The Adaptive Generalized Total Variation (AGTV) model for image denoising has the shortages that it cannot locate image edge accurately and extract enough edge information. In order to improve the effectiveness and Peak Signal-to-Noise Ratio (PSNR) of image denoising, an Improved AGTV(IAGTV) model for image denoising was presented. On the one hand, another gradient calculating method with higher accuracy was adopted, in order to locate image edge more accurately than AGTV. On the other hand, for optimizing the filtering of image preprocess, the united Gauss-Laplace conversion which was good at image edge information detection was chosen to take place of Gaussian smoothing filter, so as to prevent edge information from reduction while denoising. Numerical simulation experiments show that the restored image PSNR of IAGTV was increased approximately by 1 dB than that of GTV with the fixed value p and at least 0.2 dB than that of AGTV. The experimental results show that IAGTV has good ability of image denoising.

In order to improve the operational efficiency of SemiDefinite Programming (SDP), a new nonmonotonic trust region algorithm was proposed. The SDP problem and its duality problem were transformed into unconstrained optimization problem and the trust region subproblem was constructed, the trust region radius correction condition was modified. When the initial search point was near the canyon, the global optimal solution still could be found. The experimental results show that the number of iterations of the algorithm is less than the classical interior point algorithm for small and medium scale semidefinite programming problems, and the proposed algorithm works faster.