分数阶全变分泊松去噪的快速线性化增广拉格朗日方法

Fast linearized augmented Lagrangian method for Poisson denoising using fractional-order total variation

近年来,有关分数阶全变分(FOTV)的图像去噪问题被广为研究。快速傅里叶变换(FFT)是求解相关子问题最常用的方法,但是FFT只适用于周期边界条件。为了能在非周期边界条件下也能实现好的去噪效果,针对FOTV泊松图像去噪模型,结合增广拉格朗日方法(ALM)和线性化技术提出新的算法。实验表明,在周期边界条件下,与采用FFT的增广拉格朗日方法相比,本文提出的算法在达到几乎相同的去噪效果时,收敛速度较快。而且在零Dirichlet边界条件时,也能实现好的去噪效果。

In recent years,the problem of image denoising using fractional-order total variation(FOTV)has been widely studied.Fast Fourier transform(FFT)is the most universal method to solve related subproblems,but it’s only suitable for periodic boundary conditions.In order to achieve good denoising effect under non-periodic boundary conditions,a new algorithm is proposed for FOTV-based Poisson image denoising model combining the augmented Lagrangian method(ALM)and the linearization technique.Experiments show that compared with ALM using FFT,under periodic boundary conditions,our proposed algorithm converges faster when achieving almost the same denoising effect.Moreover,good denoising effect can also be obtained under zero Dirichlet boundary conditions.