
تعداد نشریات | 21 |
تعداد شمارهها | 642 |
تعداد مقالات | 9,391 |
تعداد مشاهده مقاله | 68,106,018 |
تعداد دریافت فایل اصل مقاله | 35,770,413 |
CAV block-column iterative method for computed tomographic (CT) problems | ||
International Journal of Nonlinear Analysis and Applications | ||
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 11 مرداد 1404 اصل مقاله (1.03 M) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29520.4193 | ||
نویسندگان | ||
Shaghayegh Heidarzadeh؛ Touraj Nikazad* | ||
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran | ||
تاریخ دریافت: 20 دی 1401، تاریخ پذیرش: 13 اسفند 1401 | ||
چکیده | ||
This study revolves around the investigation of tomography and its mathematical modelling. In this regard, the CAV block-column iterative algorithm is proposed to reconstruct a high-quality image of a specific object. Indeed, this algorithm is applied for solving the problem of image reconstruction associated with computed tomography (CT). Then, the effects of both the relaxation parameter and the number of blocks are investigated on the convergence speed and the control of the semi-convergence phenomenon in this kind of iterative algorithm. Results show that a significant improvement in convergence speed and relative error can be achieved by a suitable choice of the relaxation parameter value. | ||
کلیدواژهها | ||
Tomography؛ Component averaging (CAV) Iterative method؛ Relaxation parameter؛ Block-column algorithm؛ Semi-convergence phenomenon | ||
مراجع | ||
[1] A.H. Andersen and A.C. Kak, Simultaneous algebraic reconstruction technique (SART): A superior implementation of the ART algorithm, Ultrasonic Imag. 6 (1984), no. 1, 81–94. [2] Z.-Z. Bai and C.-H. Jin, Column-decomposed relaxation methods for the overdetermined systems of linear equations, Int. J. Appl. Math. 13 (2003), no. 1, 71–82. [3] M. Bierlaire, Ph.L. Toint, and D. Tuyttens, On iterative algorithms for linear least squares problems with bound constraints, Linear Alg. Appl. 143 (1991), 111–143. [4] ˚A. Bjorck and T. Elfving, Accelerated projection methods for computing pseudoinverse solutions of systems of linear equations, BIT Numer. Math. 19 (1979), no. 2, 145–163. [5] W.L. Briggs and V.E. Henson, The DFT: An Owner’s Manual for the Discrete Fourier Transform, SIAM, 1995. [6] Y. Censor, Row-action methods for huge and sparse systems and their applications, SIAM Rev. 23 (1981), no. 4, 444–466. [7] Y. Censor and T. Elfving, Block-iterative algorithms with diagonally scaled oblique projections for the linear feasibility problem, SIAM J. Matrix Anal. Appl. 24 (2002), no. 1, 40–58. [8] Y. Censor, T. Elfving, G.T. Herman, and T. Nikazad, On diagonally relaxed orthogonal projection methods, SIAM J. Sci. Comput. 30 (2008), no. 1, 473–504. [9] Y. Censor, D. Gordon, and R. Gordon, Bicav: A block-iterative parallel algorithm for sparse systems with pixel-related weighting, IEEE Trans. Med. Imag. 20 (2001), no. 10, 1050–1060. [10] Y. Censor, D. Gordon, and R. Gordon, Component averaging: An efficient iterative parallel algorithm for large and sparse unstructured problems, Parallel Comput. 27 (2001), no. 6, 777–808. [11] Y. Censor, S.A. Zenios, Parallel Optimization: Theory, Algorithms, and Applications, Oxford University Press on Demand, 1997. [12] G. Cimmino, Cacolo approssimato per le soluzioni dei systemi di equazioni lineari, La Ric. Sci. (Roma) 1 (1938), 326–333. [13] T. Elfving, Block-iterative methods for consistent and inconsistent linear equations, Numer. Math. 35 (1980), no. 1, 1–12. [14] T. Elfving, P.C. Hansen, and T. Nikazad, Semiconvergence and relaxation parameters for projected SIRT algorithms, SIAM J. Sci. Comput. 34 (2012), no. 4, A2000–A2017. [15] T. Elfving, P.C. Hansen, and T. Nikazad, Semi-convergence properties of Kaczmarz’s method, Inverse Problems 30 (2014), no. 5, 055007. [16] T. Elfving, P.C. Hansen, and T. Nikazad, Convergence analysis for column-action methods in image reconstruction, Numerical Algorithms 74 (2017), no. 3, 905–924. [17] T. Elfving and T. Nikazad, Properties of a class of block-iterative methods, Inverse Problems 25 (2009), no. 11, 115–011. [18] T. Elfving, T. Nikazad, and P.C. Hansen, Semi-convergence and relaxation parameters for a class of sirt algorithms, Electronic Trans. Numer. Anal. 37 (2010), no. 274, 321–336. [19] E. Garduno, G.T. Herman, and R. Davidi, Reconstruction from a few projections by ℓ1-minimization of the Haar transform, Inverse Problems 27 (2011), no. 5, 055006. [20] P.C. Hansen and M. Saxild-Hansen, Air tools: A MATLAB package of algebraic iterative reconstruction methods, J. Comput. Appl. Math. 236 (2012), no. 8, 2167–2178. [21] G.T. Herman, Image reconstruction from projections, Real-Time Imag. 1 (1995), no. 1, 3–18. [22] G.T. Herman and R. Davidi, Image reconstruction from a small number of projections, Inverse Problems 24 (2008), no. 4, 045011. [23] H. Ji and Y. Li, Block conjugate gradient algorithms for least squares problems, J. Comput. Appl. Math. 317 (2017), 203–217. [24] M. Jiang and G. Wang, Convergence studies on iterative algorithms for image reconstruction, IEEE Trans. Med. Imag. 22 (2003), no. 5, 569–579. [25] S. Kaczmarz, Angenaherte auflosung von systemen linearer gleichungen, Bull. Int. Acad. Pol. Sic. Let., Cl. Sci. Math. Nat. (1937), 355–357. [26] J. Klukowska, R. Davidi, and G.T. Herman, Snark09–A software package for reconstruction of 2d images from 1d projections, Comput. Meth. Prog. Biomed. 110 (2013), no. 3, 424–440. [27] D.I. Marcussen and C.H. Trinderup, Radon transform in tomographic image reconstruction, B.S. Thesis, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark, 2009. [28] J.G. Nagy and K.M. Palmer, Steepest descent, CG, and iterative regularization of ill-posed problems, BIT Numer. Math. 43 (2003), no. 5, 1003–1017. [29] F. Natterer, The Mathematics of Computerized Tomography, SIAM, 2001. [30] F. Natterer and F. Wubbeling, Mathematical Methods in Image Reconstruction, SIAM, 2001. [31] T. Nikazad and M. Abbasi, A unified treatment of some perturbed fixed point iterative methods with an infinite pool of operators, Inverse Problems 33 (2017), no. 4, 044–002. [32] D.W. Watt, Column-relaxed algebraic reconstruction algorithm for tomography with noisy data, Appl. Optics 33 (1994), no. 20, 4420–4427. [33] S.J. Wright, Coordinate descent algorithms, Math. Program. 151 (2015), no. 1, 3–34. | ||
آمار تعداد مشاهده مقاله: 16 تعداد دریافت فایل اصل مقاله: 8 |