3-D adaptive digital signal processing for video signal

1.首次提出了一种基于方程误差的分母函数可分离的二维级联IIR自适应滤波器的去偏算法。众所周知，基于方程误差的自适应IIR滤波算法具有收敛速度快、具有单峰均方误差曲面等优点。然而，在存在测量噪声的情况下，它们收敛于有偏的参数估计。为了处理偏差问题，该算法使用每个级联段的输出误差的比例值作为相应段更新过程的信号部分中嵌入的加性噪声的估计。因此，在保持方程误差IIR滤波器良好收敛特性的同时，抑制了测量噪声的影响。进行了输入输出稳定性分析，推导出了保持稳定所需的约束条件。其次，本研究考虑了二维LMS自适应滤波算法的稳态均方误差(MSE)分析，在该算法中，滤波器的权值在垂直和水平方向上都被更新为一个双指标动态系统。MSE分析使用众所周知的独立性假设进行。首先，我们证明了双指标2-D LMS算法的加权误差协方差矩阵的计算需要在较大空间滞后时的加权误差相关系数的近似。然后，我们提出了一种解决这一问题的方法。对输入信号为高斯白噪声时的特殊情况进行了进一步的讨论。结果表明，均方误差意义下的收敛发生在步长明显小于平均收敛所需步长的范围内。

1. This research first proposes a bias removal algorithm for equation error-based 2-D adaptive cascade IIR filters with separable denominator function. As well known, equation error-based adaptive IIR filtering algorithms have the advantages of fast convergence and unimodal mean-square-error surface. However, they converge to biased parameter estimates in the presence of measurement noise. To handle the bias problem, the proposed algorithm uses a scaled value of the output error of each of the cascade sections as an estimate for the additive noise embedded in the signal part of the update procedure of the corresponding section. Thus, while maintaining the good convergence properties of equation error IIR filters, the effect of the measurement noise is suppressed. Input-output stability analysis is carried out, and the constraints required to maintain stability are derived.2. This research secondly considered the steady state mean square error (MSE) analysis for 2-D LMS adaptive filtering algorithm in which the filter's weights are updated along both vertical and horizontal directions as a doubly-indexed dynamical system. The MSE analysis is conducted using the well-known independence assumption. First we show that computation of the weight-error covariance matrix for doubly-indexed 2-D LMS algorithm requires an approximation for the weight-error correlation coefficients at large spatial lags. Then we propose a method to solve this problem. Further discussion is carried out for the special case when the input signal is white Gaussian. It is shown that the convergence in the MSE sense occurs for step size range that is significantly smaller than the one necessary for the convergence of the mean.