考虑数字图像滤波处理对融线性和非线性于一体的数学模型的需求，根据Weierstrass逼近理论推导建立了通用的自回归数学模型。该模型将线性自回归模型和非线性自回归模型融合于一个统一的数学表达式中，仿真实验表明其能够较好地拟合现有的线性和非线性自回归模型。用二维向量取代标量参数，推导了通用自回归模型的二维数学表达式。通过对比分析，确定采用GM(Generalized M estimator)参数估计法进行参数估计。实验结果表明，该算法收敛较快，平均迭代次数不超过6次，线性模型平均计算耗时为150 s，二次模型平均耗时为418 s。提出的二维通用自回归模型滤波方法能较好地保留图像的细节信息，图像滤波效果好。

As the model fused a linear model and a nonlinear model is beneficial to digital image filtering, this paper explores a generalized autoregressive model on the basis of Weierstrass theory for image adaptive filtering. The model fuses both linear and nonlinear autoregressive models into a uniform expression and simulation experiments verify that the model can fit both conventional linear and nonlinear autoregressive models well. By using a bi-vector instead of a scalar parameter, the bi-dimensional expression of the model is deduced, then a generalized M-estimator is chosen to estimate parameters by a contrast analysis. The experimental results indicate that the proposed algorithm has a fast convergence speed, the average iterations are no more than 6 times and the computing time for linear model and quadratic model is 150 s and 418 s respectively. Moreover,it can remove image noises while conserve detailed image information effectively.