基于连分式的广义高斯分布的参数估计

近年来,使用广义高斯分布拟合的子带小波系数的统计模型被广泛地用于图像分类、修复、去噪和分析等图像处理中,而广义高斯分布的参数拟合问题一直是该领域中的一个重要的瓶颈问题。文章针对该问题提出用连分式迭代来实现广义高斯分布的参数估计,连分式迭代具有算法稳定、收敛域广、计算精度高、迭代速度快等特性;构造了基于连分式的广义高斯分布形状参数β的迭代格式。实验结果表明在不同方差噪声时,基于连分式迭代算法在计算时间复杂度和精度上优于牛顿迭代算法,而且收敛性不受初始值等参数制约,总能收敛到最优值附近。

Parameter estimation of generalized Gaussian distribution based on continued fractions

In recent years,the statistical model which uses the generalized Gaussian distribution(GGD) to fit the sub-band wavelet coefficients is widely used in image classification,restoration,denoising and analysis,and the parameter fitting problem of the GGD has always been a bottleneck in this field.In this paper,the continued fraction iteration,which has advantages of high calculation stability and accuracy,wide convergence domain and fast iteration speed,is used to implement the parameter estimation of the GGD.The iteration form of shape parameter β of the continued fraction based GGD is derived.The experimental results show that when different noise variance is added,the continued fraction iteration performs better than the Newton iteration in computational complexity and accuracy,and its convergence is not subject to the parameters like the initial value,and always converges to the optimal value.