511
Views
44
CrossRef citations to date
0
Altmetric
Original Articles

Projected Barzilai–Borwein method for large-scale nonnegative image restoration

&
Pages 559-583 | Received 26 Jun 2005, Accepted 16 Jun 2006, Published online: 22 Aug 2007

References

  • Bardsley, J, and Vogel, CR, 2003. A nonnegatively constrained convex programming method for image reconstruction, SIAM Journal on Scientific Computing 25 (2003), pp. 1326–1343.
  • Barzilai, J, and Borwein, J, 1988. Two-point step size gradient methods, IMA Journal of Numerical Analysis 8 (1988), pp. 141–148.
  • Bertero, M, and Boccacci, P, 1998. Introduction to Inverse Problems in Imaging. Philadelphia: Institute of Physics Publishing; 1998.
  • Dai, YH, and Fletcher, R, 2003. Projected Barzilai–Borwein methods for large-scale box-constrained quadratic programming, University of Dundee Report NA/215 (2003).
  • Eicke, B, 1992. Iteration methods for convexly constrained ill-posed problems in Hilbert space, Numerical Functional Analysis Optimization 13 (1992), pp. 413–429.
  • Fletcher, R, 1987. Practical Methods of Optimization . John Wiley and Sons: Chichester; 1987.
  • Gonzalez, RC, and Woods, RE, 2002. Digital Image Processing . Publishing Hourse of Electronics Industry: Beijing; 2002.
  • Hanke, M, Nagy, J, and Vogel, CR, 2000. Quasi-Newton approach to nonnegative image restorations, Linear Algebra and its Applications 316 (2000), pp. 223–236.
  • Hanke, M, and Nagy, J, 1996. Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques, Inverse Problems 12 (1996), pp. 157–173.
  • Hansen, PC, 1998. Rank-deficient and Discrete Ill-posed Problems: Numerical Aspects of Linear Inversion. Philadelphia: SIAM; 1998.
  • Koptelova, E, Shimanovskaya, E, Artamonov, B, Sazhin, M, Yagola, A, Bruevich, V, and Burkhonov, O, 2005. Image reconstruction technique and optical monitoring of the QSO2237 + 0305 from Maidanak Observatory in 2002-2003, Monthly Notices of Royal Astronomical Society 356 (2005), pp. 323–330.
  • Lee, KP, and Nagy, JG, 2003. Steepest descent, CG and iterative regularization of ill-posed problems, BIT 43 (2003), pp. 1003–1017.
  • Moré, J, and Toraldo, G, 1991. On the solution of large quadratic programming problems with bound constraints, SIAM Journal of Optimmization 1 (1991), pp. 93–113.
  • Nagy, J, Strakos, Z, et al., 2000. "Mathmatical Modeling, Estimation, and Imaging". In: Wilson, David C, ed. Enforcing nonnegativity in image reconstruction algorithms . Vol. 4121. 2000. pp. 182–190..
  • Nagy, J, and Perrone, L, 2004 . "Advanced Signal Processing Algorithms, Architectures, and Implementations VIII". In: Franklin, T. Luk, ed. Kronecker products in image restoration . Vol. 5205. 2004 . pp. 369–379.
  • Nashed, MZ, 1970. Steepest descent for singular linear operator equations, SIAM Journal on Numerical Analysis 7 (1970), pp. 358–362.
  • Raydan, M, 1993. On the Barzilai and Borwein choice of steplength for the gradient method, IMA Journal of Numerical Analysis 13 (1993), pp. 321–326.
  • Rojas, M, and Steihaug, T, , 2002, An Interior-Point Trust-Region-Based Method for Large-Scale Nonnegative Regularization, CERFACS Technical Report TR/PA/01/11, July 6 2001, Revised June 3, 2002.
  • Rudin, L, Osher, S, and Fatemi, E, 1992. Nonlinear total variation based noise removal algorithms, Physica D 60 (1992), pp. 259–268.
  • Tikhonov, AN, and Arsenin, VY, 1977. Solutions of Ill-posed Problems. New York: John Wiley and Sons; 1977.
  • Tikhonov, AN, Goncharsky, AV, Stepanov, VV, and Yagola, AG, 1995. Numerical Methods for the Solution of Ill-posed Problems. Dordrecht: Kluwer Academic Publishers; 1995.
  • Barrett, R, Berry, M, Chan, TF, Demmel, J, Donato, J, Dongarra, J, Eijkhout, V, Pozo, R, Romine, C, and Van der Vorst, H, 1994. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. Philadelphia: SIAM; 1994.
  • Toint, Ph. L, 1997 . A non-monotone trust region algorithm for nonlinear optimzation subject to convex constraints, Mathematical Programming 77 (1997 ), pp. 69–94.
  • Vogel, CR, and Oman, ME, 1998. A fast, robust algorithm for total variation based reconstruction of noisy, blurred images, IEEE Transactions On Image Processing 7 (1998), pp. 813–824.
  • Vogel, CR, 2002. Computational Methods for Inverse Problems. Philadelphia: SIAM; 2002.
  • Wang, YF, Yuan, YX, and Zhang, HC, 2002. A trust region-CG algorithm for deblurring problem in atmospheric image reconstruction, Science in China A 45 (2002), pp. 731–740.
  • Wang, YF, 2003. On the regularity of trust region-CG algorithm: with application to deconvolution problem, Science in China A 46 (2003), pp. 312–325.
  • Wang, YW, Wang, YF, Xue, Y, and Gao, W, 2004. A new algorithm for remotely sensed image texture classification and segmentation, International Journal of Remote Sensing 25 (2004), pp. 4043–4050.
  • Wen, ZW, and Wang, YF, 2004. "A trust region method for large scale inverse problems in atmospheric image restoration". In: Yuan, Y, ed. Numerical Linear Algebra and Optimization . Beijing/New York: Science Press; 2004. pp. 275–287.
  • Wen, ZW, and Wang, YF, 2005. A new trust region algorithm for image restoration, Science in China A 48 (2005), pp. 169–184.
  • Xiao, TY, Yu, YS, and Wang, YF, 2003. Numerical Methods for Inverse Problems. Beijing: Science Press; 2003.
  • Yuan, YX, 1993. Numerical Methods for Nonliear Programming. Shanghai: Shanghai Science and Technology Publication; 1993.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.