Image reconstruction with a shift‐variant filtration in circular cone‐beam CT

It is well known that cone‐beam data acquired with a circular orbit are insufficient for exact image reconstruction. Despite this, because a cone‐beam scanning configuration with a circular orbit is easy to implement in practice, it has been widely employed for data acquisition in, e.g., micro‐CT and CT imaging in radiation therapy. The algorithm developed by Feldkamp, Davis, and Kress (FDK) and its modifications, such as the Tent–FDK (T‐FDK) algorithm, have been used for image reconstruction from circular cone‐beam data. In this work, we present an algorithm with spatially shift‐variant filtration for image reconstruction in circular cone‐beam CT. We performed computer‐simulation studies to compare the proposed and existing algorithms. Numerical results in these studies demonstrated that the proposed algorithm has resolution properties comparable to, and noise properties better than, the FDK algorithm. As compared to the T‐FDK algorithm, our proposed algorithm reconstructs images with an improved in‐plane spatial resolution. © 2005 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 14, 213–221, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20026

[1]  Xiaochuan Pan,et al.  Half-scan fan-beam computed tomography with improved noise and resolution properties. , 2003, Medical physics.

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

[3]  Rolf Clackdoyle,et al.  A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection , 1994, IEEE Trans. Medical Imaging.

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

[5]  Ronald J. Jaszczak,et al.  Fan-beam reconstruction algorithm for a spatially varying focal length collimator , 1993, IEEE Trans. Medical Imaging.

[6]  B M Tsui,et al.  An analytical reconstruction algorithm for multifocal converging-beam SPECT. , 1994, Physics in medicine and biology.

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

[8]  S. Samarasekera,et al.  Exact cone beam CT with a spiral scan. , 1998, Physics in medicine and biology.

[9]  M. Grass,et al.  3D cone-beam CT reconstruction for circular trajectories. , 2000, Physics in medicine and biology.

[10]  Tsuneo Saito,et al.  Derivation and implementation of a cone-beam reconstruction algorithm for nonplanar orbits , 1994, IEEE Trans. Medical Imaging.

[11]  Kyle J. Myers,et al.  Ideal Observer Models of Visual Signal Detection , 2000 .

[12]  G T Gullberg,et al.  A cone-beam tomography algorithm for orthogonal circle-and-line orbit. , 1992, Physics in medicine and biology.

[13]  Ruola Ning,et al.  A cone-beam reconstruction algorithm for circle-plus-arc data-acquisition geometry , 1999, IEEE Transactions on Medical Imaging.

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

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

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

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

[18]  Hui Hu,et al.  AN IMPROVED CONE-BEAM RECONSTRUCTION ALGORITHM FOR THE CIRCULAR ORBIT , 2006 .

[19]  Rolf Clackdoyle,et al.  Direct reconstruction of cone-beam data acquired with a vertex path containing a circle , 1998, IEEE Trans. Image Process..

[20]  Xiaochuan Pan,et al.  Optimal noise control in and fast reconstruction of fan-beam computed tomography image. , 1999, Medical physics.

[21]  Xiaochuan Pan,et al.  Image reconstruction with shift-variant filtration and its implication for noise and resolution properties in fan-beam computed tomography. , 2003, Medical physics.