Science in China Series A: Mathematics

, Volume 46, Issue 3, pp 312–325

# On the regularity of trust region-cg algorithm: With application to deconvolution problem

Article

## Abstract

Deconvolution problem is a main topic in signal processing. Many practical applications are required to solve deconvolution problems. An important example is image reconstruction. Usually, researchers like to use regularization method to deal with this problem. But the cost of computation is high due to the fact that direct methods are used. This paper develops a trust region-cg method, a kind of iterative methods to solve this kind of problem. The regularity of the method is proved. Based on the special structure of the discrete matrix, FFT can be used for calculation. Hence combining trust region-cg method with FFT is suitable for solving large scale problems in signal processing.

### Keywords

ill- posed problems efficient implementation trust region- cg method regularity

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