Inverse Problems最新文献

{"title":"Fourier series-based approximation of time-varying parameters in ordinary differential equations","authors":"Anna Fitzpatrick, Molly Folino, Andrea Arnold","doi":"10.1088/1361-6420/ad1fe5","DOIUrl":"https://doi.org/10.1088/1361-6420/ad1fe5","url":null,"abstract":"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 to estimate time-varying parameters (TVPs) in deterministic dynamical systems modeled with ordinary differential equations. Using ensemble Kalman filtering in conjunction with Fourier series-based approximation models, we detail two possible implementation schemes for sequentially updating the time-varying parameter estimates given noisy observations of the system states. We demonstrate the capabilities of the proposed approach in estimating periodic parameters, both when the period is known and unknown, as well as non-periodic TVPs of different forms with several computed examples using a forced harmonic oscillator. Results emphasize the importance of the frequencies and number of approximation model terms on the time-varying parameter estimates and corresponding dynamical system predictions.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"23 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"V-line 2-tensor tomography in the plane","authors":"Gaik Ambartsoumian, Rohit Kumar Mishra, Indrani Zamindar","doi":"10.1088/1361-6420/ad1f83","DOIUrl":"https://doi.org/10.1088/1361-6420/ad1f83","url":null,"abstract":"In this article, we introduce and study various V-line transforms (VLTs) defined on symmetric 2-tensor fields in <inline-formula>\u0000<tex-math><?CDATA $mathbb{R}^2$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:math>\u0000<inline-graphic xlink:href=\"ipad1f83ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>. 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 concepts defined for straight-line paths of integration. We characterize the kernels of the VLTs and derive exact formulas for reconstruction of tensor fields from various combinations of these transforms. The star transform on tensor fields is an extension of the corresponding concepts that have been previously studied on vector fields and scalar fields (functions). We describe all injective configurations of the star transform on symmetric 2-tensor fields and derive an exact, closed-form inversion formula for that operator.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"8 2 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Regularization of the inverse Laplace transform by mollification","authors":"Pierre Maréchal, Faouzi Triki, Walter C Simo Tao Lee","doi":"10.1088/1361-6420/ad1609","DOIUrl":"https://doi.org/10.1088/1361-6420/ad1609","url":null,"abstract":"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. We show that by taking the optimal value of this parameter we improve significantly the convergence of the method. Finally, making use of the holomorphic extension of the Laplace transform, we suggest a new PDEs based numerical method for the computation of the solution. The effectiveness of the proposed regularization method is demonstrated through several numerical examples.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139506590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Determining a parabolic system by boundary observation of its non-negative solutions with biological applications","authors":"Hongyu Liu, Catharine W K Lo","doi":"10.1088/1361-6420/ad149f","DOIUrl":"https://doi.org/10.1088/1361-6420/ad149f","url":null,"abstract":"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 can both ensure the positivity of the solutions and effectively tackle the nonlinear inverse problem. This enables us to establish several novel unique identifiability results for the inverse problem in a rather general setup. For a theoretical perspective, our study addresses an important topic in partial differential equation (PDE) analysis on how to characterise the function spaces generated by the products of non-positive solutions of parabolic PDEs. As a typical and practically interesting application, we apply our general results to inverse problems for ecological population models, where the positive solutions signify the population densities.