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A new trust region algorithm for image restoration

Science china mathematics 2005年第2期48卷 169-184页

作者： wen zaiwen & wang yanfei state key laboratory of scientific engineering computing, institute of computational mathematics and scientific/engineering computing, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china National key laboratory on Remote Sensing Science, institute of Remote Sensing Applications, chinese academy of sciences, beijing 100101, china 1. state key laboratory of scientific engineering computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. National key laboratory on Remote Sensing Science Institute of Remote Sensing Applications Chinese Academy of Sciences 100101 Beijing China

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.

关键词： trust region algorithm, image restoration, Lanczos method, Kronecker matrix-vector product, preconditioning.

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