Related papers: A learning-based method for solving ill-posed nonl…
Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse…
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 paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
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 the past few years, deep learning-based methods have demonstrated enormous success for solving inverse problems in medical imaging. In this work, we address the following question:\textit{Given a set of measurements obtained from real…
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…
Electrical impedance tomography (EIT) is a non-invasive imaging technique, capable of reconstructing images of the electrical conductivity of tissues and materials. It is popular in diverse application areas, from medical imaging to…
The aim of Electrical Impedance Tomography (EIT) is to determine the electrical conductivity distribution inside a domain by applying currents and measuring voltages on its boundary. Mathematically, the EIT reconstruction task can be…
This paper provides a new regularization method which is particularly suitable for linear exponentially ill-posed problems. Under logarithmic source conditions (which have a natural interpretation in terms of Sobolev spaces in the…
Regularization methods using prior knowledge are essential in solving ill-posed inverse problems such as Electrical Impedance Tomography (EIT). However, designing effective regularization and integrating prior information into EIT remains…
For electrical impedance tomography (EIT), most practical reconstruction methods are based on linearizing the underlying non-linear inverse problem. Recently, it has been shown that the linearized problem still contains the exact shape…
Electrical Impedance Tomography (EIT) aims to recover the internal conductivity and permittivity distributions of a body from electrical measurements taken on electrodes on the surface of the body. The reconstruction task is a severely…
This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…
Electrical impedance tomography (EIT) is a non-invasive functional imaging technology. In order to enhance the quality of lung EIT images, novel algorithms, namely LSTM-LSTM, LSTM-BiLSTM, BiLSTM-LSTM, and BiLSTM-BiLSTM, leveraging LSTM or…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
We review developments, issues and challenges in Electrical Impedance Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT, Manchester 2003. We focus on the necessity for three dimensional data collection and…
In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and…
Online optimisation studies the convergence of optimisation methods as the data embedded in the problem changes. Based on this idea, we propose a primal dual online method for nonlinear time-discrete inverse problems. We analyse the method…
Electrical Impedance Tomography (EIT) is a widely employed imaging technique in industrial inspection, geophysical prospecting, and medical imaging. However, the inherent nonlinearity and ill-posedness of EIT image reconstruction present…