773 research outputs found
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
Application of constrained optimisation techniques in electrical impedance tomography
A Constrained Optimisation technique is described for the reconstruction of temporal resistivity images. The approach solves the Inverse problem by optimising a cost function under constraints, in the form of normalised boundary potentials.
Mathematical models have been developed for two different data collection methods for the chosen criterion. Both of these models express the reconstructed image in terms of one dimensional (I-D) Lagrange multiplier functions. The reconstruction problem becomes one of estimating these 1-D functions from the
normalised boundary potentials. These models are based on a cost criterion of the minimisation of the variance between the reconstructed resistivity distribution and the true resistivity distribution.
The methods presented In this research extend the algorithms previously developed for X-ray systems. Computational efficiency is enhanced by exploiting the structure of the associated system matrices. The structure of the system matrices was preserved in the Electrical Impedance Tomography (EIT) implementations by applying a weighting due to non-linear current distribution during the backprojection of the Lagrange multiplier functions.
In order to obtain the best possible reconstruction it is important to consider the effects of noise in the boundary data. This is achieved by using a fast algorithm which matches the statistics of the error in the approximate inverse of the associated system matrix with the statistics of the noise error in the boundary data. This yields the optimum solution with the available boundary data. Novel approaches have been developed to produce the Lagrange multiplier functions.
Two alternative methods are given for the design of VLSI implementations of hardware accelerators to improve computational efficiencies. These accelerators are designed to implement parallel geometries and are modelled using a verification
description language to assess their performance capabilities
Stretched sinograms for limited-angle tomographic reconstruction with neural networks
We present a direct method for limited angle tomographic reconstruction using
convolutional networks. The key to our method is to first stretch every tilt
view in the direction perpendicular to the tilt axis by the secant of the tilt
angle. These stretched views are then fed into a 2-D U-Net which directly
outputs the 3-D reconstruction. We train our networks by minimizing the mean
squared error between the network's generated reconstruction and a ground truth
3-D volume. To demonstrate and evaluate our method, we synthesize tilt views
from a 3-D image of fly brain tissue acquired with Focused Ion Beam Scanning
Electron Microscopy. We compare our method to using a U-Net to directly
reconstruct the unstretched tilt views and show that this simple stretching
procedure leads to significantly better reconstructions. We also compare to
using a network to clean up reconstructions generated by backprojection and
filtered backprojection, and find that this simple stretching procedure also
gives lower mean squared error on previously unseen images
Fast algorithms and efficient GPU implementations for the Radon transform and the back-projection operator represented as convolution operators
The Radon transform and its adjoint, the back-projection operator, can both
be expressed as convolutions in log-polar coordinates. Hence, fast algorithms
for the application of the operators can be constructed by using FFT, if data
is resampled at log-polar coordinates. Radon data is typically measured on an
equally spaced grid in polar coordinates, and reconstructions are represented
(as images) in Cartesian coordinates. Therefore, in addition to FFT, several
steps of interpolation have to be conducted in order to apply the Radon
transform and the back-projection operator by means of convolutions.
Both the interpolation and the FFT operations can be efficiently implemented
on Graphical Processor Units (GPUs). For the interpolation, it is possible to
make use of the fact that linear interpolation is hard-wired on GPUs, meaning
that it has the same computational cost as direct memory access. Cubic order
interpolation schemes can be constructed by combining linear interpolation
steps which provides important computation speedup.
We provide details about how the Radon transform and the back-projection can
be implemented efficiently as convolution operators on GPUs. For large data
sizes, speedups of about 10 times are obtained in relation to the computational
times of other software packages based on GPU implementations of the Radon
transform and the back-projection operator. Moreover, speedups of more than a
1000 times are obtained against the CPU-implementations provided in the MATLAB
image processing toolbox
Neural network Hilbert transform based filtered backprojection for fast inline x-ray inspection
X-ray imaging is an important tool for quality control since it allows to inspect the interior of products in a non-destructive way. Conventional x-ray imaging, however, is slow and expensive. Inline x-ray inspection, on the other hand, can pave the way towards fast and individual quality control, provided that a sufficiently high throughput can be achieved at a minimal cost. To meet these criteria, an inline inspection acquisition geometry is proposed where the object moves and rotates on a conveyor belt while it passes a fixed source and detector. Moreover, for this acquisition geometry, a new neural-network-based reconstruction algorithm is introduced: the neural network Hilbert transform based filtered backprojection. The proposed algorithm is evaluated both on simulated and real inline x-ray data and has shown to generate high quality reconstructions of 400 x 400 reconstruction pixels within 200 ms, thereby meeting the high throughput criteria
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