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

Optical tomography: Image improvement using mixed projection of parallel and fan beam modes

Mixed parallel and fan beam projection is a technique used to increase the quality images. This research focuses on enhancing the image quality in optical tomography. Image quality can be defined by measuring the Peak Signal to Noise Ratio (PSNR) and Normalized Mean Square Error (NMSE) parameters. The findings of this research prove that by combining parallel and fan beam projection, the image quality can be increased by more than 10%in terms of its PSNR value and more than 100% in terms of its NMSE value compared to a single parallel beam

Reconstruction of binary matrices from fan-beam projections

The problem of the reconstruction of binary matrices from their fan-beam projections is investigated here. A fan-beam projection model is implemented and afterwards employed in systematic experiments to determine the optimal parameter values for a data acquisition and reconstruction algorithm. The fan-beam model, the reconstruction algorithm which uses the optimization method of Simulated Annealing, the simulation experiments, and the results are then discussed in turn

Singular value decomposition for the 2D fan-beam Radon transform of tensor fields

In this article we study the fan-beam Radon transform ${\cal D}_m$ of symmetrical solenoidal 2D tensor fields of arbitrary rank $m$ in a unit disc $\mathbb D$ as the operator, acting from the object space ${\mathbf L}_{2}(\mathbb D; {\bf S}_m)$ to the data space $L_2([0,2\pi)\times[0,2\pi)).$ The orthogonal polynomial basis ${\bf s}^{(\pm m)}_{n,k}$ of solenoidal tensor fields on the disc $\mathbb D$ was built with the help of Zernike polynomials and then a singular value decomposition (SVD) for the operator ${\cal D}_m$ was obtained. The inversion formula for the fan-beam tensor transform ${\cal D}_m$ follows from this decomposition. Thus obtained inversion formula can be used as a tomographic filter for splitting a known tensor field into potential and solenoidal parts. Numerical results are presented.Comment: LaTeX, 37 pages with 5 figure

A new method of observing weak extended x-ray sources with RHESSI

We present a new method, fan-beam modulation, for observing weak extended x-ray sources with the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI). This space-based solar x-ray and gamma-ray telescope has much greater sensitivity than previous experiments in the 3-25 keV range, but is normally not well suited to detecting extended sources since their signal is not modulated by RHESSI's rotating grids. When the spacecraft is offpointed from the target source, however, the fan-beam modulation time-modulates the transmission by shadowing resulting from exploiting the finite thickness of the grids. In this paper we detail how the technique is implemented and verify its consistency with sources with clear known signals that have occurred during RHESSI offpointing: microflares and the Crab Nebula. In both cases the results are consistent with previous and complementary measurements. Preliminary work indicates that this new technique allows RHESSI to observe the integrated hard x-ray spectrum of weak extended sources on the quiet Sun.Comment: Publishe