Efficient 3D grids for image reconstruction using spherically-symmetric volume elements

Incorporation of spherically-symmetric volume elements (blobs), instead of the conventional voxels, into iterative image reconstruction algorithms, has been found in the authors' previous studies to lead to significant improvement in the quality of the reconstructed images. Furthermore, for 3D positron emission tomography, the 3D algebraic reconstruction technique using blobs can reach comparable or even better duality than the 3D filtered backprojection method after only one cycle through the projection data. The only shortcoming of the blob reconstruction is an increased computational demand, because of the overlapping nature of the blobs. These encouraging results mere obtained in the authors' previous studies for the case when the blobs were placed on the same 3D simple cubic grid used for voxel basis functions. For basis functions which are spherically-symmetric, there are more advantageous arrangements of the 3D grid, enabling a more isotropic distribution of the spherical functions in the 3D space and a, better packing efficiency of the image spectrum. A good arrangement is the body centered cubic grid. The authors' studies confirmed that, when using this type of 3D grid, the number of grid points can be effectively reduced, decreasing the computational and memory demands while preserving the quality of the reconstructed images.<<ETX>>

[1]  Gabor T. Herman,et al.  Algebraic reconstruction techniques can be made computationally efficient [positron emission tomography application] , 1993, IEEE Trans. Medical Imaging.

[2]  R. Lewitt Reconstruction algorithms: Transform methods , 1983, Proceedings of the IEEE.

[3]  Robert M. Lewitt,et al.  Practical considerations for 3-D image reconstruction using spherically symmetric volume elements , 1996, IEEE Trans. Medical Imaging.

[4]  G. W. Wecksung,et al.  Local basis-function approach to computed tomography. , 1985, Applied optics.

[5]  Paul Kinahan,et al.  Analytic 3D image reconstruction using all detected events , 1989 .

[6]  Sérgio Shiguemi Furuie,et al.  Relevance of statistically significant differences between reconstruction algorithms , 1996, IEEE Trans. Image Process..

[7]  Samuel Matej,et al.  Image representation and tomographic reconstruction using spherically-symmetric volume elements , 1992, IEEE Conference on Nuclear Science Symposium and Medical Imaging.

[8]  Gabor T. Herman,et al.  Programs for Evaluation of 3D PET Reconstruction Algorithms , 1994 .

[9]  David Middleton,et al.  Sampling and Reconstruction of Wave-Number-Limited Functions in N-Dimensional Euclidean Spaces , 1962, Inf. Control..

[10]  R. Lewitt Alternatives to voxels for image representation in iterative reconstruction algorithms , 1992, Physics in medicine and biology.

[11]  Samuel Matej,et al.  A comparison of transform and iterative reconstruction techniques for a volume-imaging PET scanner with a large axial acceptance angle , 1994, Proceedings of 1994 IEEE Nuclear Science Symposium - NSS'94.

[12]  T K Narayan,et al.  A methodology for testing for statistically significant differences between fully 3D PET reconstruction algorithms. , 1994, Physics in medicine and biology.

[13]  T. K. Narayan,et al.  Evaluation of task-oriented performance of several fully 3D PET reconstruction algorithms. , 1994, Physics in medicine and biology.

[14]  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.

[15]  C. Kittel Introduction to solid state physics , 1954 .