Abstract
Based on the polynomial transform theory we show applications for noise reduction, deconvolution and coding in astronomical images. The proper interpretation of an astronomical image, requires to obtain relevant information from the structures contained in it. This procedure requires to process the data locally. For our applications, it is required that the image data, which are given as an array of intensity values, be interpreted into meaningful patterns. For this purpose, we use the Hermite transform. This transform is an image representation model that analyzes an image by locally expanding it into a weighted sum of orthogonal polynomials. The applications that we propose are developed on pyramidal structures. Their purpose is to analyze optical astronomical images at different spatial scales.
