Tomographic reconstruction of a three-dimensional magnetization vector field

Using x-ray magnetic nanotomography the internal magnetization structure within extended samples can be determined with high spatial resolution and element specificity, without the need for assumptions or prior knowledge of the magnetic properties of a sample. Here we present the details of a new algorithm for the reconstruction of a three-dimensional magnetization vector field, discussing both the mathematical description of the problem, and details of the gradient-based iterative reconstruction routine. To test the accuracy of the algorithm the method is demonstrated for a complex simulated magnetization configuration obtained from micromagnetic simulations. The reconstruction of the complex three-dimensional magnetic nanostructure, including the surroundings of magnetic singularities (or Bloch points), exhibits an excellent qualitative and quantitative agreement with the simulated magnetic structure. This method provides a robust route for the reconstruction of internal three-dimensional magnetization structures obtained from x-ray magnetic tomographic datasets, which can be acquired with either hard or soft x-rays, and can be applied to a wide variety of three-dimensional magnetic systems

Tomographic Image Reconstruction of Fan-Beam Projections with Equidistant Detectors using Partially Connected Neural Networks

We present a neural network approach for tomographic imaging problem using interpolation methods and fan-beam projections. This approach uses a partially connected neural network especially assembled for solving tomographic\ud reconstruction with no need of training. We extended the calculations to perform reconstruction with interpolation and to allow tomography of fan-beam geometry. The main goal is to aggregate speed while maintaining or improving the quality of the tomographic reconstruction process

Three-dimensional reconstruction from projections

summary:Computerized tomograhphy is a technique for computation and visualization of density (i.e. X- or $\gamma$-ray absorption coefficients) distribution over a cross-sectional anatomic plane from a set of projections. Three-dimensional reconstruction may be obtained by using a system of parallel planes. For the reconstruction of the transverse section it is necessary to choose an appropriate method taking into account the geometry of the data collection, the noise in projection data, the amount of data, the computer power available, the accuracy required etc. In the paper the theory related to the convolution reconstruction methods is reviewed. The principal contribution consists in the exact mathematical treatment of Radon's inverse transform based on the concepts of the regularization of a function and the generalized function. This approach naturally leads to the employment of the generalized Fourier transform. Reconstructions using simulated projection data are presented for both the parallel and divergent-ray collection geometries

Toward optimal X-ray flux utilization in breast CT

A realistic computer-simulation of a breast computed tomography (CT) system and subject is constructed. The model is used to investigate the optimal number of views for the scan given a fixed total X-ray fluence. The reconstruction algorithm is based on accurate solution to a constrained, TV-minimization problem, which has received much interest recently for sparse-view CT data.Comment: accepted to the 11th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine 201