Related papers: Discrete Tomography: Reconstruction under periodic…
Dual-energy X-ray tomography is considered in a context where the target under imaging consists of two distinct materials. The materials are assumed to be possibly intertwined in space, but at any given location there is only one material…
Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their…
Conventional Magnetic Resonance Imaging (MRI) is hampered by long scan times and only qualitative image contrasts that prohibit a direct comparison between different systems. To address these limitations, model-based reconstructions…
The reconstruction of an unknown function $f$ from its line sums is the aim of discrete tomography. However, two main aspects prevent reconstruction from being an easy task. In general, many solutions are allowed due to the presence of the…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
Tomography deals with the reconstruction of objects from their projections, acquired along a range of angles. Discrete tomography is concerned with objects that consist of a small number of materials, which makes it possible to compute…
Accelerating the data acquisition of dynamic magnetic resonance imaging (MRI) leads to a challenging ill-posed inverse problem, which has received great interest from both the signal processing and machine learning community over the last…
In parallel magnetic resonance imaging (pMRI), to find a joint solution for the image and coil sensitivity functions is a nonlinear and nonconvex problem. A class of algorithms reconstruct sensitivity encoded images of the coils first…
Current state-of-the-art methods for solving discrete optimization problems are usually restricted to convex settings. In this paper, we propose a general approach based on cutting planes for solving nonlinear, possibly nonconvex, binary…
The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…
We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…
Many practical problems involve the recovery of a binary matrix from partial information, which makes the binary matrix completion (BMC) technique received increasing attention in machine learning. In particular, we consider a special case…
Reconstructing the unknown spectrum of a given X-ray source is a common problem in a wide range of X-ray imaging tasks. For high-energy sources, transmission measurements are mostly used to recover the X-ray spectrum, as a solution to an…
The paper surveys variational approaches for image reconstruction in dynamic inverse problems. Emphasis is on methods that rely on parametrised temporal models. These are here encoded as diffeomorphic deformations with time dependent…
We consider travel time tomography problems involving detection of high contrast, discrete high velocity structures. This results in a discrete nonlinear inverse problem, for which traditional grid-based models and iterative linearized…
The aim of electrical impedance tomography is to form an image of the conductivity distribution inside an unknown body using electric boundary measurements. The computation of the image from measurement data is a non-linear ill-posed…
Deep learning has been widely used for solving image reconstruction tasks but its deployability has been held back due to the shortage of high-quality training data. Unsupervised learning methods, such as the deep image prior (DIP),…
This paper proposes a randomized optimization framework for constrained signal reconstruction, where the word "constrained" implies that data-fidelity is imposed as a hard constraint instead of adding a data-fidelity term to an objective…
Single particle reconstruction has recently emerged in 3D fluorescence microscopy as a powerful technique to improve the axial resolution and the degree of fluorescent labeling. It is based on the reconstruction of an average volume of a…
Thinning is the removal of contour pixels/points of connected components in an image to produce their skeleton with retained connectivity and structural properties. The output requirements of a thinning procedure often vary with…