A Fast Operator-splitting Method for Beltrami Color Image Denoising

The Beltrami framework is a successful technique for color image denosing by regarding color images as manifolds embedded in a five dimensional spatial-chromatic space. It can ideally model the coupling between the color channels rather than treating them as if they were independent. However, the resulting model with high nonlinearity makes the related optimization problems difficult to solve numerically. In this paper, we propose an operator-splitting method for a variant of the Beltrami regularization model. From the optimality conditions associated with the minimization of the Beltrami regularized functional, we derive an initial value problem (gradient flow). We solve the gradient flow problem by an operator-splitting scheme involving three fractional steps. All three subproblem solutions can be obtained in closed form or computed by one-step Newton’s method. We demonstrate the efficiency and robustness of the proposed algorithm by conducting a series of experiments on real image denoising problems, where more than half of the computational time is saved compared to the existing augmented Lagrangian method (ALM) based algorithm for solving the Beltrami minimization model.