Studies on Palamodov's algorithm for cone-beam CT along a general curve

Inspired by Katsevich's exact helical cone-beam formula, Palamodov made the first attempt to perform exact image reconstruction from cone-beam data collected along a general scanning trajectory [1]. In contrast to the well-known general exact cone-beam reconstruction schemes formulated by Tuy, Smith, Grangeat and Katsevich, respectively, Palamodov's algorithm was intended to work with truncated data and without the need to specify any weighting function. In this paper, after reformulating Palamodov's formula and comparing it with Katsevich's helical cone-beam formula, we find that Palamodov's algorithm is not theoretically exact due to an inaccurate estimate. Then, we numerically implement it using a planar detector array and simulate the case of cone-beam CT with a nonstandard saddle curve as the scanning trajectory. The reconstruction results suggest that Palamodov's algorithm is an attractive algorithm for approximate cone-beam reconstruction in the case of general cone-beam scanning.

[1]  Hengyong Yu,et al.  Katsevich-type algorithms for variable radius spiral cone-beam CT , 2004, SPIE Optics + Photonics.

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

[3]  Hengyong Yu,et al.  A family of analytic algorithms for cone-beam CT , 2004, SPIE Optics + Photonics.

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

[5]  Hengyong Yu,et al.  A unified framework for exact cone-beam reconstruction formulas. , 2005, Medical physics.

[6]  A. Katsevich.  A GENERAL SCHEME FOR CONSTRUCTING INVERSION ALGORITHMS FOR CONE BEAM CT , 2003 .

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

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

[9]  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.

[10]  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.

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

[12]  Emil Y. Sidky,et al.  A consistency condition for cone-beam CT with general source trajectories , 2005, SPIE Medical Imaging.

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

[14]  Hengyong Yu,et al.  Studies on implementation of the Katsevich algorithm for spiral cone-beam CT , 2004 .

[15]  Ge Wang,et al.  Top-level design and preliminary physical analysis for the first electron-beam micro-CT scanner , 2004 .

[16]  Hengyong Yu,et al.  Exact BPF and FBP algorithms for nonstandard saddle curves. , 2005, Medical physics.

[17]  Hengyong Yu,et al.  Studies on artifacts of the Katsevich algorithm for spiral cone-beam CT , 2004, SPIE Optics + Photonics.

[18]  P. Grangeat.  Mathematical framework of cone beam 3D reconstruction via the first derivative of the radon transform , 1991 .

[19]  H. Tuy.  AN INVERSION FORMULA FOR CONE-BEAM RECONSTRUCTION* , 1983 .

[20]  Bruce D. Smith.  Image Reconstruction from Cone-Beam Projections: Necessary and Sufficient Conditions and Reconstruction Methods , 1985, IEEE Transactions on Medical Imaging.

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

[22]  Ping Chin Cheng,et al.  Scanning cone-beam reconstruction algorithms for x-ray microtomography , 1992, Optics & Photonics.

[23]  Ge Wang,et al.  Filtered backprojection formula for exact image reconstruction from cone-beam data along a general scanning curve. , 2004, Medical physics.

[24]  Hengyong Yu,et al.  A differentiable Shepp–Logan phantom and its applications in exact cone-beam CT , 2005, Physics in medicine and biology.

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

[26]  V. Palamodov,et al.  Reconstruction from ray integrals with sources on a curve , 2004 .