Iterative reconstruction of cone-beam micro-ct data

The use of x-ray computed tomography (CT) scanners has become widespread in both clinical and preclinical contexts. CT scanners can be used to noninvasively test for anatomical anomalies as well as to diagnose and monitor disease progression. However, the data acquired by a CT scanner must be reconstructed prior to use and interpretation. A reconstruction algorithm processes the data and outputs a three dimensional image representing the x-ray attenuation properties of the scanned object. The algorithms in most widespread use today are based on filtered backprojection (FBP) methods. These algorithms are relatively fast and work well on high quality data, but cannot easily handle data with missing projections or considerable amounts of noise. On the other hand, iterative reconstruction algorithms may offer benefits in such cases, but the computational burden associated with iterative reconstructions is prohibitive. In this work, we address this computational burden and present methods that make iterative reconstruction of high-resolution CT data possible in a reasonable amount of time. Our proposed techniques include parallelization, ordered subsets, reconstruction region restriction, and a modified version of the SIRT algorithm that reduces the overall run-time. When combining all of these techniques; we can reconstruct a 512 × 512 × 1022 image from acquired micro-CT data in less than thirty minutes.

[1]  Wang,et al.  Iterative X-ray Cone-Beam Tomography for Metal Artifact Reduction and Local Region Reconstruction , 1999, Microscopy and Microanalysis.

[2]  Bjorn De Sutter,et al.  A Fast Algorithm to Calculate the Exact Radiological Path through a Pixel or Voxel Space , 1998 .

[3]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.

[4]  Gengsheng Lawrence Zeng,et al.  Unmatched projector/backprojector pairs in an iterative reconstruction algorithm , 2000, IEEE Transactions on Medical Imaging.

[5]  Michael T. Heath,et al.  Scientific Computing: An Introductory Survey , 1996 .

[6]  Jerry L Prince,et al.  Medical Imaging Signals and Systems , 2005 .

[7]  K. Tanabe.  Projection method for solving a singular system of linear equations and its applications , 1971 .

[8]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[9]  B. De Man,et al.  Distance-driven projection and backprojection , 2002, 2002 IEEE Nuclear Science Symposium Conference Record.

[10]  R. Jaszczak,et al.  Implementation of an accelerated iterative algorithm for cone-beam SPECT. , 1994, Physics in medicine and biology.

[11]  Jens Gregor,et al.  Distributed iterative image reconstruction for micro-CT with ordered-subsets and focus of attention problem reduction , 2004 .

[12]  G T Herman,et al.  ART: mathematics and applications. A report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction techniques. , 1973, Journal of theoretical biology.

[13]  R. Siddon.  Fast calculation of the exact radiological path for a three-dimensional CT array. , 1985, Medical physics.

[14]  B. De Man,et al.  Distance-driven projection and backprojection in three dimensions. , 2004, Physics in medicine and biology.

[15]  A. Kak,et al.  Simultaneous Algebraic Reconstruction Technique (SART): A Superior Implementation of the Art Algorithm , 1984, Ultrasonic imaging.

[16]  Gengsheng L. Zeng,et al.  A study of reconstruction artifacts in cone beam tomography using filtered backprojection and iterative EM algorithms , 1990 .

[17]  K. Mueller,et al.  Fast implementations of algebraic methods for three-dimensional reconstruction from cone-beam data , 1999, IEEE Transactions on Medical Imaging.

[18]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[19]  A. Lent,et al.  Iterative reconstruction algorithms. , 1976, Computers in biology and medicine.

[20]  Joseph O'Rourke,et al.  Computational Geometry in C. , 1995 .

[21]  G. Hounsfield.  Computerized transverse axial scanning (tomography): Part I. Description of system. 1973. , 1973, The British journal of radiology.

[22]  Anthony Skjellum,et al.  A High-Performance, Portable Implementation of the MPI Message Passing Interface Standard , 1996, Parallel Comput..

[23]  Rafael C. González,et al.  Local Determination of a Moving Contrast Edge , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[24]  Avinash C. Kak,et al.  Principles of computerized tomographic imaging , 2001, Classics in applied mathematics.

[25]  William H. Press,et al.  Numerical recipes in C , 2002 .

[26]  Jeffrey A. Fessler,et al.  Statistical image reconstruction for polyenergetic X-ray computed tomography , 2002, IEEE Transactions on Medical Imaging.

[27]  Y. Censor.  Row-Action Methods for Huge and Sparse Systems and Their Applications , 1981 .

[28]  Klaus Mueller,et al.  Rapid 3-D cone-beam reconstruction with the simultaneous algebraic reconstruction technique (SART) using 2-D texture mapping hardware , 2000, IEEE Transactions on Medical Imaging.

[29]  K. Lange,et al.  EM reconstruction algorithms for emission and transmission tomography. , 1984, Journal of computer assisted tomography.

[30]  P. Gilbert.  Iterative methods for the three-dimensional reconstruction of an object from projections. , 1972, Journal of theoretical biology.

[31]  Å. Björck,et al.  Accelerated projection methods for computing pseudoinverse solutions of systems of linear equations , 1979 .

[32]  O. Strand.  Theory and methods related to the singular-function expansion and Landweber's iteration for integral equations of the first kind , 1974 .

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

[34]  H. Malcolm Hudson,et al.  Accelerated image reconstruction using ordered subsets of projection data , 1994, IEEE Trans. Medical Imaging.

[35]  Harrison H. Barrett,et al.  Foundations of Image Science , 2003, J. Electronic Imaging.

[36]  William Gropp,et al.  User's Guide for mpich, a Portable Implementation of MPI Version 1.2.2 , 1996 .

[37]  Joseph A. O'Sullivan,et al.  Iterative deblurring for CT metal artifact reduction , 1996, IEEE Trans. Medical Imaging.

[38]  Cristian T. Badea,et al.  CONE BASED 3D RECONSTRUCTION: A FDK - SART COMPARISON FOR LIMITED NUMBER OF PROJECTIONS , 2001 .

[39]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[40]  Gene H. Golub,et al.  Matrix computations , 1983 .

[41]  K. Mueller,et al.  Anti-aliased three-dimensional cone-beam reconstruction of low-contrast objects with algebraic methods , 1999, IEEE Transactions on Medical Imaging.

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

[43]  M. Defrise,et al.  Iterative reconstruction for helical CT: a simulation study. , 1998, Physics in medicine and biology.

[44]  L. Landweber.  An iteration formula for Fredholm integral equations of the first kind , 1951 .

[45]  J. O´Rourke,et al.  Computational Geometry in C: Arrangements , 1998 .

[46]  M Grass,et al.  Angular weighted hybrid cone-beam CT reconstruction for circular trajectories. , 2001, Physics in medicine and biology.

[47]  G. Herman,et al.  Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography. , 1970, Journal of theoretical biology.