Rosasco, Silvia Villa
Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to select a meaningful solution is to introduce a regularizer. While for most applications the regularizer is convex, in many cases it is neither smooth nor strongly convex. In this paper, we propose and study two new iterative regularization methods, based on
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On the uniqueness theorems for transmission problems related to models of elasticity, diffusion and electrocardiography J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-10-26 Alexander Shlapunov, Yulia Shefer
We consider a generalization of the inverse problem of the electrocardiography in the framework of the theory of elliptic and parabolic differential operators. More precisely, starting with the standard bidomain mathematical model related to the problem of the reconstruction of the transmembrane potential in the myocardium from known body surface potentials, we formulate a more general transmission
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On the X-ray transform of planar symmetric tensors J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-10-03 David Omogbhe, Kamran Sadiq
In this article we characterize the range of the attenuated and non-attenuated X-ray transform of compactly supported symmetric tensor fields in the Euclidean plane. The characterization is in terms of a Hilbert-transform associated with A-analytic maps in the sense of Bukhgeim.
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Correctness and regularization of stochastic problems J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-10-03 Irina V. Melnikova, Vadim A. Bovkun
The paper is devoted to the regularization of ill-posed stochastic Cauchy problems in Hilbert spaces: (0.1) d u ( t ) = A u ( t ) d t + B d W ( t ) , t > 0 , u ( 0 ) = ξ . du(t)=Au(t)dt+BdW(t),\quad t>0,\qquad u(0)=\xi. The need for regularization is connected with the fact that in the general case the operator A is not supposed to generate a strongly continuous semigroup and with
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A note on the degree of ill-posedness for mixed differentiation on the d-dimensional unit cube J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-10-03 Bernd Hofmann, Hans-Jürgen Fischer
Numerical differentiation of a function over the unit interval of the real axis, which is contaminated with noise, by inverting the simple integration operator J mapping in L 2 {L^{2}} is discussed extensively in the literature. The complete singular system of the compact operator J is explicitly given with singular values σ n ( J ) {\sigma_{n}(J)} asymptotically proportional to 1 n {\frac{1}{n}}
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A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-10-03 Dmitrii Sergeevich Anikonov, Sergey G. Kazantsev, Dina S. Konovalova
We study the problem of the integral geometry, in which the functions are integrated over hyperplanes in the n-dimensional Euclidean space, n = 2 m + 1 {n=2m+1} . The integrand is the product of a function of n variables called the density and weight function depending on 2 n {2n} variables. Such an integration is called here the weighted Radon transform, which coincides with the classical one
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Simultaneous inversion for a fractional order and a time source term in a time-fractional diffusion-wave equation J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-09-20 Kaifang Liao, Lei Zhang, Ting Wei
In this article, we consider an inverse problem for determining simultaneously a fractional order and a time-dependent source term in a multi-dimensional time-fractional diffusion-wave equation by a nonlocal condition. Based on a uniformly bounded estimate of the Mittag-Leffler function given in this paper, we prove the uniqueness of the inverse problem and the Lipschitz continuity properties for the
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An extrapolation method for improving the quality of tomographic images using multiple short-pulse irradiations J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-09-20 Ivan P. Yarovenko, Igor V. Prokhorov
This paper investigates the inverse problem for the non-stationary radiation transfer equation, which involves finding the attenuation coefficient using the data of serial irradiation of the medium with pulses of various durations. In the framework of single and double scattering approximations, we obtain asymptotic estimates of the scattered radiation flux density for a short duration of the probing
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Inverse problem for Dirac operators with two constant delays J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-08-24 Biljana Vojvodić, Vladimir Vladičić, Nebojša Djurić
We study inverse spectral problems for Dirac-type functional-differential operators with two constant delays greater than two fifths the length of the interval, under Dirichlet boundary conditions. The inverse problem of recovering operators from four spectra has been studied. We consider cases when delays are greater or less than half the length of the interval. The main result of the paper refers
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Tensor tomography of the residual stress field in graded-index YAG’s single crystals J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-08-24 Alfred Puro, Egor Marin
This work presents an application of tensor field tomography for non-destructive reconstructions of axially symmetric residual stresses in a graded-index YAG single crystal for the case of beam deflection. The axis of the cylinder coincides with the crystallographic axis [001] of the single crystal and it has an axially symmetric refractive index distribution. The transformation of the polarization
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Weighted sparsity regularization for source identification for elliptic PDEs J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-08-22 Ole Løseth Elvetun, Bjørn Fredrik Nielsen
This investigation is motivated by PDE-constrained optimization problems arising in connection with electrocardiograms (ECGs) and electroencephalography (EEG). Standard sparsity regularization does not necessarily produce adequate results for these applications because only boundary data/observations are available for the identification of the unknown source, which may be interior. We therefore study
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Inverse vector problem of diffraction by inhomogeneous body with a piecewise smooth permittivity J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-08-22 Mikhail Y. Medvedik, Yury G. Smirnov, Aleksei A. Tsupak
The vector problem of reconstruction of an unknown permittivity of an inhomogeneous body is considered. The original problem for Maxwell’s equations with an unknown permittivity and a given permeability is reduced to the system of integro-differential equations. The solution to the inverse problem is obtained in two steps. First, a solution to the vector integro-differential equation of the first kind
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Hölder stability estimates in determining the time-dependent coefficients of the heat equation from the Cauchy data set J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-07-31 Imen Rassas
In this paper, we address stability results in determining the time-dependent scalar and vector potentials appearing in the convection-diffusion equation from the knowledge of the Cauchy data set. We prove Hölder-type stability estimates. The key tool used in this work is the geometric optics solution.