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139506406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deep unfolding as iterative regularization for imaging inverse problems","authors":"Zhuoxu Cui, Qingyong Zhu, Jing Cheng, Bo Zhang, Dong Liang","doi":"10.1088/1361-6420/ad1a3c","DOIUrl":"https://doi.org/10.1088/1361-6420/ad1a3c","url":null,"abstract":"\u0000 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 this, we reevaluate unfolded DNNs and observe that their algorithmically-driven cascading structure exhibits a closer resemblance to iterative regularization. Recognizing this, we propose a modified training approach and configure termination criteria for unfolded DNNs, thereby establishing the unfolding method as an iterative regularization technique. Specifically, our method involves the joint learning of a convex penalty function using an input-convex neural network (ICNN) to quantify distance to a real data manifold. Then, we train a DNN unfolded from the proximal gradient descent algorithm, incorporating this learned penalty. Additionally, we introduce a new termination criterion for the unfolded DNN. Under the assumption that the real data manifold intersects the solutions of the inverse problem with a unique real solution, even when measurements contain perturbations, we provide a theoretical proof of the stable convergence of the unfolded DNN to this solution. Furthermore, we demonstrate with an example of MRI reconstruction that the proposed method outperforms original unfolding methods and traditional regularization methods in terms of reconstruction quality, stability, and convergence speed.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"14 6","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139451521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical recovery of a time-dependent potential in subdiffusion *","authors":"Bangti Jin, Kwancheol Shin, Zhi Zhou","doi":"10.1088/1361-6420/ad14a0","DOIUrl":"https://doi.org/10.1088/1361-6420/ad14a0","url":null,"abstract":"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 recovering the unknown coefficient. In addition, we establish rigorous error bounds on the discrete approximation. These results are obtained by crucially using smoothing properties of the solution operators and suitable choice of a weighted <inline-formula>\u0000<tex-math><?CDATA $L^p(0,T)$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math>\u0000<inline-graphic xlink:href=\"ipad14a0ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> norm. The efficiency and accuracy of the scheme are showcased on several numerical experiments in one- and two-dimensions.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"30 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139095803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adaptive minimax optimality in statistical inverse problems via SOLIT—Sharp Optimal Lepskiĭ-Inspired Tuning","authors":"Housen Li, Frank Werner","doi":"10.1088/1361-6420/ad12e0","DOIUrl":"https://doi.org/10.1088/1361-6420/ad12e0","url":null,"abstract":"We consider statistical linear inverse problems in separable Hilbert spaces and filter-based reconstruction methods of the form &lt;inline-formula&gt;\u0000&lt;tex-math&gt;&lt;?CDATA $widehat f_alpha = q_alpha left(T,^*Tright)T,^*Y$?