Dimensionality Reduction Techniques for Modelling Point Spread Functions in Astronomical Images

Even though 96% of the Universe is consisted of dark matter and dark energy, their nature is unknown since modern physics are not adequate to define their characteristics. One new approach that cosmologists are using, tries to define the dark Universe by precisely measuring the shear effects on galaxy images due to gravitational lensing. Except the shear effect on the galaxies, there is also another factor that causes distortion on the images, called the Point Spread Function (PSF). The PSF is caused by atmospheric conditions, imperfections on the telescopes and the pixelisation of the images when they are digitally stored. This means that before trying to calculate the shear effect, the PSF must be accurately calculated. This dissertation is part of the GREAT10 star challenge, which is on predicting the PSF on non-star position with high accuracy. This work focuses on calculating the PSF at star positions with high accuracy so that these values can later on be used to interpolate the PSF on non-star positions. For the purposes of this dissertation, dimensionality reduction techniques are used to reduce the noise levels in the star images and to accurately capture their PSF. The techniques used are Principal Component Analysis (PCA), Independent Component Analysis (ICA) and kernel PCA. Their reconstructed stars are further processed with the Laplacian of Gaussian edge detection for capturing the boundary of the stars and removing any noise that is outside this boundary. The combination of these techniques had promising results in the specific task and outperformed the baseline approaches that use quadrupole moments.