THE COMPLEX CEPSTRUM APPLIED TO 2-DIMENSIONAL IMAGES

The purpose of this paper is to provide an analytical understanding of the two-dimensional (2D) complex cepstrum and to apply the cepstrum in image processing. The analytical cepstrum is first developed in one dimension for the single echo case. This is followed by a more valuable analytical derivation for multiple echoes in one and two dimensions. The 2D, digital implementation of the forward and inverse cepstrum is then described. Three key applications are presented for 2D images: echo removal, automatic intensity control, and enhancement of repetitive features. A significant recommendation for future research is to investigate optimal filtering techniques based on the described analytical results.