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Inverse problems, such as accelerated MRI reconstruction, are ill-posed and an infinite amount of possible and plausible solutions exist. This may not only lead to uncertainty in the reconstructed image but also in downstream tasks such as…
We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam hardening. If…
We consider the problem of reconstructing the position and the time-dependent optical properties of a linear dispersive medium from OCT measurements. The medium is multi-layered described by a piece-wise inhomogeneous refractive index. The…
We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on coarse measurements. The approach is motivated by quasi-local numerical effective forward…
For photoacoustic image reconstruction, certain parameters such as sensor positions and speed of sound have a major impact in the reconstruction process and must be carefully determined before data acquisition. Uncertainties in these…
This paper is concerned with inverse source problems for the acoustic wave equation in the full space R^3, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability…
This work is concerned with uncertainty quantification problems for image reconstructions in quantitative photoacoustic imaging (PAT), a recent hybrid imaging modality that utilizes the photoacoustic effect to achieve high-resolution…
We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…
We consider the reconstruction of the diffusion and absorption coefficients of the diffusion equation from the internal information of the solution obtained from the first step of the inverse photoacoustic tomography (PAT). In practice, the…
This paper deals with an inverse source problem for the $1$D time-fractional diffusion equation by using boundary measurement. The conditional stability in identification of the unknown source term is proved on the basis of the Fourier…
This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…
This paper presents a fast and robust numerical method for reconstructing point-like sources in the time-harmonic Maxwell's equations given Cauchy data at a fixed frequency. This is an electromagnetic inverse source problem with broad…
This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by…
Image reconstruction methods based on deep neural networks have shown outstanding performance, equalling or exceeding the state-of-the-art results of conventional approaches, but often do not provide uncertainty information about the…
We present a quantitative study of coherent array imaging of remote sources in randomly perturbed waveguides with bounded cross-section. We study how long range cumulative scattering by perturbations of the boundary and the medium impedes…
In some super-resolution techniques, adjacent points are illuminated at different times. Thereby, their locations and light intensities can be detected even if the images are very blurred due to diffraction. According to conventional…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
While diffusion models excel at generating high-quality images, their tendency to memorize training data poses significant privacy and copyright risks. In this work, we for the first time identify that memorization induces internal…
In this work we investigate an inverse problem of recovering point sources and their time-dependent strengths from {a posteriori} partial internal measurements in a subdiffusion model which involves a Caputo fractional derivative in time…
An approach to diffraction tomography is investigated for two-dimensional image reconstruction of objects surrounded by an arbitrarily-shaped curve of sources and receivers. Based on the integral theorem of Helmholtz and Kirchhoff, the…