Computation of the exact Cramer–Rao lower bound for the parameters of a nonsymmetric half-plane 2-D ARMA model

The Cramer–Rao lower bound (CRLB) that gives the minimal achievable variance/standard deviation for any unbiased estimator offers a useful tool for an assessment of the consistency of parameter estimation techniques. In this paper, a closed-form expression for the computation of the exact CRLB on unbiased estimates of the parameters of a two-dimensional (2-D) autoregressive moving average (ARMA) model with a nonsymmetric half-plane (NSHP) region of support is developed. The proposed formulation is mainly based on a matrix representation of 2-D real-valued discrete and homogeneous random field characterized by the NSHP ARMA model. Assuming that the random field is Gaussian, the covariance matrix of the NSHP ARMA random field is first expressed in terms of the model parameters. Then, using this matrix structure, a closed-form expression of the exact Fisher information matrix required for the CRLB computation of the NSHP ARMA model parameters is developed. Finally, the main formulas derived for the NSHP ARMA model are rearranged for its autoregressive and moving average counterparts, separately. Numerical simulations are included to demonstrate the behavior of the derived CRLB formulas.     

基于卡尔曼滤波的SAR图像边缘检测方法

针对传统 Canny 边缘检测算法对合成孔径雷达(SAR)图像的相干斑噪声抑制程度 太高,导致大量边缘的真实信息丢失问题,提出一种新型 Canny 算子边缘检测算法。首先建立 合适的非对称半平面区域(NSHP)图像模型,将空间模型转换成卡尔曼滤波可适用的系统状态方 程;然后用“预测+反馈”的方式对图像去噪;最后通过双阈值算法提取图像的边缘。仿真实验表 明,该方法可以有效地抑制 SAR 图像中的相干斑噪声,同时能较好地保留图像的边缘信息,相 对于传统的 Canny 算法有较好的检测效果。