Abstract:

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.

Key words: image inpainting; variational method; partial differential equations; Split Bregman algorithm; Euler’s elastica term