Concerning the problem that images captured by optical system suffer unsteady degradation including noise, blurring and geometric distortion when imaging process is affected by defocusing, motion, atmospheric disturbance and photoelectric noise, a generic framework of image restoration based on natural patch likelihood and sparse prior was proposed. Firstly, on the basis of natural image sparse prior model, several patch likelihood models were compared. The results indicate that the image patch likelihood model can improve the restoration performance. Secondly, the image expected patch log likelihood model was constructed and optimized, which reduced the running time and simplified the learning process. Finally, image restoration based on optimized expected log likelihood and Gaussian Mixture Model (GMM) was accomplished through the approximate Maximum A Posteriori (MAP) algorithm. The experimental results show that the proposed approach can restore degraded images by kinds of blur and additive noise, and its performance outperforms the state-of-the-art image restoration methods based on sparse prior in both Peak Signal-to-Noise Ratio (PSNR) and Structural SIMilarity (SSIM) with a better visual effect.

Focusing on the problem of nonlinear time series prediction in the field of analog circuit fault prediction and the problem of error accumulation in traditional Support Vector Regression (SVR) multi-step prediction, a new adaptive SVR prediction algorithm based on phase space reconstruction was proposed. Firstly, the significance of SVR multi-step prediction method for time series trend prediction and the error accumulation problem caused by multi-step prediction were analyzed. Secondly, phase space reconstruction technique was introduced into SVR prediction, the phase space of the time series of the analog circuit state was reconstructed, and then the SVR prediction was carried out. Thirdly, on the basis of the two SVR prediction of the error accumulated sequence generated in the multi-step prediction process, the adaptive correction of the initial prediction error was realized. Finally, the proposed algorithm was simulated and verified. The simulation verification results and experimental results of the health degree prediction of the analog circuit show that the proposed algorithm can effectively reduce the error accumulation caused by multi-step prediction, and significantly improve the accuracy of regression estimation, and better predict the change trend of analog circuit state.