Related papers: Non-linearity in monochromatic transmission tomogr…
Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions,…
The multiple passages of light through an absorption inhomogeneity of finite size deep within a turbid medium is analyzed for optical imaging using the ``self-energy'' diagram. The nonlinear correction becomes more important for an…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…
We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a non-iterative reconstruction method using measurements of the radiating flux at the boundary. The attenuation and scattering…
This paper refers to an imaging problem in the presence of nonlinear materials. Specifically, the problem we address falls within the framework of Electrical Resistance Tomography and involves two different materials, one or both of which…
In computed tomography (CT), the forward model consists of a linear Radon transform followed by an exponential nonlinearity based on the attenuation of light according to the Beer-Lambert Law. Conventional reconstruction often involves…
We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on coarse measurements. The approach is motivated by quasi-local numerical effective forward…
In this paper, we study the inverse medium scattering problem to reconstruct unknown inhomogeneous medium from far field patterns of scattered waves. In the first part of our work, the linear inverse scattering problem was discussed, while…
This paper concerns with nonuniform sampling and interpolation methods combined with variational models for the solution of a generalized image inpainting problem and the restoration of digital signals. In particular, we discuss the problem…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
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…
In this work we consider the inverse problem of reconstructing the optical properties of a layered medium from an elastography measurement where optical coherence tomography is used as the imaging method. We hereby model the sample as a…
This paper aims to combine the advantages of the Jordan-Moore-Gibson-Thompson JMGT equation as an advanced model in nonlinear acoustics with a frequency domain formulation of the forward and inverse problem of acoustic nonlinearity…
The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…
The hard x-ray gamma-ray absorption by cylindrically symmetric U-238 test objects is studied by means of gamma-ray transmission measurements. To make a precise comparison between the theoretically modelled values and the absorption…
This paper is a review of recent mathematical and computational advances in optical tomography. We discuss the physical foundations of forward models for light propagation on microscopic, mesoscopic and macroscopic scales. We also consider…
To produce images that are suitable for display, tone-mapping is widely used in digital cameras to map linear color measurements into narrow gamuts with limited dynamic range. This introduces non-linear distortion that must be undone,…
We present several nonlinear wavefront sensing techniques for few-mode sensors, all of which are empirically calibrated and agnostic to the choice of wavefront sensor. The first class of techniques involves a straightforward extension of…
We introduce a method to experimentally measure the monochromatic transmission matrix of a complex medium in optics. This method is based on a spatial phase modulator together with a full-field interferometric measurement on a camera. We…
This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with unbroken rays and for…