Related papers: Qualitative reconstruction methods for imaging int…
Multi-segment reconstruction (MSR) problem consists of recovering a signal from noisy segments with unknown positions of the observation windows. One example arises in DNA sequence assembly, which is typically solved by matching short reads…
In acousto-electric tomography the goal is to reconstruct the electric conductivity in a domain from electrostatic boundary measurements of corresponding currents and voltages, while the domain is penetrated by a time-dependent acoustic…
We study the inverse problem of recovering the spatial support of parameter variations in a system of partial differential equations (PDEs) from boundary measurements. A reconstruction method is developed based on the monotonicity…
This work implements and numerically tests the direct reconstruction algorithm introduced in [Garde & Hyv\"onen, SIAM J. Math. Anal., 2024] for two-dimensional linearized electrical impedance tomography. Although the algorithm was…
In the framework of the optimal wave energy absorption, we solve theoretically and numerically a parametric shape optimization problem to find the optimal distribution of absorbing material in the reflexive one defined by a characteristic…
In this paper, we deal with the problem of determining perfectly insulating regions (cavities) from one boundary measurement in a nonlinear elliptic equation arising from cardiac electrophysiology. Based on the results obtained in [9] we…
We consider an optimal recovery problem for the Poisson problem when the boundary data is unknown. Compensating information is provided in the form of a finite number of measurements of the solution. A finite element algorithm for this…
One of the major challenges of coupled problems is to manage nonconforming meshes at the interface between two models and/or domains, due to different numerical schemes or domains discretizations employed. Moreover, very often complex…
We present a non-iterative algorithm to reconstruct the isotropic acoustic wave speed from the measurement of the Neumann-to-Dirichlet map. The algorithm is designed based on the boundary control method and involves only computations that…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
Electrical Impedance Tomography can be cost-effective, portable, non-invasive imaging technique. It has preclinical and a few of them already proven industrial applications. This technique can only recover images of low spatial and contrast…
The random feature method (RFM), a mesh-free machine learning-based framework, has emerged as a promising alternative for solving PDEs on complex domains. However, for large three-dimensional nonlinear problems, attaining high accuracy…
Electron tomography (ET) has become a standard technique for 3D characterization of materials at the nano-scale. Traditional reconstruction algorithms such as weighted back projection suffer from disruptive artifacts with insufficient…
We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…
This article develops a solution for an inverse problem through the generalized method of lines. We consider a Laplace equation on a domain with internal and external boundaries with standard Dirichlet boundary conditions. Also, we specify…
Regression with a spherical response is challenging due to the absence of linear structure, making standard regression models inadequate. Existing methods, mainly parametric, lack the flexibility to capture the complex relationship induced…
We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in $\mathbb{R}^3$ via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann…
Received signal strength based radio tomographic imaging is a popular device-free indoor localization method which reconstructs the spatial loss field of the environment using measurements from a dense wireless network. Existing methods…
Nonlinear ultrasound imaging leverages harmonic wave generation to enhance contrast and spatial resolution beyond the capabilities of conventional linear techniques. This behavior is commonly modeled by the Westervelt equation, which…
Here we present new joint reconstruction and regularization techniques inspired by ideas in microlocal analysis and lambda tomography, for the simultaneous reconstruction of the attenuation coefficient and electron density from X-ray…