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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…
In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the…
We propose a direct imaging method based on the reverse time migration to reconstruct extended obstacles in the half space with finite aperture elastic scattering data at a fixed frequency. We prove the resolution of the reconstruction…
An efficient and accurate image reconstruction algorithm for ultrasound tomography (UST) is described and demonstrated, which can recover accurate sound speed distribution from acoustic time series measurements made in soft tissue. The…
We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT. We prove new inversion formulas for integrable functions,…
In this work, we propose Regularization-by-Equivariance (REV), a novel structure-adaptive regularization scheme for solving imaging inverse problems under incomplete measurements. This regularization scheme utilizes the equivariant…
The algorithm for inverting covariant exterior derivative is provided. It works for a sufficiently small star-shaped region of a fibered set - a local subset of a vector bundle and associated vector bundle. The algorithm contains some…
This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors…
Waveform inversion is theoretically a powerful tool to reconstruct subsurface structures, but a usually encountered problem is that accurate sources are very rare, causing the computation unstable and divergent. This challenging problem,…
Photoacoustic computed tomography (PACT), also known as optoacoustic tomography, is an emerging imaging technique that holds great promise for biomedical imaging. PACT is a hybrid imaging method that can exploit the strong endogenous…
Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…
Quantitative Photoacoustic tomography (QPAT) is an emerging medical imaging modality which offers the possibility of combining the high resolution of the acoustic waves and large contrast of optical waves by quantifying the molecular…
This report extends our recent progress in tackling a challenging 3D inverse scattering problem governed by the Helmholtz equation. Our target application is to reconstruct dielectric constants, electric conductivities and shapes of front…
Computed tomography (CT) is a widely used medical imaging technique to scan internal structures of a body, typically involving collimation and mechanical rotation. Compton scatter tomography (CST) presents an interesting alternative to…
This article presents the numerical verification and validation of several inversion algorithms for V-line transforms (VLTs) acting on symmetric 2-tensor fields in the plane. The analysis of these transforms and the theoretical foundation…
In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the…
Tomography can be used to reveal internal properties of a 3D object using any penetrating wave. Advanced tomographic imaging techniques, however, are vulnerable to both systematic and random errors associated with the experimental…
We consider an inverse problem for the elastic wave of simultaneously reconstructing the impedance and the geometric information of the bounded body that is occupied by a homogeneous and isotropic elastic medium from the measured Cauchy…
In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse…