A factorization approach for cone-beam reconstruction on a circular short-scan

In this paper, we introduce a new algorithm for 3-D image reconstruction from cone-beam (CB) projections acquired along a partial circular scan. Our algorithm is based on a novel, exact factorization of the initial 3-D reconstruction problem into a set of independent 2-D inversion problems, each of which corresponds to finding the object density on one, single plane. Any such 2-D inversion problem is solved numerically using a projected steepest descent iteration scheme. We present a numerical evaluation of our factorization algorithm using computer-simulated CB data, without and with noise, of the FORBILD head phantom and of a disk phantom. First, we study quantitatively the impact of the reconstruction parameters on the algorithm performance. Next, we present reconstruction results for visual assessment of the achievable image quality and provide, for comparison, results obtained with two other state-of-the-art reconstruction algorithms for the circular short-scan.

[1]  A. Bakushinskii,et al.  Ill-Posed Problems: Theory and Applications , 1994 .

[2]  O. Nelles,et al.  An Introduction to Optimization , 1996, IEEE Antennas and Propagation Magazine.

[3]  Li Zhang,et al.  An error-reduction-based algorithm for cone-beam computed tomography. , 2004, Medical physics.

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

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

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

[7]  A. Iusem.  On the convergence properties of the projected gradient method for convex optimization , 2003 .

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

[9]  Satoshi Kawata,et al.  Optical microscope tomography. II. Nonnegative constraint by a gradient-projection method , 1988 .

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

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

[12]  Lei Zhu,et al.  An Efficient Estimation Method for Reducing the Axial Intensity Drop in Circular Cone-Beam CT , 2008, Int. J. Biomed. Imaging.

[13]  D. Parker.  Optimal short scan convolution reconstruction for fan beam CT , 1982 .

[14]  Günter Lauritsch,et al.  Cone-beam Reconstruction on a Circular Short-Scan using the Factorization Approach , .

[15]  Hengyong Yu,et al.  Feldkamp-type VOI reconstruction from super-short-scan cone-beam data. , 2004, Medical physics.

[16]  Y. Yao,et al.  On Early Stopping in Gradient Descent Learning , 2007 .

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

[18]  Rebecca Fahrig,et al.  ResearchArticle An Efficient Estimation Method for Reducing the Axial Intensity Drop in Circular Cone-Beam CT , 2008 .

[19]  J. Hsieh,et al.  A practical cone beam artifact correction algorithm , 2000, 2000 IEEE Nuclear Science Symposium. Conference Record (Cat. No.00CH37149).

[20]  Y. Liu,et al.  Half-scan cone-beam x-ray microtomography formula. , 2008, Scanning.

[21]  David V. Finch.  CONE BEAM RECONSTRUCTION WITH SOURCES ON A CURVE , 1985 .

[22]  Jiang Hsieh,et al.  Conjugate backprojection approach for cone beam artifact reduction , 2006, SPIE Medical Imaging.

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

[24]  Dominic J. Heuscher,et al.  Image reconstruction from cone-beam data on a circular short-scan , 2002, SPIE Medical Imaging.

[25]  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.

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

[27]  Emil Y. Sidky,et al.  Region of interest reconstruction from truncated data in circular cone-beam CT , 2006, IEEE Transactions on Medical Imaging.

[28]  Guang-Hong Chen,et al.  Arc based cone-beam reconstruction algorithm using an equal weighting scheme , 2007 .

[29]  Frank Natterer,et al.  Mathematical methods in image reconstruction , 2001, SIAM monographs on mathematical modeling and computation.