Related papers: Shape-constrained reconstruction in diffuse optica…
Ill-posed imaging inverse problems remain challenging due to the ambiguity in mapping degraded observations to clean images. Diffusion-based generative priors have recently shown promise, but typically rely on computationally intensive…
Beamforming in ultrasound imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum is still extensively used nowadays in…
We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…
Image reconstruction in optoacoustic tomography (OAT) is a trending learning task highly dependent on measured physical magnitudes present at sensing time. The large number of different settings, and also the presence of uncertainties or…
We study numerical methods of tomography in domains with a reflecting obstacle. It will be shown that tomography with sets containing both broken rays, i.e. rays reflecting at the obstacle, as well as unbroken rays, has a smaller error…
In this article a nonlocal analogue of an inverse problem in diffuse optical tomography is considered. We show that whenever one has given two pairs of diffusion and absorption coefficients $(\gamma_j,q_j)$, $j=1,2$, such that there holds…
Four-dimensional computed tomography (4DCT) is essential for medical imaging applications like radiotherapy, which demand precise respiratory motion representation. Traditional methods for reconstructing 4DCT data suffer from artifacts and…
The iterative refinement method (IRM) has been very successfully applied in many different fields for examples the modern quantum chemical calculation and CT image reconstruction. It is proved that the refinement method can create an exact…
In this contribution, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such…
In this paper we provide a mathematical model for imaging an anisotropic, orthotropic medium with Polarization-Sensitive Optical Coherence Tomography (PS-OCT). The imaging problem is formulated as an inverse scattering problem in three…
The article presents an efficient image reconstruction algorithm for single scattering optical tomography (SSOT) in circular geometry of data acquisition. This novel medical imaging modality uses photons of light that scatter once in the…
In Optical diffraction tomography, the multiply scattered field is a nonlinear function of the refractive index of the object. The Rytov method is a linear approximation of the forward model, and is commonly used to reconstruct images.…
Doppler tomography is a method to compute the emissivity distribution within the co-rotating frames of binary stars from observations of their emission line profiles at multiple orbital phases. A key assumption of the method as it is…
Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
To date, high-resolution (< 1 nm) imaging of extended objects in three-dimensions (3D) has not been possible. A restriction known as the Crowther criterion forces a tradeoff between object size and resolution for 3D reconstructions by…
In numerous practical applications, especially in medical image reconstruction, it is often infeasible to obtain a large ensemble of ground-truth/measurement pairs for supervised learning. Therefore, it is imperative to develop unsupervised…
In this article, we investigate an inverse problem for a semi-linear wave equation posed on bounded domain in $\mathbb{R}^{n+1}$, with $n \geq 2$. Our primary objective is to reconstruct the damping coefficient, the linear and nonlinear…
This paper is concerned with the inverse scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surface from the scattered near-field Cauchy data generating by point sources and…
Source extension is a reformulation of inverse problems in wave propagation, that at least in some cases leads to computationally tractable iterative solution methods. The core subproblem in all source extension methods is the solution of a…