Restoration of rotational motion blurred image based on Chebyshev polynomial interpolations

Abstract

The restoration of rotational motion blurred image involves a lot of interpolations operators in rectangular-to-polar transformation and its inversion of polar-to-rectangular. The technique of interpolation determines the quality of restoration and computational complexity. In this paper, we incorporate orthogonal chebyshev polynomials interpolations into the processing of restoration of rotational motion blurred image, in which the space-variant blurs are decomposed into a series of space-invariant blurs along the blurring paths, and the blurred gray-values of the discrete pixels of the blurring paths are calculated by using of orthogonal chebyshev polynomials' interpolations and the space-variant blurs can be removed along the blurring paths in the polar system. At same way, we use orthogonal chebyshev polynomials' interpolations to perform polar-to-rectangular transformation to put the restored image back to its original rectangular format. In order to overcome the interference of noise, an optimization restoration algorithm based on regularizations is presented, in which non-negative and edge-preserving smoothing are incorporated into the process of restoration. A series of experiments have been performed to test the proposed interpolation method, which show that the proposed interpolations are effective to preserve edges.