&gt;&lt;/tex-math&gt;\u0000&lt;mml:math overflow=\"scroll\"&gt;&lt;mml:msub&gt;&lt;mml:mover&gt;&lt;mml:mi&gt;f&lt;/mml:mi&gt;&lt;mml:mo&gt;ˆ&lt;/mml:mo&gt;&lt;/mml:mover&gt;&lt;mml:mi&gt;α&lt;/mml:mi&gt;&lt;/mml:msub&gt;&lt;mml:mo&gt;=&lt;/mml:mo&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;q&lt;/mml:mi&gt;&lt;mml:mi&gt;α&lt;/mml:mi&gt;&lt;/mml:msub&gt;&lt;mml:mfenced close=\")\" open=\"(\"&gt;&lt;mml:mrow&gt;&lt;mml:msup&gt;&lt;mml:mi&gt;T&lt;/mml:mi&gt;&lt;mml:mo&gt;∗&lt;/mml:mo&gt;&lt;/mml:msup&gt;&lt;mml:mi&gt;T&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:mfenced&gt;&lt;mml:msup&gt;&lt;mml:mi&gt;T&lt;/mml:mi&gt;&lt;mml:mo&gt;∗&lt;/mml:mo&gt;&lt;/mml:msup&gt;&lt;mml:mi&gt;Y&lt;/mml:mi&gt;&lt;/mml:math&gt;\u0000&lt;inline-graphic xlink:href=\"ipad12e0ieqn1.gif\" xlink:type=\"simple\"&gt;&lt;/inline-graphic&gt;\u0000&lt;/inline-formula&gt;, where &lt;italic toggle=\"yes\"&gt;Y&lt;/italic&gt; is the available data, &lt;italic toggle=\"yes\"&gt;T&lt;/italic&gt; the forward operator, &lt;inline-formula&gt;\u0000&lt;tex-math&gt;&lt;?CDATA $left(q_alpharight)_{alpha in mathcal A}$?&gt;&lt;/tex-math&gt;\u0000&lt;mml:math overflow=\"scroll\"&gt;&lt;mml:msub&gt;&lt;mml:mfenced close=\")\" open=\"(\"&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;q&lt;/mml:mi&gt;&lt;mml:mi&gt;α&lt;/mml:mi&gt;&lt;/mml:msub&gt;&lt;/mml:mfenced&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;α&lt;/mml:mi&gt;&lt;mml:mo&gt;∈&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;A&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;/mml:math&gt;\u0000&lt;inline-graphic xlink:href=\"ipad12e0ieqn2.gif\" xlink:type=\"simple\"&gt;&lt;/inline-graphic&gt;\u0000&lt;/inline-formula&gt; an ordered filter, and &lt;italic toggle=\"yes\"&gt;α&lt;/italic&gt; &gt; 0 a regularization parameter. Whenever such a method is used in practice, &lt;italic toggle=\"yes\"&gt;α&lt;/italic&gt; has to be appropriately chosen. Typically, the aim is to find or at least approximate the best possible &lt;italic toggle=\"yes\"&gt;α&lt;/italic&gt; in the sense that mean squared error (MSE) &lt;inline-formula&gt;\u0000&lt;tex-math&gt;&lt;?CDATA $mathbb{E} [Vert widehat f_alpha - f^daggerVert^2]$?&gt;&lt;/tex-math&gt;\u0000&lt;mml:math overflow=\"scroll\"&gt;&lt;mml:mrow&gt;&lt;mml:mi mathvariant=\"double-struck\"&gt;E&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;[&lt;/mml:mo&gt;&lt;mml:mo&gt;∥&lt;/mml:mo&gt;&lt;mml:msub&gt;&lt;mml:mover&gt;&lt;mml:mi&gt;f&lt;/mml:mi&gt;&lt;mml:mo&gt;ˆ&lt;/mml:mo&gt;&lt;/mml:mover&gt;&lt;mml:mi&gt;α&lt;/mml:mi&gt;&lt;/mml:msub&gt;&lt;mml:mo&gt;−&lt;/mml:mo&gt;&lt;mml:msup&gt;&lt;mml:mi&gt;f&lt;/mml:mi&gt;&lt;mml:mo&gt;†&lt;/mml:mo&gt;&lt;/mml:msup&gt;&lt;mml:mrow&gt;&lt;mml:msup&gt;&lt;mml:mo&gt;∥&lt;/mml:mo&gt;&lt;mml:mn&gt;2&lt;/mml:mn&gt;&lt;/mml:msup&gt;&lt;/mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;]&lt;/mml:mo&gt;&lt;/mml:math&gt;\u0000&lt;inline-graphic xlink:href=\"ipad12e0ieqn3.gif\" xlink:type=\"simple\"&gt;&lt;/inline-graphic&gt;\u0000&lt;/inline-formula&gt; w.r.t. the true solution &lt;inline-formula&gt;\u0000&lt;tex-math&gt;&lt;?CDATA $f^dagger$?&gt;&lt;/tex-math&gt;\u0000&lt;mml:math overflow=\"scroll\"&gt;&lt;mml:msup&gt;&lt;mml:mi&gt;f&lt;/mml:mi&gt;&lt;mml:mo&gt;†&lt;/mml:mo&gt;&lt;/mml:msup&gt;&lt;/mml:math&gt;\u0000&lt;inline-graphic xlink:href=\"ipad12e0ieqn4.gif\" xlink:type=\"simple\"&gt;&lt;/inline-graphic&gt;\u0000&lt;/inline-formula&gt; is minimized. In this paper, we introduce the Sharp Optimal Lepskiĭ-Inspired Tuning (SOLIT) method, which yields an &lt;italic toggle=\"yes\"&gt;a posteriori&lt;/italic&gt; parameter choice rule ensuring adaptive minimax rates of convergence. It depends only on &lt;italic toggle=\"yes\"&gt;Y&lt;/italic&gt; and the noise level &lt;italic toggle=\"yes\"&gt;σ&lt;/italic&gt; as well as the operator &lt;italic toggle=\"yes\"&gt;T&lt;/italic&gt; and th","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"43 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139051602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solving inverse scattering problems via reduced-order model embedding procedures","authors":"Jörn Zimmerling, Vladimir Druskin, Murthy Guddati, Elena Cherkaev, Rob Remis","doi":"10.1088/1361-6420/ad149d","DOIUrl":"https://doi.org/10.1088/1361-6420/ad149d","url":null,"abstract":"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 theory of ‘optimal grids,’ where the ROMs are interpreted as two-point finite-difference discretisations of an underlying set of equations of a first-order continuous system on