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Regularization of backward parabolic equations in Banach spaces by generalized Sobolev equations J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-07-27 Nguyen Van Duc, Dinh Nho Hào, Maxim Shishlenin
Let X be a Banach space with norm ∥ ⋅ ∥ {\|\cdot\|} . Let A : D ( A ) ⊂ X → X {A:D(A)\subset X\rightarrow X} be an (possibly unbounded) operator that generates a uniformly bounded holomorphic semigroup. Suppose that ε > 0 {\varepsilon>0} and T > 0 {T>0} are two given constants. The backward parabolic equation of finding a function u : [ 0 , T ] → X {u:[0,T]\rightarrow X} satisfying u t + A u =
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Inverse scattering problem for nonstrict hyperbolic system on the half-axis with a nonzero boundary condition J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-07-26 Mansur I. Ismailov, Tynysbek S. Kal’menov
The paper considers the scattering problem for the first-order system of hyperbolic equations on the half-axis with a nonhomogeneous boundary condition. This problem models the phnomennon of wave propagation in a nonstationary medium where an incoming wave unaffected by a potential field. The scattering operator on the half-axis with a nonzero boundary condition is defined and the uniqueness of the
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Reverse time migration for imaging periodic obstacles with electromagnetic plane wave J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-07-24 Lide Cai, Junqing Chen
We propose novel reverse time migration (RTM) methods for the imaging of periodic obstacles using only measurements from the lower or upper side of the obstacle arrays at a fixed frequency. We analyze the resolution of the lower side and upper side RTM methods in terms of propagating modes of the Rayleigh expansion, Helmholtz–Kirchhoff equation and the distance of the measurement surface to the obstacle
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A projected gradient method for nonlinear inverse problems with 𝛼ℓ1 − 𝛽ℓ2 sparsity regularization J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-07-24 Zhuguang Zhao, Liang Ding
The non-convex α ∥ ⋅ ∥ ℓ 1 − β ∥ ⋅ ∥ ℓ 2 \alpha\lVert\,{\cdot}\,\rVert_{\ell_{1}}-\beta\lVert\,{\cdot}\,\rVert_{\ell_{2}} ( α ≥ β ≥ 0 \alpha\geq\beta\geq 0 ) regularization is a new approach for sparse recovery. A minimizer of the α ∥ ⋅ ∥ ℓ 1 − β ∥ ⋅ ∥ ℓ 2 \alpha\lVert\,{\cdot}\,\rVert_{\ell_{1}}-\beta\lVert\,{\cdot}\,\rVert_{\ell_{2}} regularized function can be computed by applying the ST-(
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On the uniqueness of solutions in inverse problems for Burgers’ equation under a transverse diffusion J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-06-28 Andrey Baev
We consider the inverse problems of restoring initial data and a source term depending on spatial variables and time in boundary value problems for the two-dimensional Burgers equation under a transverse diffusion in a rectangular and on a half-strip, like the Hopf–Cole transformation is applied to reduce Burgers’ equation to the heat equation with respect to the function that can be measured to obtain
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The problem of determining multiple coefficients in an ultrahyperbolic equation J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-06-26 Fikret Gölgeleyen
In this article, we discuss an inverse problem of determining unknown coefficients of the first-order derivatives in an ultrahyperbolic equation. By a finite set of measurements, we prove the uniqueness of solution of the problem in semi-geodesic coordinates under some conditions on the principal coefficients of the equation. Our main tool is a Carleman estimate.
