A multilevel domain decomposition algorithm for fast O(N2logN) reprojection of tomographic images

A novel algorithm for fast computation of tomographic image projections is presented. The method comprises a decomposition of an image into subimages followed by an aggregation of projections computed for the subimages. The multilevel domain decomposition algorithm is formulated as a recursive procedure. The computational cost of the proposed algorithm is comparable to that of FFT-based techniques while it appears to be more flexible than the latter. Numerical results demonstrate the effectiveness of the method.

[1]  J. Ollinger.  Iterative reconstruction-reprojection and the expectation-maximization algorithm. , 1990, IEEE transactions on medical imaging.

[2]  D.-C. Yu,et al.  Study of reprojection methods in terms of their resolution loss and sampling errors , 1992, IEEE Conference on Nuclear Science Symposium and Medical Imaging.

[3]  F. Natterer.  The Mathematics of Computerized Tomography , 1986 .

[4]  Norbert J. Pelc,et al.  High Speed Reprojection And Its Applications , 1988, Medical Imaging.

[5]  J. Ollinger.  Reconstruction-reprojection processing of transmission scans and the variance of PET images , 1991, Conference Record of the 1991 IEEE Nuclear Science Symposium and Medical Imaging Conference.

[6]  Yoram Bresler,et al.  A fast and accurate Fourier algorithm for iterative parallel-beam tomography , 1996, IEEE Trans. Image Process..

[7]  Achi Brandt,et al.  Fast Calculation of Multiple Line Integrals , 1999, SIAM J. Sci. Comput..

[8]  S. Deans.  The Radon Transform and Some of Its Applications , 1983 .

[9]  Eric C. Frey,et al.  A fast projector-backprojector pair modeling the asymmetric, spatially varying scatter response function for scatter compensation in SPECT imaging , 1993 .

[10]  P. Joseph.  An Improved Algorithm for Reprojecting Rays through Pixel Images , 1983, IEEE Transactions on Medical Imaging.

[11]  Martin L. Brady,et al.  A Fast Discrete Approximation Algorithm for the Radon Transform , 1998, SIAM J. Comput..

[12]  John J. Knab,et al.  Interpolation of band-limited functions using the approximate prolate series (Corresp.) , 1979, IEEE Trans. Inf. Theory.

[13]  R M Lewitt,et al.  Multidimensional digital image representations using generalized Kaiser-Bessel window functions. , 1990, Journal of the Optical Society of America. A, Optics and image science.

[14]  E. Michielssen,et al.  A multilevel matrix decomposition algorithm for analyzing scattering from large structures , 1996 .

[15]  B. F. Logan,et al.  The Fourier reconstruction of a head section , 1974 .

[16]  D. Slepian.  Some comments on Fourier analysis, uncertainty and modeling , 1983 .

[17]  P. Joseph,et al.  A Method for Correcting Bone Induced Artifacts in Computed Tomography Scanners , 1978, Journal of computer assisted tomography.

[18]  Jorge L. C. Sanz,et al.  P3E: New Life for Projection-Based Image Processing , 1987, J. Parallel Distributed Comput..

[19]  W. A. Götz,et al.  A fast digital Radon transform--An efficient means for evaluating the Hough transform , 1995, Pattern Recognit..

[20]  A. Lindgren,et al.  Sampling the 2-D Radon transform , 1981 .

[21]  S.-C. Huang,et al.  Capability evaluation of a sinogram error detection and correction method in computed tomography , 1991, Conference Record of the 1991 IEEE Nuclear Science Symposium and Medical Imaging Conference.

[22]  Gary H. Glover,et al.  An algorithm for the reduction of metal clip artifacts in CT reconstructions. , 1981 .

[23]  C R Crawford,et al.  Reprojection using a parallel backprojector. , 1986, Medical physics.

[24]  Martin L. Brady,et al.  Fast parallel discrete approximation algorithms for the radon transform , 1992, SPAA '92.

[25]  Achi Brandt,et al.  A Fast and Accurate Multilevel Inversion of the Radon Transform , 1999, SIAM J. Appl. Math..

[26]  A. Requicha,et al.  The zeros of entire functions: Theory and engineering applications , 1980, Proceedings of the IEEE.

[27]  Jan Timmer,et al.  The gridding method for image reconstruction by Fourier transformation , 1995, IEEE Trans. Medical Imaging.

[28]  G. Gullberg,et al.  A rotating and warping projector/backprojector for fan-beam and cone-beam iterative algorithm , 1994 .

[29]  Jorge L. C. Sanz,et al.  Computing projections of digital images in image processing pipeline architectures , 1987, IEEE Trans. Acoust. Speech Signal Process..

[30]  G Henrich,et al.  A simple computational method for reducing streak artifacts in CT images. , 1980, Computerized tomography.

[31]  Yoram Bresler,et al.  Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography , 1998, IEEE Trans. Image Process..