this special grid. Here, we extend this line of work to wave equations and introduce a new embedding technique, which we call <italic toggle=\"yes\">Krein embedding</italic>, since it is inspired by Krein’s seminal work on vibrations of a string. In this embedding approach, an adaptive grid and a set of medium parameters can be directly extracted from a ROM and we show that several limitations of optimal grid embeddings can be avoided. Furthermore, we show how Krein embedding is connected to classical optimal grid embedding and that convergence results for optimal grids can be extended to this novel embedding approach. Finally, we also briefly discuss Krein embedding for open domains, that is, semi-infinite domains that extend to infinity in one direction.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"10 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139055341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chilled sampling for uncertainty quantification: a motivation from a meteorological inverse problem *","authors":"P Héas, F Cérou, M Rousset","doi":"10.1088/1361-6420/ad141f","DOIUrl":"https://doi.org/10.1088/1361-6420/ad141f","url":null,"abstract":"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. The difficulty of estimating errors stems from the specificity of the posterior distribution, which is both very high dimensional, and highly ill-conditioned due to a singular likelihood, which becomes critical in particular in the case of missing data (unobserved pixels). Motivated by this difficult inverse problem, this work studies the evaluation of the (expected) estimation errors using gradient-based Markov chain Monte Carlo (MCMC) algorithms. The main contribution is to propose a general strategy, called here ‘chilling’, which amounts to sampling a local approximation of the posterior distribution in the neighborhood of a point estimate. From a theoretical point of view, we show that under regularity assumptions, the family of chilled posterior distributions converges in distribution as temperature decreases to an optimal Gaussian approximation at a point estimate given by the maximum <italic toggle=\"yes\">a posteriori</italic>, also known as the Laplace approximation. Chilled sampling therefore provides access to this approximation generally out of reach in such high-dimensional nonlinear contexts. From an empirical perspective, we evaluate the proposed approach based on some quantitative Bayesian criteria. Our numerical simulations are performed on synthetic and real meteorological data. They reveal that not only the proposed chilling exhibits a significant gain in terms of accuracy of the AMV point estimates and of their associated expected error estimates, but also a substantial acceleration in the convergence speed of the MCMC algorithms.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"44 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139055266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantitative parameter reconstruction from optical coherence tomographic data","authors":"Leopold Veselka, Peter Elbau, Leonidas Mindrinos, Lisa Krainz, Wolfgang Drexler","doi":"10.1088/1361-6420/ad0fab","DOIUrl":"https://doi.org/10.1088/1361-6420/ad0fab","url":null,"abstract":"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 samples with a layered structure, meaning that the refractive index as a function of depth is well approximated by a piecewise constant function. For the reconstruction, we present a layer-by-layer method where in every step the refractive index is obtained via a discretized least squares minimization. For an approximated form of the minimization problem, we present an existence and uniqueness result. The applicability of the proposed method is then verified by reconstructing refractive indices of layered media from both simulated and experimental OCT data.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"38 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139051400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}