Regions of Backprojection and Comet Tail Artifacts for Pi-Line Reconstruction Formulas in Tomography

We explore two characteristic features of x-ray computed tomography inversion formulas in two and three dimensions that are dependent on $\pi$-lines. In such formulas the data from a given source position contribute only to the reconstruction of $f(\mathbf{x})$ for $\mathbf{x}$ in a certain region, called the region of backprojection. The second characteristic is a certain small artifact in the reconstruction called a comet tail artifact. We propose that the comet tail artifact is closely related to the boundary of the region of backprojection and make this relationship precise, developing a general theory of the region of backprojection, its boundary, and the location of the artifact in helical and fan-beam tomography. This theory is applied to a number of specific examples and confirmed by numerical experiments. Furthermore it is demonstrated that a strong comet tail artifact appears in numerical reconstructions from misaligned fan-beam data. A numerical method for using the artifact to find the correct...

[1]  Alexander Katsevich,et al.  A Study of 1PI Algorithms for a General Class of Curves , 2008, SIAM J. Imaging Sci..

[2]  Xiaochuan Pan,et al.  Image reconstruction in regions-of-interest from truncated projections in a reduced fan-beam scan , 2005, Physics in medicine and biology.

[3]  Steven H. Izen,et al.  A fast algorithm to compute the -line through points inside a helix cylinder , 2006 .

[4]  Hengyong Yu,et al.  A general exact reconstruction for cone-beam CT via backprojection-filtration , 2005, IEEE Transactions on Medical Imaging.

[5]  Adel Faridani,et al.  Numerical and theoretical explorations in helical and fan-beam tomography , 2008 .

[6]  Xiaochuan Pan,et al.  An extended data function and its generalized backprojection for image reconstruction in helical cone-beam CT. , 2004, Physics in medicine and biology.

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

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

[9]  Stephen F. Keevil,et al.  IEEE Nuclear Science Symposium Conference Record , 2013 .

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

[11]  Per-Erik Danielsson,et al.  An improved PI-method for reconstruction from helical cone-beam projections , 1999, 1999 IEEE Nuclear Science Symposium. Conference Record. 1999 Nuclear Science Symposium and Medical Imaging Conference (Cat. No.99CH37019).

[12]  I. Gel'fand,et al.  Crofton's function and inversion formulas in real integral geometry , 1991 .

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

[14]  Hiroyuki Kudo,et al.  Truncated Hilbert transform and image reconstruction from limited tomographic data , 2006 .

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

[16]  M. Bandstra,et al.  Measurements of Fukushima fallout by the Berkeley Radiological Air and Water Monitoring project , 2011, 2011 IEEE Nuclear Science Symposium Conference Record.

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

[18]  Ryan Andrew Hass.  pi-Line reconstruction formulas in computed tomography , 2009 .

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

[20]  Alexander Katsevich,et al.  Local Tomography and the Motion Estimation Problem , 2011, SIAM J. Imaging Sci..

[21]  M. Defrise,et al.  A solution to the long-object problem in helical cone-beam tomography. , 2000, Physics in medicine and biology.

[22]  M. Glas,et al.  Principles of Computerized Tomographic Imaging , 2000 .