Image decomposition using nonconvex functional

This paper proposes a new model for image decomposition by nonconvex functional minimization. Instead of using the Banach norm as the fidelity term, we use the integral of the square of residual component divided by its gradient as the fidelity term. This nonconvex fidelity term has very low value for the texture image and high value for the geometric image, so it is appropriate for image decomposition. The gradient descent procedure is used to solve the proposed minimization problem, which leads to evolve a new nonlinear second-order partial differential equation to steady state. The experimental results demonstrate the proposed model makes visual improvements compared with the classical OSV model, which includes that the cartoon component has less texture and the texture component has less cartoon information.