一种自适应Tikhonov正则化参数估计方法

An adaptive Tikhonov regularization parameter estimation method

为了解决离散线性反问题中正则化参数选择困难的问题,在Tikhonov正则化方法等效统计模型的基础上,提出了一种自适应Tikhonov正则化参数估计方法.将正则化参数选择的问题转换为关于被测信号和测量噪声的超参数的统计推断问题;基于测量噪声潜在的高斯分布特性,可在独立于测量噪声水平的条件下自适应地估计正则化参数.仿真结果表明:从最大化重建信号后验概率分布的角度来看,自适应Tikhonov正则化参数估计方法计算得到的正则化参数可视为具有随机分布特性的最佳正则化参数的近似折中,其对应的重建信号准确度接近于最优重建信号的准确度,且收敛速度较快.

To deal with the problem of regularization parameter determination in the discrete linear in- verse problem, an adaptive Tikhonov regularization parameter estimation method （ATRPEM） was proposed based on the equivalent statistical model of the Tikhonov regularization method. The idea of ATRPEM was to recast the regularization parameter determination as the statistical inference of the hyperparameters about the signal measured and the measure noise. Based on the implicit Gaussian dis- tribution property of the measure noise, ATRPEM could adaptively estimate the regularization param- eter without the measure noise level. The simulations show that, from view point of maximizing the posterior density of the reconstructed signal, the parameter estimated by ATRPEM can be seen as the approximately trade-off estimate of the optimum regularization parameter with random property, and the accuracy of the signal reconstructed by ATRPEM approximates to which of the optimum recon- structed signal.