The Convergence of Two Algorithms for Compressed Sensing Based Tomography

Show more

References

[1] A. C. Kak and M. Slaney, “Principles of Computerized Tomographic Imaging,” Society of Industrial and Applied Mathematics, Philadelphia, 2001.
doi:10.1137/1.9780898719277

[2] P. B. Eggermont, G. T. Herman and A. Lent, “Iterative Algorithm for Larger Partitioned Linear Systems, with Applications to Image Reconstruction,” Linear Algebra and Its Applications, Vol. 40, 1981, pp. 37-67.
doi:10.1016/0024-3795(81)90139-7

[3] G. Cimmino, “Calcolo Approssimato Per le Soluzioni dei Sistemi di Equazioni Lineari,” La Ricerca Scientifica, Series II, Vol. 9, 1938, pp. 326-333.

[4] Y. Censor, D. Gordan and R. Gordan, “Component Aveging: An Efficient Iterative Parallel Algorithm for Large and Sparse Unstructured Problems,” Parallel Computing, Vol. 27, No. 6, 2001, pp. 777-808.
doi:10.1016/S0167-8191(00)00100-9

[5] Y. Censor, T. Elfving, G. T. Herman and T. Nikazad. “On Diagonally-Relaxed Orthogonal Projection Methods,” SIAM Journal on Scientific Computing, Vol. 30, No. 1, 2008, pp. 473-504. doi:10.1137/050639399

[6] R. Aharoni and Y. Censor, “Block-Iterative Projection Methods for Parallel Computation of Solutions to Convex Feasibility Problems,” Linear Algebra and Its Applications, Vol. 120, 1989, pp. 65-175.
doi:10.1016/0024-3795(89)90375-3

[7] Y. Censor and Z. Stavors, “Parallel Optimization: Theory, Algorithms, and Applications,” Oxford University Press, Oxford, 1997.

[8] E. Candes, J. Romberg and T. Tao, “Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information,” IEEE Transactions on Information Theory, Vol. 52, No. 2, 2006, pp. 489-509.
doi:10.1109/TIT.2005.862083

[9] E. Candes and M. Wakin, “An Introduction to Compressive Sampling,” IEEE Signal Processing Magazine, Vol. 25, No. 2, 2008, pp. 21-30.
doi:10.1109/MSP.2007.914731

[10] D. Donoho, “Compressed Sensing,” IEEE Transactions on Information Theory, Vol. 52, No. 4, 2006, pp. 1289-1306.
doi:10.1109/TIT.2006.871582

[11] C. E. Shannon, “Communication in the Presence of Noise,” Proceedings of the IEEE, Vol. 86, No. 2, 1998, pp. 447-457.
doi:10.1109/JPROC.1998.659497

[12] E. Candes and M. Wakin, “Enhancing Sparsity by Reweighted L1 Minimization,” Journal of Fourier Analysis and Applications, Vol. 14, No. 5-6, 2008, pp. 877-905.
doi:10.1007/s00041-008-9045-x

[13] H. Yu and G. Wang, “Compressed Sensing Based Interior Tomography,” Physics in Medicine and Biology, Vol. 54, No. 9, 2009, pp. 2791-2805.
doi:10.1088/0031-9155/54/9/014

[14] X. Li and J. Zhu, “Convergence of Block Cyclic Projection and Cimmino Algorithms for Compressed Sensing Based Tomography,” Journal of X-Ray Science and Technology, Vol. 18, No. 4, 2010, pp. 1-11.

[15] D. Butnariu, R. Davidi, G. T. Herman and I. G. Kazantsev, “Stable Convergence Behavior under Summable Perturbation of a Class Projection Methods for Convex Feasibility and Optimization Problems,” IEEE Journal of Selected Topics in Signal Processing, Vo. 1, No. 4, 2007, pp. 540547.

[16] J. Zhu, X. Li, Y. Ye and G. Wang, “Analysis on the StripBased Projection for Discrete Tomography,” Discrete Applied Mathematics, Vol. 156, No. 12, 2008, pp. 2359-2367.
doi:10.1016/j.dam.2007.10.011

[17] X. Li and J. Zhu, “A Note of Reconstruction Algorithm of the Strip-Based Projection Model for Discrete Tomography,” Journal of X-Ray Science and Technology, Vol. 16, No. 4, 2008, pp. 253-260.