We present a method to model optical images of galaxies using Expectation Maximization Principal Components Analysis (EMPCA). The method relies on the data alone and does not assume any pre-established model or fitting formula. It preserves the statistical properties of the sample, minimizing possible biases. The precision of the reconstructions appears to be suited for photometric, morphological and weak lensing analysis, as well as the realization of mock astronomical images. Here, we put some emphasis on the latter because weak gravitational lensing is entering a new phase in which systematics are becoming the major source of uncertainty. Accurate simulations are necessary to perform a reliable calibration of the ellipticity measurements on which the final bias depends. As a test case, we process $7038$ galaxies observed with the ACS/WFC stacked images of the Hubble eXtreme Deep Field (XDF) and measure the accuracy of the reconstructions in terms of their moments of brightness, which turn out to be comparable to what can be achieved with well-established weak-lensing algorithms.
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