Study Of2D-ARMA Parameter Estimation And Blind Image Restoration Algorithms

Blind digital image restoration is a major content of digital image processing, ithas been widely used in national defence, mining, medical, remote sensing, spaceexploration and other fields. ARMA (autoregressive moving average) parametersestimation is an important method in blind image restoration. Current researchesreports show that ARMA parameter estimation methods not only have good statisticalproperties, but also dosen’t requires a priori knowledge of degraded images. Thisthesis, by exploring the existing two-dimensional (2D) ARMA parameter estimationmethods, develops a fast2D-ARMA parameter estimation algorithm and blind imagerestoration algorithm.The first part of the thesis first investigate the computational complexity of tworepresentative2D-ARMA parameter estimation，and then proposed a fast2D-ARMAparameters estimation algorithm. The proposed algorithm uses the2D-ARMA modeltransfer function to derive an equivalent2D-AR model, and emploies theYule-Walker equation to obtain a low-order linear equation for solving2D-ARMAparameters. The proposed algorithm has low computational complexity and is suitablefor solving2D-ARMA parameter estimation problem with large size. Simulationresults show that the proposed algorithm has better estimation accuracy and shortercomputing time than the existing two algorithms.The second part of the paper studies the blind image restoration algorithm. Wefirst reformulate the degraded image model as a non-symmetric half plane2D-ARMAmodel. Blind image restoration problem is thus transformed into one rebuiltnon-symmetric half plane2D-ARMA parameter estimation problem. Based on thefast2D-ARMA estimation algorithm proposed in the first part, we propose two fastblind image restoration algorithms: one is called the joint algorithm of2D-ARMAparameter estimation and Wiener filtering, another is called the joint algorithm of2D-ARMA parameter estimation and Kalman filtering. Because of fast convergenceof the2D-ARMA parameter estimation algorithm, the point spread function is quicklyobtained. Computed results show that two proposed joint algorithms are able to obtainrestored image in a short time, and has a good restoration performance and smallerestimation error.