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Our goal is to reconstruct tomographic images with few measurements and a low signal-to-noise ratio. In clinical imaging, this helps to improve patient comfort and reduce radiation exposure. As quantum computing advances, we propose to use…
Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the…
Image restoration is rather challenging in adverse weather conditions, especially when multiple degradations occur simultaneously. Blind image decomposition was proposed to tackle this issue, however, its effectiveness heavily relies on the…
Computational imaging plays a pivotal role in determining hidden information from sparse measurements. A robust inverse solver is crucial to fully characterize the uncertainty induced by these measurements, as it allows for the estimation…
We consider the ultrasound imaging problem governed by a nonlinear wave equation of Westervelt type with variable wave speed. We show that the coefficient of nonlinearity can be recovered uniquely from knowledge of the Dirichlet-to-Neumann…
In this paper, we revisit the bioluminescence tomography (BLT) problem, where one seeks to reconstruct bioluminescence signals (an internal light source) from external measurements of the Cauchy data. As one kind of optical imaging, the BLT…
In ultrasound (US) imaging, individual channel RF measurements are back-propagated and accumulated to form an image after applying specific delays. While this time reversal is usually implemented using a hardware- or software-based…
Gravitational lensing distorts the cosmic microwave background (CMB) anisotropies and imprints a characteristic pattern onto it. The distortions depend on the projected matter density between today and redshift $z \sim 1100$. In this paper…
Scanning microscopy systems, such as confocal and multiphoton microscopy, are powerful imaging tools for probing deep into biological tissue. However, scanning systems have an inherent trade-off between acquisition time, field of view,…
We propose a novel framework for joint magnetic resonance image reconstruction and uncertainty quantification using under-sampled k-space measurements. The problem is formulated as a Bayesian linear inverse problem, where prior…
When the inverse problem of diffuse optical tomography (DOT) is solved with the Born or Rytov approximation, the size of the matrix of the linear inverse problem becomes large if the volume (or area) of the domain in biological tissue used…
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…
Uncertainty quantification in inverse medical imaging tasks with deep learning has received little attention. However, deep models trained on large data sets tend to hallucinate and create artifacts in the reconstructed output that are not…
This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…
During the past few years, inverse problem formulations of ultrasound beamforming have attracted a growing interest. They usually pose beamforming as a minimization problem of a fidelity term resulting from the measurement model plus a…
Performing magnetic resonance imaging (MRI) reconstruction from under-sampled k-space data can accelerate the procedure to acquire MRI scans and reduce patients' discomfort. The reconstruction problem is usually formulated as a denoising…
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…
Ultrasonic guided waves are commonly used to localize structural damage in infrastructures such as buildings, airplanes, bridges. Damage localization can be viewed as an inverse problem. Physical model based techniques are popular for…
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…
Pre-trained diffusion models have been successfully used as priors in a variety of linear inverse problems, where the goal is to reconstruct a signal from noisy linear measurements. However, existing approaches require knowledge of the…