Science in China Series A: Mathematics

, Volume 48, Issue 2, pp 169–184 | Cite as

A new trust region algorithm for image restoration

  • Zaiwen Wen
  • Yanfei Wang


The image restoration problems play an important role in remote sensing and astronomical image analysis. One common method for the recovery of a true image from corrupted or blurred image is the least squares error (LSE) method. But the LSE method is unstable in practical applications. A popular way to overcome instability is the Tikhonov regularization. However, difficulties will encounter when adjusting the so-called regularization parameter α. Moreover, how to truncate the iteration at appropriate steps is also challenging. In this paper we use the trust region method to deal with the image restoration problem, meanwhile, the trust region subproblem is solved by the truncated Lanczos method and the preconditioned truncated Lanczos method. We also develop a fast algorithm for evaluating the Kronecker matrix-vector product when the matrix is banded. The trust region method is very stable and robust, and it has the nice property of updating the trust region automatically. This releases us from tedious finding the regularization parameters and truncation levels. Some numerical tests on remotely sensed images are given to show that the trust region method is promising.


trust region algorithm image restoration Lanczos method Kronecker matrix-vector product preconditioning 


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Copyright information

© Science in China Press 2005

Authors and Affiliations

  • Zaiwen Wen
    • 1
  • Yanfei Wang
    • 2
  1. 1.State Key Laboratory of Scientific Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System SciencesChinese Academy of SciencesBeijingChina
  2. 2.National Key Laboratory on Remote Sensing Science, Institute of Remote Sensing ApplicationsChinese Academy of SciencesBeijingChina

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