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We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function $f$ from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these…
We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…
We propose a method to reconstruct the optical properties of a scattering medium with subwavelength resolution. The method is based on the solution to the inverse scattering problem with photoactivated internal sources. Numerical…
The motivation of this work is the detection of cerebrovascular accidents by microwave tomographic imaging. This requires the solution of an inverse problem relying on a minimization algorithm (for example, gradient-based), where successive…
This paper surveys inverse problems arising in several coupled-physics imaging modalities for both medical and geophysical purposes. These include Photo-acoustic Tomography (PAT), Thermo-acoustic Tomography (TAT), Electro-Seismic…
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…
The iterative refinement method (IRM) has been very successfully applied in many different fields for examples the modern quantum chemical calculation and CT image reconstruction. It is proved that the refinement method can create an exact…
Consider an inverse problem of the simultaneous recovery of boundary impedance and internal conductivity in the electrical impedance tomography (EIT) model using local internal measurement data, which is governed by a boundary value problem…
We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary $\partial \Om$ of a smooth convex bounded domain $\Om \subset \R^2$. As a main result we establish…
This paper develops 'covariant tomography', a local framework for solving Inverse Boundary Value Problems (IBVP) for parallel transport equation on star-shaped domains. By integrating geometric decomposition with specific interior…
We deal with the problem of determining the shape of an inclusion embedded in a homogenous background medium. The multifre-quency electrical impedance tomography is used to image the inclusion. For different frequencies, a current is…
A novel reconstruction method is introduced for the severely ill-posed inverse problem of limited-angle tomography. It is well known that, depending on the available measurement, angles specify a subset of the wavefront set of the unknown…
For finite dimensional CMV matrices the mixed inverse spectral problem of reconstruction the matrix by its submatrix and a part of its spectrum is considered. A general rational interpolation problem which arises in solving the mixed…
The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…
Magnetic Induction Tomography (MIT) is a promising modality for noninvasive imaging due to its contactless and nonionizing technology. In this imaging method, a primary magnetic field is applied by excitation coils to induce eddy currents…
This paper presents an improved technique for solving the inverse problem in magnetic induction tomography (MIT) by considering skin and proximity effects in coils. MIT is a non-contact, noninvasive, and low-cost imaging modality for…
This is Part II of the paper series on data-compatible T-matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series contains theory and here we present simulations for inverse scattering of…
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…
Electrical impedance tomography (EIT) is a non-invasive imaging technique, which has been widely used in the fields of industrial inspection, medical monitoring and tactile sensing. However, due to the inherent non-linearity and…