Acceleration Of Image Restoration Algorithms Based On Polynomial Extrapolation

The significance of accelerating the nonlinear iterative image restoration algorithm is that it can improve the computing efficiency and reduce computational complexity. The nonlinear iterative algorithm can achieve better results than linear filtering method, but it needs a large amount of computation and high requirements on computing hardware. In the fields of atmospheric turbulence-degraded images and aero-optical effects, where is high demand for time, it will have a great significance to speed up such algorithms.At present, the commonly used accelerated methods for nonlinear iterative algorithm are auto-acceleration method proposed by Biggs and Andrews, and modified exponential method proposed by Meinel. There is no related research about using the extrapolation method to accelerate the nonlinear iterative algorithm. Auto-acceleration method and the modified exponential methods speed up the convergence of the algorithm by predicting a new eatimate with the results at hand. There is a very good acceleration effect, but it is not satisfactory in reducing the computation burden. In this paper, the extrapolation method is used to accelerate the iterative algorithm.This paper, we study the problems about how to use the extrapolation method to accelerate the nonlinear iterative restoration algorithms in the field of image restorationd. The damping R-L algorithm is based on Richardson-Lucy (R-L) algorithm, which can effectively prevent the amplification of the noise in the image restoration process. The algorithm can also be used in blind deconvolution. The theory of polynomial extrapolation is quite mature, and has been widely used in the various fields of numerical calculation. This article will study how to use the polynomial extrapolation to accelerate image reconstruction algorithm with the damping R-L algorithm. Based on the comparison, analysis, and numerical simulation results, we can draw the following conclusions:1) We should use discontinuous approach to accelerate the damping R-L algorithm by the polynomial extrapolation. Otherwise, the polynomial extrapolation will destroy the correlation between the estimates, and image restoration process will fail.2) Better performance of acceleration can be obtained using more extrapolation nodes.3) When we use the polynomial extrapolation method, using the type of extrapolation points like 1/(n+1) can get a more significant acceleration effect than other types.4) The polynomial extrapolation is used to speed up the damping R-L algorithm with the noise-free degraded images, and the results of restoration show that this algorithm is better when the image is smooth.5) The polynomial extrapolation is used to speed up the damping R-L algorithm with the noisy degraded images, and the results of restoration show that this algorithm is more effective when the noise degraded image has a high signal to noise ratio.