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Industrial X-ray cone-beam CT (XCT) scanners are widely used for scientific imaging and non-destructive characterization. Industrial CBCT scanners use large detectors containing millions of pixels and the subsequent 3D reconstructions can…
In this work, we investigate the use of spatio-temporalImplicit Neural Representations (INRs) for dynamic X-ray computed tomography (XCT) reconstruction under interlaced acquisition schemes. The proposed approach combines ADMM-based…
Discrete-time models are very convenient to simulate a nonlinear system on a computer. In order to build the discrete-time simulation models for the nonlinear feedback systems (which is a very important class of systems in many…
Iterative projection methods may become trapped at non-solutions when the constraint sets are nonconvex. Two kinds of parameters are available to help avoid this behavior and this study gives examples of both. The first kind of parameter,…
We consider estimators obtained by iterates of the conjugate gradient (CG) algorithm applied to the normal equation of prototypical statistical inverse problems. Stopping the CG algorithm early induces regularisation, and optimal…
Computed tomography (CT) relies on precise patient immobilization during image acquisition. Nevertheless, motion artifacts in the reconstructed images can persist. Motion compensation methods aim to correct such artifacts post-acquisition,…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
Almost all known image reconstruction algorithms for photoacoustic and thermoacoustic tomography assume that the acoustic waves leave the region of interest after a finite time. This assumption is reasonable if the reflections from the…
We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…
The aim of this paper is to investigate the use of an entropic projection method for the iterative regularization of linear ill-posed problems. We derive a closed form solution for the iterates and analyze their convergence behaviour both…
In this paper we propose a new approach for tomographic reconstruction with spatially varying regularization parameter. Our work is based on the SA-TV image restoration model proposed in [3] where an automated parameter selection rule for…
We analyze inexact fixed point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed point…
This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from…
In the last years, the design of image reconstruction methods in the field of quantitative Magnetic Resonance Imaging (qMRI) has experienced a paradigm shift. Often, when dealing with (quantitative) MR image reconstruction problems, one is…
Computed tomography (CT) has been developed as a non-destructive technique for observing minute internal images of samples. It has been difficult to obtain photo-realistic (clean or clear) CT images due to various unwanted artifacts…
Iterative learning to infer approaches have become popular solvers for inverse problems. However, their memory requirements during training grow linearly with model depth, limiting in practice model expressiveness. In this work, we propose…
Randomized subspace embedding methods have had a great impact on the solution of a linear least squares (LS) problem by reducing its row dimension, leading to a randomized or sketched LS (sLS) problem, and use the solution of the sLS…
Among the fundamental questions in computer science, at least two have a deep impact on mathematics. What can computation compute? How many steps does a computation require to solve an instance of the 3-SAT problem? Our work addresses the…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
We propose a new modeling approach for scatter estimation and descattering in polyenergetic X-ray computed tomography (CT) based on fitting models to local neighborhoods of a training set. X-ray CT is widely used in medical and industrial…