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...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 a.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.展开更多
The adaptive regularization method is first proposed by Ryzhikov et al.for the deconvolution in elimination of multiples.This method is stronger than the Tikhonov regularization in the sense that itis adaptive,i.e.it ...The adaptive regularization method is first proposed by Ryzhikov et al.for the deconvolution in elimination of multiples.This method is stronger than the Tikhonov regularization in the sense that itis adaptive,i.e.it eliminates the small eigenvalues of theadjoint operator when it is nearly singular.We will show in this paper that the adaptive regularization can be implemented iterately.Some properties of the proposed non-stationary iterated adaptive regularization method are analyzed.The rate of convergence for inexact data is proved.Therefore the iterative implementation of the adaptive regularization can yield optimality.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.19731010 and 10231060)the Knowledge Innovation Program of CAS+1 种基金was supported by SRF for ROSS,SEMpartially supported by the Special Innovation Fund for graduate students of CAS.
文摘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 a.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.
基金This work was supported by the research program of College of Arts and Science of Beijing Union University and SRF for ROCS,SEM.
文摘The adaptive regularization method is first proposed by Ryzhikov et al.for the deconvolution in elimination of multiples.This method is stronger than the Tikhonov regularization in the sense that itis adaptive,i.e.it eliminates the small eigenvalues of theadjoint operator when it is nearly singular.We will show in this paper that the adaptive regularization can be implemented iterately.Some properties of the proposed non-stationary iterated adaptive regularization method are analyzed.The rate of convergence for inexact data is proved.Therefore the iterative implementation of the adaptive regularization can yield optimality.
