The Split Bregman method of variational OSV model for image decomposition

Images can be decomposed into structural component and textural component with the variational OSV (Osher-Sole-Vese) model for image decomposition, but the minimization problem must be realized through solving some 4^th order partial differential equations (PDE) by means of complex finite difference scheme for Laplacian of curvature which leads to low computational efficiency. The Split Bregman method for OSV model is proposed in this paper by means of introducing some auxiliary variables and Bregman iterative parameters, and the minimization problem is transformed into solving some simple Euler-Lagrange equations of primal variables and some soft threshold formulas of auxiliary variables with closed form. Additionally, inspired by TV-L¹ model of image diffusion, a modified OSV model is proposed by replacing the data terms of the original model with total variational form and the related Split Bregman algorithm is also designed, which can improve the quality of textures and reduce the loss of geometry of the structural component. Finally, some experiments are provided to validate the proposed algorithms and compared with the results obtained through dual method in computation efficiency and decomposition quality.