## Image Processing Algorithm

An algorithm to process optical images was developed as a Master Thesis by Santiago Venegas, a student in the School of Engineering at the National Autonomous University of Mexico in Mexico City.

The Algorithm is based in polynomial transforms, in particular, Hermite transform. This transform is a representation model that analizes an optical image expanding locally as a weighted sum of orthogonal polynomials. The algorithm was applied to astronomical images (this is my contribution) from optical telescopes with CCD cameras.

Astronomical images taken with optical telescopes have noise as a result from the optics of the instrument, the atmosphere and the structure of the dome and telescope. This algorithm is based on analizing the image by means of overlapping windows and representing the local image content as a sum of weighted polynomials that are orthogonal with respect to the analysis window. In the case of a Gaussian analysis window, the orthogonal polynomials coorespond to the Hermite function.

The operators used to obtain the weighting polynomial coefficients can be shown to be derivatives of Gaussian functions. There are a number of parameters that have to be chosen in the definition of a polynomial transform. First, a Gaussian window function was selected. The orthogonal polynomials associated with the Gaussian window are the Hermite polynomials and their transform is called the Hermite transform. Second, the size of the window function needs to be set, this would be the spatial scale of the polynomial transform.

A basic problem in noise reduction leads to a compromise between smoothing noisy regions and preserving sharpness of important image features. The noise reduction problem is treated by explicitly making a systematic distinction between edges and homogeneous regions so that the smoothing process adapts itself to the image content. (1997 RMxAA, 33, 173) [21].

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J. Antonio Garcia-Barreto (tony@astroscu.unam.mx)
(Created: August 20, 1998. Updated: August 20, 1998)