Fast Algorithm for Gradient Domain Optimization on Image

In many digital image processing problems,the objective function is a constraint on the image gradient and the objective energy includes the regularization term and fidelity term.In this paper,we propose a new optimization formulation and an alternating direction method of multipliers(ADMM)based method to solve these problems.With this new formulation,the original optimization problem can be decomposed into many small problems,and each sub-problem has closed form solution.The time complexity of the proposed algorithm in each iteration is proportional to the image resolution.Besides,the algorithm can be further parallelized based on segmenting the image.We apply the proposed algorithm to two classic image processing problems:L0 norm based image smoothing and Poisson image editing.Compared with the existing iterative algorithms,our proposed algorithm can achieve faster computation speed and cost less memory while achieving similar results.