A New Weighting Scheme for Fan-beam and Circle Cone-beam CT Reconstructions

In this paper, we first present an arc based algorithm for fan-beam computed tomography (CT) reconstruction via applying Katsevich’s helical CT formula to 2D fan-beam CT reconstruction. Then, we propose a new weighting function to deal with the redundant projection data. By extending the weighted arc based fan-beam algorithm to circle cone-beam geometry, we also obtain a new FDK-similar algorithm for circle cone-beam CT reconstruction. Experiments show that our methods can obtain higher PSNR and SSIM compared to the Parker-weighted conventional fan-beam algorithm and the FDK algorithm for super-short-scan trajectories.

[1]  Hiroyuki Kudo,et al.  Image reconstruction from fan-beam projections on less than a short scan , 2002, Physics in medicine and biology.

[2]  G. Herman,et al.  Fast Image Reconstruction Based on a Radon Inversion Formula Appropriate for Rapidly Collected Data , 1977 .

[3]  Alexander Katsevich,et al.  Theoretically Exact Filtered Backprojection-Type Inversion Algorithm for Spiral CT , 2002, SIAM J. Appl. Math..

[4]  K. Taguchi,et al.  Practical hybrid convolution algorithm for helical CT reconstruction , 2004, IEEE Transactions on Nuclear Science.

[5]  A note on computing the derivative at a constant direction. , 2011, Physics in medicine and biology.

[6]  Xiaochuan Pan,et al.  Exact image reconstruction on PI-lines from minimum data in helical cone-beam CT. , 2004, Physics in medicine and biology.

[7]  G. Wang,et al.  A general cone-beam reconstruction algorithm , 1993, IEEE Trans. Medical Imaging.

[8]  Hiroyuki Kudo,et al.  Exact and approximate algorithms for helical cone-beam CT. , 2004, Physics in medicine and biology.

[9]  Shaojie Tang,et al.  Axial Cone-Beam Reconstruction by Weighted BPF/DBPF and Orthogonal Butterfly Filtering , 2016, IEEE Transactions on Biomedical Engineering.

[10]  F. Noo,et al.  A two-step Hilbert transform method for 2D image reconstruction. , 2004, Physics in medicine and biology.

[11]  Karl Stierstorfer,et al.  Accurate helical cone-beam CT reconstruction with redundant data. , 2009, Physics in medicine and biology.

[12]  C. McCollough.  TU-FG-207A-04: Overview of the Low Dose CT Grand Challenge. , 2016, Medical physics.

[13]  J. Hsieh,et al.  A three-dimensional weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT under a circular source trajectory , 2005, Physics in medicine and biology.

[14]  Hiroyuki Kudo,et al.  New super-short-scan algorithms for fan-beam and cone-beam reconstruction , 2002, 2002 IEEE Nuclear Science Symposium Conference Record.

[15]  Frédéric Noo,et al.  Exact helical reconstruction using native cone-beam geometries. , 2003, Physics in medicine and biology.

[16]  Berthold K. P. Horn.  Fan-beam reconstruction methods , 1979, Proceedings of the IEEE.

[17]  Katsuyuki Taguchi,et al.  A new weighting scheme for cone-beam helical CT to reduce the image noise. , 2004, Physics in medicine and biology.

[18]  Gengsheng Lawrence Zeng,et al.  Hilbert Transform Based FBP Algorithm for Fan-Beam CT Full and Partial Scans , 2007, IEEE Transactions on Medical Imaging.

[19]  Guang-Hong Chen,et al.  A new framework of image reconstruction from fan beam projections. , 2003, Medical physics.

[20]  L. Feldkamp,et al.  Practical cone-beam algorithm , 1984 .

[21]  Xiaochuan Pan,et al.  A rebinned backprojection-filtration algorithm for image reconstruction in helical cone-beam CT , 2007, Physics in medicine and biology.

[22]  Tianye Niu,et al.  Three-Dimensional Weighting in Cone Beam FBP Reconstruction and Its Transformation Over Geometries , 2018, IEEE Transactions on Biomedical Engineering.

[23]  J. Hsieh,et al.  A three-dimensional-weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT—helical scanning , 2006, Physics in medicine and biology.

[24]  M D Silver.  A method for including redundant data in computed tomography. , 2000, Medical physics.

[25]  Xiaochuan Pan,et al.  Image reconstruction with a shift‐variant filtration in circular cone‐beam CT , 2004, Int. J. Imaging Syst. Technol..

[26]  Zhengrong Liang,et al.  Adaptive-weighted total variation minimization for sparse data toward low-dose x-ray computed tomography image reconstruction , 2012, Physics in medicine and biology.

[27]  Alexander Katsevich,et al.  An improved exact filtered backprojection algorithm for spiral computed tomography , 2004, Adv. Appl. Math..

[28]  K. Stierstorfer,et al.  Weighted FBP--a simple approximate 3D FBP algorithm for multislice spiral CT with good dose usage for arbitrary pitch. , 2004, Physics in medicine and biology.

[29]  Günter Lauritsch,et al.  A new scheme for view-dependent data differentiation in fan-beam and cone-beam computed tomography. , 2007, Physics in medicine and biology.

[30]  D L Parker,et al.  Optimal short scan convolution reconstruction for fanbeam CT. , 1982, Medical physics.