Learning sparse representations on the sphere

TL;DR

This paper introduces adaptive methods to learn sparse representations directly from spherical data, enabling improved feature extraction and denoising for astrophysical applications.

Contribution

It proposes two novel approaches: a patch-based dictionary learning method and a parametrized family of representations called alpha-shearlets.

Findings

The learned representations outperform fixed systems in denoising tasks.

Adaptive methods effectively capture complex structures on spherical astrophysical data.

The approaches demonstrate versatility across different data sets.

Abstract

Many representation systems on the sphere have been proposed in the past, such as spherical harmonics, wavelets, or curvelets. Each of these data representations is designed to extract a specific set of features, and choosing the best fixed representation system for a given scientific application is challenging. In this paper, we show that we can learn directly a representation system from given data on the sphere. We propose two new adaptive approaches: the first is a (potentially multi-scale) patch-based dictionary learning approach, and the second consists in selecting a representation among a parametrized family of representations, the {\alpha}-shearlets. We investigate their relative performance to represent and denoise complex structures on different astrophysical data sets on the sphere.