Scalar Wiener filter based on discrete trigonometric transforms and symmetric convolution

摘要

This paper presents a scalar Wiener filter derived in the transform domain of discrete trigonometric transforms. The implementation of the filter is through symmetric convolution, the underlying form of convolution for discrete trigonometric transforms. The symmetric convolution of two sequences is equivalent to their multiplication in the transform domain of discrete trigonometric transforms. This symmetric convolution-multiplication property and the fact that a type-II discrete cosine transform is asymptotically equivalent to the eigenvectors of the correlation matrix of a Markov-I process allows this scalar Wiener filter to be nearly optimum for Markov-I models. The performance of the filter is analyzed for the case of recovering an object corrupted by a 2D Gaussian filter in the presence of noise.