相关论文: Diffuse optical tomography in time domain with the…

Diffusion models have achieved remarkable success in imaging inverse problems owing to their powerful generative capabilities. However, existing approaches typically rely on models trained for specific degradation types, limiting their…

Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…

Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…

This study formally adapts the time-domain linear sampling method (TLSM) for ultrasonic imaging of stationary and evolving fractures in safety-critical components. The TLSM indicator is then applied to the laboratory test data of [22, 18]…

Consider the scattering of a time-harmonic plane wave by heterogeneous media consisting of linear or nonlinear point scatterers and extended obstacles. A generalized Foldy-Lax formulation is developed to take fully into account of the…

This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…

We consider the inverse source problem arising in thermo- and photo-acoustic tomography. It consists in reconstructing the initial pressure from the boundary measurements of the acoustic wave. Our goal is to extend versatile time reversal…

This paper is concerned with backward problem for nonlinear space fractional diffusion with additive noise on the right-hand side and the final value. To regularize the instable solution, we develop some new regularized method for solving…

A new approach for solving the optical inverse problem of quantitative photoacoustic tomography is introduced, which interpolates between the well-known diffusion approximation and a radiative transfer equation based model. The proposed…

Diffuse optical tomography (DOT) is an imaging modality which uses near-infrared light. Although iterative numerical schemes are commonly used for its inverse problem, correct solutions are not obtained unless good initial guesses are…

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…

In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse-time migration (RTM). In the process, the explicit evaluation of the…

Photon transport through a diffusing slab can be described by the radiative transfer equation (RTE). When the slab is highly scattering and weakly absorbing, the RTE simplifies to the diffusion equation. In this paper, an inverse diffusion…

Optoacoustic tomography image reconstruction has been a problem of interest in recent years. By exploiting the exceptional generative power of the recently proposed diffusion models we consider a scheme which is based on a conditional…

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…

Nonlinear parametric inverse problems appear in many applications. Here, we focus on diffuse optical tomography (DOT) in medical imaging to recover unknown images of interest, such as cancerous tissue in a given medium, using a mathematical…

We propose a method for approximating the large deviation rate function of time-integrated observables of diffusion processes, used in statistical physics to characterize the fluctuations of nonequilibrium systems. The method is based on…

Magnetic resonance imaging (MRI) is a potent diagnostic tool, but suffers from long examination times. To accelerate the process, modern MRI machines typically utilize multiple coils that acquire sub-sampled data in parallel. Data-driven…

The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color…

We demonstrate that the spatial resolution of images in optical tomography is not limited to the fundamental length scale of one transport mean free path. This result is facilitated by the introduction of novel corrections to the standard…