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Magnetic particle imaging (MPI) is a medical imaging modality of recent origin, and it exploits the nonlinear magnetization phenomenon to recover the spatially dependent concentration of the nanoparticles. Currently, image reconstruction in…
A long-standing challenge in tomography is the 'missing wedge' problem, which arises when the acquisition of projection images within a certain angular range is restricted due to geometrical constraints. This incomplete dataset results in…
The aim of this paper is to provide a solid mathematical discussion of the inverse problem in Magnetorelaxometry Imaging (MRXI), a currently developed technique for quantitative biomedical imaging using magnetic nanoparticles. We provide a…
In the reconstruction process of unknown multiple scattering objects in inverse medium scattering problems, the first important step is to effectively locate some approximate domains that contain all inhomogeneous media. Without such an…
We consider a mathematical model of thermoacoustic tomography and other multi-wave imaging techniques with variable sound speed and attenuation. We find that a Neumann series reconstruction algorithm, previously studied under the assumption…
We study the inverse problem of recovering primordial perturbations from anisotropies of Cosmic Microwave Background (CMB) using the kinetic model. Mathematically, the problem in concern is the inverse source problem for the linear…
Many important microscopy samples, such as liquid crystals, biological tissue, or starches, are birefringent in nature. They scatter light differently depending on the light polarization and molecular orientations. The complete…
We discuss the algorithmic information approach to the analysis of the observational data on the Universe. Kolmogorov complexity is proposed as a descriptor of the Cosmic Microwave Background (CMB) radiation maps. An algorithm of…
Computed Tomography (CT) is a technology that reconstructs cross-sectional images using X-ray images taken from multiple directions. In CT, hundreds of X-ray images acquired as the X-ray source and detector rotate around a central axis, are…
We consider time-dependent inverse problems in a mathematical setting using Lebesgue-Bochner spaces. Such problems arise when one aims to recover a function from given observations where the function or the data depend on time.…
Most problems in gravitational lensing require numerical solutions. The most frequent types of problems are (1) finding multiple images of a single source and classifying the images according to their properties like magnification or…
In this paper, we consider the inverse shape problem of recovering isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. Motivated by recent work, we…
In this paper, we consider two time-harmonic inverse scattering problems of reconstructing penetrable inhomogeneous obstacles from near field measurements. First we appeal to the Born approximation for reconstructing small isotropic…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for medical cone-beam computed X-ray…
This article adapts the framework of metamorphosis to solve inverse problems in imaging that includes joint reconstruction and image registration. The deformations in question have two components, one that is a geometric deformation moving…
These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…
We present a method to reconstruct the dielectric susceptibility (scattering potential) of an inhomogeneous scattering medium, based on the solution to the inverse scattering problem with internal sources. We employ the theory of…
A rigorous mathematical model and an efficient computational method are proposed to solving the inverse elastic surface scattering problem which arises from the near-field imaging of periodic structures. We demonstrate how an enhanced…
In this paper, we study the inverse acoustic medium scattering problem to reconstruct the unknown inhomogeneous medium from far field patterns of scattered waves. We propose the reconstruction scheme based on the Kalman filter, which…