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A new regularization for time-fractional backward heat conduction problem J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-06-26 M. Thamban Nair, P. Danumjaya
It is well known that the backward heat conduction problem of recovering the temperature u ( ⋅ , t ) {u(\,\cdot\,,t)} at a time t ≥ 0 {t\geq 0} from the knowledge of the temperature at a later time, namely g := u ( ⋅ , τ ) {g:=u(\,\cdot\,,\tau)} for τ > t {\tau>t} , is ill-posed, in the sense that small error in g can lead to large deviation in u ( ⋅ , t ) {u(\,\cdot\,,t)} . However, in the case
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Convergence analysis of Inexact Newton–Landweber iteration with frozen derivative in Banach spaces J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-06-26 Gaurav Mittal, Ankik Kumar Giri
In this paper, we study the convergence analysis of the inexact Newton–Landweber iteration method (INLIM) with frozen derivative in Hilbert as well as Banach spaces. To study the convergence analysis, we incorporate the Hölder stability of the inverse mapping and Lipschitz continuity of the Fréchet derivative of the forward mapping. Moreover, we derive the convergence rates of INLIM in Hilbert as well
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Rough surfaces reconstruction via phase and phaseless data by a multi-frequency homotopy iteration method J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-06-26 Shuqin Liu, Lei Zhang
This paper is concerned with the inverse scattering of the rough surfaces with multi-frequency phase and phaseless measurements. We present a high-order recursive iteration method based on the homotopy iteration technique to reconstruct the rough surfaces. The convergence for the multi-frequency homotopy iteration method is obtained under some conditions. Some numerical experiments show the effectiveness
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Stability properties for a class of inverse problems J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-06-13 Darko Volkov
We establish Lipschitz stability properties for a class of inverse problems. In that class, the associated direct problem is formulated by an integral operator A m \mathcal{A}_{m} depending nonlinearly on a parameter 𝑚 and operating on a function 𝑢. In the inversion step, both 𝑢 and 𝑚 are unknown, but we are only interested in recovering 𝑚. We discuss examples of such inverse problems for the
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On an inverse problem for a linearized system of Navier–Stokes equations with a final overdetermination condition J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-05-31 Muvasharkhan T. Jenaliyev, Maktagali A. Bektemesov, Madi G. Yergaliyev
The theory of inverse problems is an actively studied area of modern differential equation theory. This paper studies the solvability of the inverse problem for a linearized system of Navier–Stokes equations in a cylindrical domain with a final overdetermination condition. Our approach is to reduce the inverse problem to a direct problem for a loaded equation. In contrast to the well-known works in
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On the recovery of internal source for an elliptic system by neural network approximation J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-05-31 Hui Zhang, Jijun Liu
Consider a source detection problem for a diffusion system at its stationary status, which is stated as the inverse source problem for an elliptic equation from the measurement of the solution specified only in part of the domain. For this linear ill-posed problem, we propose to reconstruct the interior source applying neural network algorithm, which projects the problem into a finite-dimensional space
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Regularization operators versus regularization strategies J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-05-31 Thi-An Nguyen, Chun-Kong Law
In this note, we shall compare two important concepts of “regularization operators” and “regularization strategies” that appear in different classical monographs. The definition of a regularization operator is related to the Moore–Penrose inverse of the operator. In general, a regularization operator is a regularization strategy. We shall show that the converse is also true under some conditions. It
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The game model with multi-task for image denoising and edge extraction J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-05-31 Wenyang Wei, Xiangchu Feng, Bingzhe Wei
Image denoising and edge extraction are two main tasks in image processing. In this paper, a game model is proposed to solve the image denoising and edge extraction, which combines an adaptive improved total variation (AdITV) model for image denoising and a global sparse gradient (GSG) model for edge extraction. The AdITV model is a forward-and-backward diffusion model. In fact, forward diffusion is
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On the identification of Lamé parameters in linear isotropic elasticity via a weighted self-guided TV-regularization method J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-05-31 Vanessa Markaki, Drosos Kourounis, Antonios Charalambopoulos
Recently in [V. Markaki, D. Kourounis and A. Charalambopoulos, A dual self-monitored reconstruction scheme on the TV \mathrm{TV} -regularized inverse conductivity problem, IMA J. Appl. Math. 86 2021, 3, 604–630], a novel reconstruction scheme has been developed for the solution of the inclusion problem in the inverse conductivity problem on the basis of a weighted self-guided regularization process
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The mean field games system: Carleman estimates, Lipschitz stability and uniqueness J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-05-02 Michael V. Klibanov
An overdetermination is introduced in an initial condition for the second order mean field games system (MFGS). This makes the resulting problem close to the classical ill-posed Cauchy problems for PDEs. Indeed, in such a problem an overdetermination in boundary conditions usually takes place. A Lipschitz stability estimate is obtained. This estimate implies uniqueness. A new Carleman estimate is derived
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The inverse scattering problem for an inhomogeneous two-layered cavity J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-05-02 Jianguo Ye, Guozheng Yan
In this paper, we consider the inverse scattering problem of identifying a two-layered cavity by internal acoustic measurements under the condition that the interior interface has a mixed transmission boundary condition. We focus on the mathematical analysis of recovering the shape of the interior interface by using the linear sampling method, including reconstructing the surface conductivity by the
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On recovery of an unbounded bi-periodic interface for the inverse fluid-solid interaction scattering problem J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-05-02 Yanli Cui, Fenglong Qu, Changkun Wei
This paper is concerned with the inverse scattering of acoustic waves by an unbounded periodic elastic medium in the three-dimensional case. A novel uniqueness theorem is proved for the inverse problem of recovering a bi-periodic interface between acoustic and elastic waves using the near-field data measured only from the acoustic side of the interface, corresponding to a countably infinite number
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Approximate Lipschitz stability for phaseless inverse scattering with background information J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-05-02 Vladimir N. Sivkin
We prove approximate Lipschitz stability for monochromatic phaseless inverse scattering with background information in dimension d ≥ 2 {d\geq 2} . Moreover, these stability estimates are given in terms of non-overdetermined and incomplete data. Related results for reconstruction from phaseless Fourier transforms are also given. Prototypes of these estimates for the phased case were given in [R. G.
