Model-based PDE method and model-free PDE method for motion de-blurring

Abstract

Once image motion is accurately estimated, we can utilize those motion estimates for image sharpening and we can remove motion blurs. First, for the motion de-blurring, this paper presents a model-based PDE method that minimizes the regularized energy functional defined with a spatially variant model of motion blurs. Unlike the case of spatially invariant image blurs, the minimization of the energy functional cannot be achieved in a closed non-iterative way, and we derive its iterative algorithm. The standard regularization method uses a square function to measure energy of its solution function, and employs the energy functional composed of the data-fidelity energy term to measure a deviation of a solution function from the assumed model of motion blurs and the regularization energy term to impose smoothness constraints on a solution function. However, the standard variational method is not proper for the motion de-blurring, because it is sensitive to model errors, and occurrence of errors are inevitable in motion estimation. To improve the robustness against the model errors, we employ a nonlinear robust estimation function for measuring energy to be minimized. Secondly, this paper experimentally compares the model-based PDE method with our previously presented model-free PDE method that does not need any accurate blur model. In the model-error-free case the model-based PDE method outperforms the model-free PDE method, whereas in the model-error case the latter works better than the former.