GPU-Based Volume Reconstruction from Very Few Arbitrarily Aligned X-Ray Images

This paper presents a three-dimensional GPU-accelerated algebraic reconstruction method in a few-projection cone-beam setting with arbitrary acquisition geometry. To achieve artifact-reduced reconstructions in the challenging case of unconstrained geometry and extremely limited input data, we use linear methods and an artifact-avoiding projection algorithm to provide high reconstruction quality. We apply the conjugate gradient method in the linear case of Tikhonov regularization and the two-point-step-size gradient method in the nonlinear case of total variation regularization to solve the system of equations. By taking advantage of modern graphics hardware we achieve acceleration of up to two orders of magnitude over classical CPU implementations.

[1]  Tao Wu,et al.  A comparison of reconstruction algorithms for breast tomosynthesis. , 2004, Medical physics.

[2]  Per Christian Hansen,et al.  Regularization methods for large-scale problems , 1993 .

[3]  Claus-E. Liedtke,et al.  3D Reconstruction of Volume Defects from Few X-Ray Images , 1999, CAIP.

[4]  C. Vogel.  Computational Methods for Inverse Problems , 1987 .

[5]  山本 一普,et al.  Tuned-Aperture Computed Tomography(TACT)の画像精度に影響する因子について : University of Louisvilleにおける研究報告 , 1999 .

[6]  E. Somersalo,et al.  Statistical and computational inverse problems , 2004 .

[7]  Matti Lassas,et al.  Wavelet-based reconstruction for limited-angle X-ray tomography , 2006, IEEE Transactions on Medical Imaging.

[8]  Klaus Mueller,et al.  Why do commodity graphics hardware boards (GPUs) work so well for acceleration of computed tomography? , 2007, Electronic Imaging.

[9]  Lubomir M. Hadjiiski,et al.  A comparative study of limited-angle cone-beam reconstruction methods for breast tomosynthesis. , 2006, Medical physics.

[10]  J B Ludlow,et al.  Tuned-aperture computed tomography (TACT). Theory and application for three-dimensional dento-alveolar imaging. , 1997, Dento maxillo facial radiology.

[11]  Jari P. Kaipio,et al.  Parallelized Bayesian inversion for three-dimensional dental X-ray imaging , 2006, IEEE Transactions on Medical Imaging.

[12]  C. W. Groetsch,et al.  The theory of Tikhonov regularization for Fredholm equations of the first kind , 1984 .

[13]  O. Weinheimer,et al.  Accurate registration of random radiographic projections based on three spherical references for the purpose of few-view 3D reconstruction. , 2008, Medical physics.

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

[15]  J. Borwein,et al.  Two-Point Step Size Gradient Methods , 1988 .

[16]  Klaus Mueller,et al.  Hardware acceleration vs. algorithmic acceleration: can GPU-based processing beat complexity optimization for CT? , 2007, SPIE Medical Imaging.

[17]  G C Sharp,et al.  GPU-based streaming architectures for fast cone-beam CT image reconstruction and demons deformable registration , 2007, Physics in medicine and biology.

[18]  Jari P. Kaipio,et al.  Bayesian inversion method for 3D dental X-ray imaging , 2007, Elektrotech. Informationstechnik.

[19]  K. Mueller,et al.  Fast and accurate three-dimensional reconstruction from cone-beam projection data using algebraic methods , 1998 .

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

[21]  E Somersalo,et al.  Statistical inversion for medical x-ray tomography with few radiographs: I. General theory. , 2003, Physics in medicine and biology.

[22]  V Kolehmainen,et al.  Bayesian multiresolution method for local tomography in dental x-ray imaging , 2007, Physics in medicine and biology.

[23]  J. Navarro-Pedreño.  Numerical Methods for Least Squares Problems , 1996 .

[24]  E Somersalo,et al.  Statistical inversion for medical x-ray tomography with few radiographs: II. Application to dental radiology. , 2003, Physics in medicine and biology.

[25]  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.

[26]  Klaus Mueller,et al.  IOP PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY , 2007 .

[27]  Fang Xu,et al.  Accelerating popular tomographic reconstruction algorithms on commodity PC graphics hardware , 2005, IEEE Transactions on Nuclear Science.

[28]  Michael Knaup,et al.  Hyperfast parallel-beam and cone-beam backprojection using the cell general purpose hardware. , 2007, Medical physics.

[29]  Frank Natterer,et al.  Numerical methods in tomography , 1999, Acta Numerica.

[30]  E. Sidky,et al.  Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT , 2009, 0904.4495.

[31]  Michael A. Saunders,et al.  LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares , 1982, TOMS.