相关论文: Reconstruction of a piecewise smooth absorption co…

We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport…

Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid…

We propose a numerical algorithm for the reconstruction of a piecewise constant leading coefficient of an elliptic problem. The inverse problem is reduced to a shape reconstruction problem. The proposed algorithm is based on the…

In this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological derivative based algorithm for the reconstruction of…

In this paper, two problems that show great similarities are examined. The first problem is the reconstruction of the angular-domain periodogram from spatial-domain signals received at different time indices. The second one is the…

Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…

Quantitative photoacoustic tomography (QPAT) is a recent hybrid imaging modality that couples optical tomography with ultrasound imaging to achieve high resolution imaging of optical properties of scattering media. Image reconstruction in…

Ultrasound-modulated optical tomography is an emerging biomedical imaging modality which uses the spatially localised acoustically-driven modulation of coherent light as a probe of the structure and optical properties of biological tissues.…

The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…

The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…

We present several results on smoothness in $L_{p}$ sense of filtering densities under the Lipschitz continuity assumption on the coefficients of a partially observable diffusion processes. We obtain them by rewriting in divergence form…

This paper presents a diffusion process with a novel resetting mechanism in which the amplitude of the process is instantaneously converted to a proportion of its value at random times. This model is described by a Langevin equation with…

Random pulse sequences are a powerful method for qubit noise spectroscopy, enabling efficient reconstruction of sparse noise spectra. Here, we advance this method in two complementary directions. First, we extend the method using a…

Photoacoustic tomography is an emerging medical imaging technology whose primary aim is to map the high-contrast optical properties of biological tissues by leveraging high-resolution ultrasound measurements. Mathematically, this can be…

Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm…

This paper concerns the reconstruction of a diffusion coefficient in an elliptic equation from knowledge of several power densities. The power density is the product of the diffusion coefficient with the square of the modulus of the…

Ultrasound modulated optical tomography, also called acousto-optics tomography, is a hybrid imaging modality that aims to combine the high contrast of optical waves with the high resolution of ultrasound. We follow the model of the…

Purpose: To develop an algorithm for robust partial Fourier (PF) reconstruction applicable to diffusion-weighted (DW) images with non-smooth phase variations. Methods: Based on an unrolled proximal splitting algorithm, a neural network…

We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…

Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…