3-D adaptive digital signal processing for video signal

1. 本文首先提出了一种基于方程误差的二维自适应级联IIR滤波器的滤波算法。众所周知，基于方程误差的自适应IIR滤波算法具有快速收敛和单峰均方误差面等优点。然而，在测量噪声存在的情况下，它们收敛到有偏参数估计。为了解决偏置问题，该算法使用每个级联部分的输出误差的缩放值作为嵌入在相应部分更新过程的信号部分的加性噪声的估计。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，导出了保持稳定性所需的约束条件。其次，研究了作为双指标动态系统的二维LMS自适应滤波算法的稳态均方误差（MSE）分析，该算法的权重沿垂直和水平方向更新。MSE分析是使用众所周知的独立性假设进行的。首先，我们证明了双索引二维LMS算法的权重误差协方差矩阵的计算需要对大空间滞后的权重误差相关系数进行近似。然后，我们提出了一种解决这一问题的方法。对输入信号为白高斯信号的特殊情况进行了进一步的讨论。结果表明，当步长范围明显小于均值收敛所需的步长范围时，MSE意义上的收敛发生。

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.