Learning sparse representations on the sphere

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 α-shearlets. We investigate their relative performance to represent and denoise complex structures on different astrophysical data sets on the sphere.

References in corpus (9)

• The NumPy array: a structure for efficient numerical computation
• Full-Sky Weak Lensing Simulation with 70 Billion Particles
• Planck CMB Anomalies: Astrophysical and Cosmological Secondary Effects and the Curse of Masking
• Wavelet-Bayesian inference of cosmic strings embedded in the cosmic microwave background
• Polarized wavelets and curvelets on the sphere
• Wavelet reconstruction of E and B modes for CMB polarisation and cosmic shear analyses
• The cosmic microwave background Cold Spot anomaly: the impact of sky masking and the expected contribution from the Integrated Sachs-Wolfe effect
• Sparse point-source removal for full-sky CMB experiments: application to WMAP 9-year data
• Analysis vs. synthesis sparsity for $\alpha$-shearlets