Fast and Stable Computation of the Charlier Moments and Their Inverses Using Digital Filters and Image Block Representation

TLDR: A new method of fast and stable calculation of the discrete orthogonal moments of Charlier and their inverses with digital filters based on the Z-transform to accelerate the computation time and improve the quality of images reconstruction.

Abstract: In this paper, we suggest a new method of fast and stable calculation of the discrete orthogonal moments of Charlier and their inverses. This method is meant to accelerate the computation time and improve the quality of images reconstruction. In this method, we have combined two main concepts. The first concept is the digital filters based on the Z-transform to accelerate the calculation process of the discrete orthogonal moments of Charlier. The second concept is the partitioning of the image into a set of blocks of fixed sizes where each block is processed independently. The significant reduction in the image space during partitioning makes it possible to represent the minute details of the image with only low orders of Charlier’s discrete orthogonal moments, which ensures the digital stability during the processing of the image. In order to demonstrate the efficiency, stability, and precision of our method compared to other existing methods, some simulations have been performed on different types of binary images and gray images with and without noise.