Yan Xia, Martin Berger, Sebastian Bauer, Shiyang Hu, Andre Aichert, Andreas Maier
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An Improved Extrapolation Scheme for Truncated CT Data Using 2D Fourier-Based Helgason-Ludwig Consistency Conditions.
We improve data extrapolation for truncated computed tomography (CT) projections by using Helgason-Ludwig (HL) consistency conditions that mathematically describe the overlap of information between projections. First, we theoretically derive a 2D Fourier representation of the HL consistency conditions from their original formulation (projection moment theorem), for both parallel-beam and fan-beam imaging geometry. The derivation result indicates that there is a zero energy region forming a double-wedge shape in 2D Fourier domain. This observation is also referred to as the Fourier property of a sinogram in the previous literature. The major benefit of this representation is that the consistency conditions can be efficiently evaluated via 2D fast Fourier transform (FFT). Then, we suggest a method that extrapolates the truncated projections with data from a uniform ellipse of which the parameters are determined by optimizing these consistency conditions. The forward projection of the optimized ellipse can be used to complete the truncation data. The proposed algorithm is evaluated using simulated data and reprojections of clinical data. Results show that the root mean square error (RMSE) is reduced substantially, compared to a state-of-the-art extrapolation method.
期刊介绍:
The International Journal of Biomedical Imaging is managed by a board of editors comprising internationally renowned active researchers. The journal is freely accessible online and also offered for purchase in print format. It employs a web-based review system to ensure swift turnaround times while maintaining high standards. In addition to regular issues, special issues are organized by guest editors. The subject areas covered include (but are not limited to):
Digital radiography and tomosynthesis
X-ray computed tomography (CT)
Magnetic resonance imaging (MRI)
Single photon emission computed tomography (SPECT)
Positron emission tomography (PET)
Ultrasound imaging
Diffuse optical tomography, coherence, fluorescence, bioluminescence tomography, impedance tomography
Neutron imaging for biomedical applications
Magnetic and optical spectroscopy, and optical biopsy
Optical, electron, scanning tunneling/atomic force microscopy
Small animal imaging
Functional, cellular, and molecular imaging
Imaging assays for screening and molecular analysis
Microarray image analysis and bioinformatics
Emerging biomedical imaging techniques
Imaging modality fusion
Biomedical imaging instrumentation
Biomedical image processing, pattern recognition, and analysis
Biomedical image visualization, compression, transmission, and storage
Imaging and modeling related to systems biology and systems biomedicine
Applied mathematics, applied physics, and chemistry related to biomedical imaging
Grid-enabling technology for biomedical imaging and informatics