Science-driven 3D data compression

TL;DR

This paper introduces a novel 3D data compression method based on the Karhunen-Loève transform, effectively reducing data dimensionality while preserving key cosmological information from galaxy surveys and weak lensing.

Contribution

It presents a new KL-based compression technique that outperforms traditional tomographic methods in extracting uncorrelated modes for cosmological analysis.

Findings

Most of the signal-to-noise can be compressed into a single mode for weak lensing.

A small number of modes suffices for optimal constraints in galaxy clustering.

The method simplifies analysis by reducing the number of modes needed for accurate results.

Abstract

Photometric redshift surveys map the distribution of matter in the Universe through the positions and shapes of galaxies with poorly resolved measurements of their radial coordinates. While a tomographic analysis can be used to recover some of the large-scale radial modes present in the data, this approach suffers from a number of practical shortcomings, and the criteria to decide on a particular binning scheme are commonly blind to the ultimate science goals. We present a method designed to separate and compress the data into a small number of uncorrelated radial modes, circumventing some of the problems of standard tomographic analyses. The method is based on the Karhunen-Lo\`{e}ve transform (KL), and is connected to other 3D data compression bases advocated in the literature, such as the Fourier-Bessel decomposition. We apply this method to both weak lensing and galaxy clustering. In the case of galaxy clustering, we show that the resulting optimal basis is closely associated with the Fourier-Bessel basis, and that for certain observables, such as the effects of magnification bias or primordial non-Gaussianity, the bulk of the signal can be compressed into a small number of modes. In the case of weak lensing we show that the method is able to compress the vast majority of the signal-to-noise into a single mode, and that optimal cosmological constraints can be obtained considering only three uncorrelated KL eigenmodes, considerably simplifying the analysis with respect to a traditional tomographic approach.