Abstract: A new adaptive total variation filtering method is presented, which depends on local information of signal. Wavelet threshold filtering is introduced. Regularization term in total variation is replaced by adaptive regularization term. Filtering strength is adjusted adaptively between total variation regularization and isotropic smoothing. Lagged diffusivity fixed point iteration is used to solve total variation minimization problem. The numerical experiments show that staircasing effect is reduced. The pseudo-Gibbs phenomenon is restrained. The detected edge and locations of discontinuity point, of the reconstructed signal, are very exact. And, the SNR is distinctly improved.

Key words: total variation, wavelet threshold denoising, adaptive regularization, anisotropic diffusion, lagged diffusivity fixed point iteration

摘要： 在整体变分方法去噪原理的基础上，通过引入小波阈值滤波，用自适应正则项代替整体变分模型中的正则项，提出了一种依赖于信号的局部信息进行滤波的自适应整体变分方法，自适应地在整体变分正则化和各向同性光滑化之间调整滤波强度。为求解整体变分极小化问题，采用了滞后扩散定点迭代的方法。数值计算结果表明：提出的方法有效地减少了传统整体变分方法去噪后恢复信号中所出现的阶梯效应，很好地抑制了小波变换中固有的伪Gibbs现象，重构信号的边缘、不连续点位置十分精确，信噪比也得到明显改善。

关键词: 整体变分, 小波阈值去噪, 自适应正则化, 各向异性扩散, 滞后扩散定点迭代