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Image Restoration from Motion Blurred Image using PDEs formalism

Image restoration is the process of recovering original image from its degraded version. One possibility of the image degradation is the relative motion between the camera and the object which may blur the captured image during its formation. In this paper, a generalized Partial Differential Equations (PDEs) based model of image is proposed to recover the original image from the blurred image in spatial domain itself. For digital implementations, the resulting PDE is discretized using Lax method which is the modified form of Forward Time Centred Space (FTCS) differencing scheme that stabilizes the FTCS scheme. Therefore, the PDE that models the motion blur and image restoration process is a 1D flux-conservative equation or wave equation with added diffusion term which is in the form of the Navier-Stokes equation for viscous fluid. The proposed method is implemented in software using MATLAB for various grey test images for various length of motion blur in pixels and the subjective analysis of the result shows desired results.