A new tool for image analysis based on Chebyshev rational functions:
  CHEF functions
  We introduce a new approach to the modelling of the light distribution of
galaxies, an orthonormal polar base formed by a combination of Chebyshev
rational functions and Fourier polynomials that we call CHEF functions, or
CHEFs. We have developed an orthonormalization process to apply this basis to
pixelized images, and implemented the method as a Python pipeline. The new
basis displays remarkable flexibility, being able to accurately fit all kinds
of galaxy shapes, including irregulars, spirals, ellipticals, highly compact
and highly elongated galaxies. It does this while using fewer components that
similar methods, as shapelets, and without producing artifacts, due to the
efficiency of the rational Chebyshev polynomials to fit quickly decaying
functions like galaxy profiles. The method is lineal and very stable, and
therefore capable of processing large numbers of galaxies in a fast and
automated way. Due to the high quality of the fits in the central parts of the
galaxies, and the efficiency of the CHEF basis modeling galaxy profiles up to
very large distances, the method provides highly accurate estimates of total
galaxy fluxes and ellipticities. Future papers will explore in more detail the
application of the method to perform multiband photometry, morphological
classification and weak shear measurements.
