6,209 research outputs found
3D Forward and Back-Projection for X-Ray CT Using Separable Footprints
Iterative methods for 3D image reconstruction have the potential to improve image quality over conventional filtered back projection (FBP) in X-ray computed tomography (CT). However, the computation burden of 3D cone-beam forward and back-projectors is one of the greatest challenges facing practical adoption of iterative methods for X-ray CT. Moreover, projector accuracy is also important for iterative methods. This paper describes two new separable footprint (SF) projector methods that approximate the voxel footprint functions as 2D separable functions. Because of the separability of these footprint functions, calculating their integrals over a detector cell is greatly simplified and can be implemented efficiently. The SF-TR projector uses trapezoid functions in the transaxial direction and rectangular functions in the axial direction, whereas the SF-TT projector uses trapezoid functions in both directions. Simulations and experiments showed that both SF projector methods are more accurate than the distance-driven (DD) projector, which is a current state-of-the-art method in the field. The SF-TT projector is more accurate than the SF-TR projector for rays associated with large cone angles. The SF-TR projector has similar computation speed with the DD projector and the SF-TT projector is about two times slower.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85876/1/Fessler5.pd
PYRO-NN: Python Reconstruction Operators in Neural Networks
Purpose: Recently, several attempts were conducted to transfer deep learning
to medical image reconstruction. An increasingly number of publications follow
the concept of embedding the CT reconstruction as a known operator into a
neural network. However, most of the approaches presented lack an efficient CT
reconstruction framework fully integrated into deep learning environments. As a
result, many approaches are forced to use workarounds for mathematically
unambiguously solvable problems. Methods: PYRO-NN is a generalized framework to
embed known operators into the prevalent deep learning framework Tensorflow.
The current status includes state-of-the-art parallel-, fan- and cone-beam
projectors and back-projectors accelerated with CUDA provided as Tensorflow
layers. On top, the framework provides a high level Python API to conduct FBP
and iterative reconstruction experiments with data from real CT systems.
Results: The framework provides all necessary algorithms and tools to design
end-to-end neural network pipelines with integrated CT reconstruction
algorithms. The high level Python API allows a simple use of the layers as
known from Tensorflow. To demonstrate the capabilities of the layers, the
framework comes with three baseline experiments showing a cone-beam short scan
FDK reconstruction, a CT reconstruction filter learning setup, and a TV
regularized iterative reconstruction. All algorithms and tools are referenced
to a scientific publication and are compared to existing non deep learning
reconstruction frameworks. The framework is available as open-source software
at \url{https://github.com/csyben/PYRO-NN}. Conclusions: PYRO-NN comes with the
prevalent deep learning framework Tensorflow and allows to setup end-to-end
trainable neural networks in the medical image reconstruction context. We
believe that the framework will be a step towards reproducible researchComment: V1: Submitted to Medical Physics, 11 pages, 7 figure
High resolution image reconstruction with constrained, total-variation minimization
This work is concerned with applying iterative image reconstruction, based on
constrained total-variation minimization, to low-intensity X-ray CT systems
that have a high sampling rate. Such systems pose a challenge for iterative
image reconstruction, because a very fine image grid is needed to realize the
resolution inherent in such scanners. These image arrays lead to
under-determined imaging models whose inversion is unstable and can result in
undesirable artifacts and noise patterns. There are many possibilities to
stabilize the imaging model, and this work proposes a method which may have an
advantage in terms of algorithm efficiency. The proposed method introduces
additional constraints in the optimization problem; these constraints set to
zero high spatial frequency components which are beyond the sensing capability
of the detector. The method is demonstrated with an actual CT data set and
compared with another method based on projection up-sampling.Comment: This manuscript appears in the proceedings of the 2010 IEEE medical
imaging conferenc
Three-Dimensional Reconstruction Algorithm for a Reverse-Geometry Volumetric CT System With a Large-Array Scanned Source
We have proposed a CT system design to rapidly produce volumetric images with negligible cone beam artifacts. The investigated system uses a large array scanned source with a smaller array of fast detectors. The x-ray source is electronically steered across a 2D target every few milliseconds as the system rotates. The proposed reconstruction algorithm for this system is a modified 3D filtered backprojection method. The data are rebinned into 2D parallel ray projections, most of which are tilted with respect to the axis of rotation. Each projection is filtered with a 2D kernel and backprojected onto the desired image matrix. To ensure adequate spatial resolution and low artifact level, we rebin the data onto an array that has sufficiently fine spatial and angular sampling. Due to finite sampling in the real system, some of the rebinned projections will be sparse, but we hypothesize that the large number of views will compensate for the data missing in a particular view. Preliminary results using simulated data with the expected discrete sampling of the source and detector arrays suggest that high resolution
Computed tomography from X-rays: old 2-D results, new 3-D problems
We consider old results on 2-D computerized tomography methods and their relevance to new fully 3-D problems. We examine the 2-D filtered back-projection method (FBP) from several perspectives to better understand how it works. Based on that understanding, we question whether stable, reliable reconstruction algorithms can be found for wide-detector cone-beam 3-D machines with their resulting large-slant beams. We use a numerical method of "point response function fitting" to compute convolution kernels H(u, v) (for use with back-projection) for a model slant-beam problem. These kernels exhibit disturbing growing and spreading oscillations which would greatly amplify errors in the projection data
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