Sparse Representation of Photometric Galaxy Redshift PDFs

Sparse Representation of Photometric Galaxy Redshift PDFs: A Dictionary Learning Approach

Zijlstra, J.

Jongbloed, G. (mentor)

Electrical Engineering, Mathematics and Computer Science

Delft Institute of Applied Mathematics (DIAM)

2016-12-06

In the past few decades telescopes have given us insight into the structures of the observable universe. Current and future astronomical research investigate problems that concern how these structures have been formed and at which rates cosmic structures grow. The redshift of galaxies plays a fundamental role in this research directions, since these redshifts are used as a measure of distance in astronomy. To obtain a good understanding of the uncertainties in the redshift estimates, astronomers are currently estimating the probability density function (PDF) of each galaxy redshift. Seeing the enormous number of observed galaxies (in the order of billions of galaxies in current and future sky surveys), storing each galaxy redshift PDF has become a major storage problem. In this thesis we are therefore investigating a method that aims to find accurate sparse representations of the redshift PDFs. This boils down to storing each PDF with a small number of basis functions without losing the shape of the PDF. An additional problem that arises from the large number of observed galaxies is the computation time per PDF during the sparse representation process. To address both the sparse representation problem and the problem concerning the computation time per PDF, we investigate a dictionary learning method in this thesis. In dictionary learning, a set of basis functions learn the complex structures of the redshift PDFs directly from the data in a statistical learning fashion. This brings a level of flexibility such that the necessary structures can be captured in a small set of learned basis functions, which favors the computation time problem. The learned basis functions are stored in a dictionary and in this thesis we use the K-SVD algorithm to learn the dictionary. We show that K-SVD yields very accurate sparse representations which are similar to the results of a successful method proposed in the literature. An interesting result is that the learned dictionary only needs 0.03\% of the time needed in the alternative method to sparsely represent a redshift PDF. A reference method with the same computation time per PDF will be examined to put the K-SVD results into perspective. Wavelet basis functions are used to this end and we show that the sparse representations obtained with K-SVD result in higher accuracies.

http://resolver.tudelft.nl/uuid:0f621923-ac98-4f57-a896-b8f3ca0516f7

Student theses

master thesis

(c) 2016 Zijlstra, J.