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Fast multilevel iteration methods for solving nonlinear ill-posed problems J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-05-02 Suhua Yang, Xingjun Luo, Rong Zhang
We propose a multilevel iteration method for the numerical solution of nonlinear ill-posed problems in the Hilbert space by using the Tikhonov regularization method. This leads to fast solutions of the discrete regularization methods for the nonlinear ill-posed equations. An adaptive choice of an a posteriori rule is suggested to choose the stopping index of iteration, and the rates of convergence
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Reconstruction of modified transmission eigenvalues using Cauchy data J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-04-26 Juan Liu, Yanfang Liu, Jiguang Sun
The modified transmission eigenvalue (MTE) problem was introduced in [S. Cogar, D. Colton, S. Meng and P. Monk, Modified transmission eigenvalues in inverse scattering theory, Inverse Problems 33 2017, 12, Article ID 125002] and used as a target signature for nondestructive testing. In this paper, we study the inverse spectral problem to reconstruct the modified transmission eigenvalues using Cauchy
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Agent-based mathematical model of COVID-19 spread in Novosibirsk region: Identifiability, optimization and forecasting J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-04-03 Olga Krivorotko, Mariia Sosnovskaia, Sergey Kabanikhin
The problem of identification of unknown epidemiological parameters (contagiosity, the initial number of infected individuals, probability of being tested) of an agent-based model of COVID-19 spread in Novosibirsk region is solved and analyzed. The first stage of modeling involves data analysis based on the machine learning approach that allows one to determine correlated datasets of performed PCR
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Inverse problem for the Atangana–Baleanu fractional differential equation J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-03-30 Santosh Ruhil, Muslim Malik
In this manuscript, we examine a fractional inverse problem of order 0 < ρ < 1 {0<\rho<1} in a Banach space, including the Atangana–Baleanu fractional derivative in the Caputo sense. We use an overdetermined condition on a mild solution to identify the parameter. The major strategies for determining the outcome are a direct approach using the Volterra integral equation for sufficiently regular data
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Inverse nodal problem for diffusion operator on a star graph with nonhomogeneous edges J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-03-30 Sevim Durak
In this study, a diffusion operator is investigated on a star graph with nonhomogeneous edges. First, the behaviors of sufficiently large eigenvalues are learned, and then the solution of the inverse problem is given to determine the potential functions and parameters of the boundary condition on the star graph with the help of a dense set of nodal points and to obtain a constructive solution to the
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Identification of the time-dependent source term in a Kuramoto–Sivashinsky equation J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-03-30 Kai Cao
The determination of an unknown time-dependent source term is investigated in a Kuramoto–Sivashinsky equation from given additional integral-type measurement. Based on Schauder’s fixed point theorem, the existence and uniqueness of such inverse problem are obtained under certain assumptions on the input data. In order to calculate the unknown source term, a time-discrete system is established, and
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On finding a penetrable obstacle using a single electromagnetic wave in the time domain J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-03-30 Masaru Ikehata
The time domain enclosure method is one of the analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell system and consists of two parts. The first part establishes the base of the time domain enclosure method for the Maxwell system using a single set of the solutions
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A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces J. Inverse Ill posed Probl. (IF 1.1) Pub Date : 2023-03-30 Yuxin Xia, Bo Han, Wei Wang
In this paper, we propose and analyze a projected homotopy perturbation method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. To expedite convergence, the approach uses two search directions given by homotopy perturbation iteration, and the new iteration is calculated as the projection of the current iteration onto the intersection of stripes decided by above