Image restoration based on a Wiener filtering technique using discrete cosine transform

This paper proposes a Wiener filtering restoration technique for a degraded image using the discrete cosine transform (DCT). The principle of the method is based on the property that the convolution that represents the degradation corresponds to the multiplication in the DCT transform domain. Using DCT, the condition assumed for the signal becomes more practical compared to conventional Wiener filtering using the discrete Fourier transform (DFT). In other words, instead of the periodic boundary condition in DFT, the even symmetry of the boundary condition is assumed. Because of this property, the generation of the false frequency component is suppressed and a better restoration is obtained. The DCT Wiener filtering is formulated using the matrix-vector representation. It is shown first that the matrices representing the image model and the degradation model are diagonalized by DCT. Then, it is shown that the filter gain is represented in terms of the eigenvalues of those matrices. As degradations, a uniform one- and two-dimensional blur, as well as a two-dimensional Gaussian blur, are considered. Through computer experiment using simulated and actual degraded images, the effectiveness of the proposed method is demonstrated. Then, the block partitioning is applied, and the adaptive processing considering the nonuniformity of the image is presented.