含Euler弹性项图像修复变分模型的快速Split Bregman算法

The fast split bregman algorithm for variational image inpainting model with euler's elastic

在图像修复的变分模型中引入Euler弹性项可有效修复大破损区域,但直接对该模型变分将导致高阶偏微分方程,其离散差分格式复杂、计算效率低。本文通过引入多个辅助变量和Bregman迭代参数将原模型转化为简单的Split Bregman迭代优化模型,并采用交替优化方法得到关于原变量和辅助变量一系列简单的Euler-Lagrange方程或广义软阈值公式。最后通过多个实验验证了算法的有效性。

The variational image inpainting model with Euler＇s elastica for regularizer can restore large broken domain,but it usually leads to higher order partial differential equations,which must be solved using complex finite difference schemes with low efficiency.The original variational model was transformed into a simple iterative optimization model of Split Bregman algorithm by introducing some auxiliary variables and Bregman iterative parameters and was solved it via alternating minimization procedure.The final equations are a series of simple Euler-Lagrange equation of the primal variable and some generalized soft thresholding formulas.Some numerical experiments validate this algorithm.