The radon-split method for helical cone-beam CT and its application to nongated reconstruction

The mathematical analysis of exact filtered back-projection algorithms is strictly related to Radon inversion. We show how filter-lines can be defined for the helical trajectory, which serve for the extraction of contributions of particular kinds of Radon-planes. Due to the Fourier-slice theorem, Radon-planes with few intersections with the helix are associated with low-frequency contributions to transversal slices. This insight leads to different applications of the new method. The application presented here enables the incorporation of an arbitrary amount of redundant data in an approximate way. This means that the back-projection is not restricted to an n-Pi interval. A detailed mathematical analysis, in which we demonstrate how the defined filter-lines work, concludes this paper

[1]  Marc Kachelriess,et al.  ECG-correlated imaging of the heart with subsecond multislice spiral CT , 2000, IEEE Transactions on Medical Imaging.

[2]  E. Sidky,et al.  Minimum data image reconstruction algorithms with shift-invariant filtering for helical, cone-beam CT , 2005, Physics in medicine and biology.

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

[4]  A. Katsevich.  On two versions of a 3π algorithm for spiral CT , 2004 .

[5]  P. Koken,et al.  Motion artefact reduction for exact cone-beam CT reconstruction algorithms , 2003, 2003 IEEE Nuclear Science Symposium. Conference Record (IEEE Cat. No.03CH37515).

[6]  Rolf Clackdoyle,et al.  Cone-beam reconstruction using the backprojection of locally filtered projections , 2005, IEEE Transactions on Medical Imaging.

[7]  Michael Grass,et al.  The n-PI-method for helical cone-beam CT , 2000, IEEE Transactions on Medical Imaging.

[8]  Willi A Kalender,et al.  Extended parallel backprojection for standard three-dimensional and phase-correlated four-dimensional axial and spiral cone-beam CT with arbitrary pitch, arbitrary cone-angle, and 100% dose usage. , 2004, Medical physics.

[9]  Alexander Katsevich,et al.  Theoretically exact FBP-type inversion algorithm for spiral CT , 2001 .

[10]  R Proksa,et al.  The frequency split method for helical cone-beam reconstruction. , 2004, Medical physics.

[11]  Thomas Köhler,et al.  EnPiT: filtered back-projection algorithm for helical CT using an n-Pi acquisition , 2005, IEEE Transactions on Medical Imaging.

[13]  Michael Grass,et al.  CEnPiT: helical cardiac CT reconstruction. , 2006, Medical physics.

[14]  S. Leng,et al.  Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data , 2004, Physics in medicine and biology.

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

[16]  R. Proksa,et al.  A quasiexact reconstruction algorithm for helical CT using a 3-Pi acquisition. , 2003, Medical physics.

[17]  F Noo,et al.  Redundant data and exact helical cone-beam reconstruction. , 2004, Physics in medicine and biology.

[18]  F. Noo,et al.  Cone-beam reconstruction using 1D filtering along the projection of M-lines , 2005 .

[19]  A. Katsevich,et al.  Exact filtered backprojection reconstruction for dynamic pitch helical cone beam computed tomography. , 2004, Physics in medicine and biology.

[20]  F. Natterer.  The Mathematics of Computerized Tomography , 1986 .

[21]  Henrik Turbell,et al.  Cone-Beam Reconstruction Using Filtered Backprojection , 2001 .

[22]  A. Katsevich.  Analysis of an exact inversion algorithm for spiral cone-beam CT. , 2002, Physics in medicine and biology.

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