Study On Several Problems Of 2-D AR Parameter Estimation

Autoregressive(AR)parameter simulation techniques are important in system identification,image interpolation and super-resolution.It is a simple and effective method for simulating random signals,and has the advantage of high resolution.The key problem of AR model parameter estimation is to estimate model parameters and noise variance.One dimensional(1-D)noisy AR model parameter estimation theory and algorithm research has been mature.However,the structure complexity of two-dimensional(2-D)noisy AR model makes its parameter estimation theory and algorithm relatively less,and the parameter estimation method of 1-D noisy AR model is difficult to extend directly to 2-D model.In this paper,the key issues of noisy 2-D AR model are studied.The main research work is as follows:1.Using matrix inner product technique,combining with the inverse filtering method and the Yule-Walker equation,this paper proposes an inverse filtering method to estimate parameters of 2-D AR model in noisy environment,and then proposes a matrix recursive algorithm to estimate the 2-D parameters.The algorithm obtains the noise variance estimations by solving the linear equations,and uses the least square method to substitute the variance estimation into the bias correction equation,and recursively correct the bias of the AR parameter estimation,thus obtain the unbiased AR parameters estimation.Simulation results show that the proposed algorithm has higher estimation accuracy.2.Using matrix inner product technique and unbiased estimation technique,an unbiased parameters estimation method of 2-D AR model in noisy environment is proposed,and then a matrix Newton iterative algorithm is proposed.The algorithm converts the observation noise variance estimate into resolving the only solution of a nonlinear equation to result in unbiased estimate of the AR parameters.Because the noise variance estimation error is reduced,the accuracy of AR parameter estimation is improved.Analysis from algorithm complexity,the proposed algorithm has less computational complexity.Simulation results show that the proposed algorithm has the advantages of higher estimation accuracy and faster speed.3.The interpolation application of 2-D AR simulation technique in image super-resolution is studied.Four image interpolation algorithms based on 2-D AR model are compared,and their performance is analyzed in terms of algorithm complexity and estimation accuracy.