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In optical diffraction tomography (ODT), a sample's 3D refractive-index (RI) is often reconstructed after illuminating it from multiple angles, with the assumption that the sample remains static throughout data collection. When the sample…
Inverse scattering involving microwave and ultrasound waves require numerical solution of nonlinear optimization problem. To alleviate the computational burden of a full three-dimensional (3-D) inverse problem, it is a common practice to…
In this paper, we present a novel reconstruction method for diffuse optical spectroscopic imaging with a commonly used tissue model of optical absorption and scattering. It is based on linearization and group sparsity, which allows…
This work is concerned with an inverse scattering problem of determining unknown scatterers from time-dependent acoustic measurements. A novel time-domain direct sampling method is developed to efficiently determine both the locations and…
This paper concerns the numerical simulation of time domain inverse acoustic scattering problems with a point-like scatterer, multiple point-like scatterers or normal size scatterers. Based on the Green's function and the application of the…
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…
Least-squares reverse time migration is well-known for its capability to generate artifact-free true-amplitude subsurface images through fitting observed data in the least-squares sense. However, when applied to realistic imaging problems,…
Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…
In image editing employing diffusion models, it is crucial to preserve the reconstruction fidelity to the original image while changing its style. Although existing methods ensure reconstruction fidelity through optimization, a drawback of…
Consider the inverse acoustic scattering of time-harmonic point sources by an unbounded locally rough interface with bounded obstacles embedded in the lower half-space. A novel version of reverse time migration is proposed to reconstruct…
The problem of reconstructing an object from the measurements of the light it scatters is common in numerous imaging applications. While the most popular formulations of the problem are based on linearizing the object-light relationship,…
We explore an alternative method to the usual shear correlation function approach for the estimation of aperture mass statistics in weak lensing survey data. Our approach builds on the direct estimator method of Schneider (1998). In this…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
A method for practical realization of the inverse scattering transform method for the Korteweg-de Vries equation is proposed. It is based on analytical representations for Jost solutions and for integral kernels of transformation operators…
The instantaneous two-dimensional wall shear rate is assessed through an inverse problem using mass transfer data from a three-segment electrodiffusion probe. The method is validated numerically in complex flow conditions involving (i) high…
In this paper we present an effective coarse space correction addressed to accelerate the solution of an algebraic linear system. The system arises from the formulation of the problem of interpolating scattered data by means of Radial Basis…
We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the…
Some novel numerical approaches to solving direct and inverse obstacle scattering problems (IOSP) are presented. Scattering by finite obstacles and by periodic structures is considered. The emphasis for solving direct scattering problem is…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
Inverse scattering problems of the reconstructions of physical properties of a medium from boundary measurements are substantially challenging ones. This work aims to verify the performance on experimental data of a newly developed…