The S2 code provides functionality to support functions defined on the sky and was developed primarily for astrophysical applications. More generally, however, any arbitrary function defined on the sphere may be represented. Both real space map and harmonic space spherical harmonic representations are supported.
Basic sky representations have been extended to simulate full sky noise distributions and Gaussian cosmic microwave background realisations. Support for the representation and convolution of beams is also provided.
S2DW provides functionality to perform the scale discretised wavelet transform on the sphere. Routines are provided to compute wavelet and scaling coefficients from the spherical harmonic coefficients of a signal on the sphere and to synthesise the spherical harmonic coefficients of the original signal from its wavelet and scaling coefficients. The reconstruction of the spherical harmonic coefficients of the original signal is exact to numerical precision.
Functionality to support functions defined on the sphere is provided by the S2 code.
S2FIL provides functionality to support optimal filtering on the sphere. Optimal directional matched (MF) and scale adaptive (SAF) filters may be constructed from a template and stochastic background process. Functionality is also incorporated to filter a sky data map with an optimal filter. Moreover, a simple object detection algorithm is implemented to extract embedded object parameters from the filtered field.
Functionality to support functions defined on the sphere is provided by the S2 code; template objects are defined in the COMB code; and functionality to perform fast directional filtering on the sphere is provided by the FastCSWT code.
S2LET provides efficient routines for fast wavelet analysis of signals on the sphere. It supports both axisymmetric and directional wavelet transforms. The wavelet transforms are theoretically exact, i.e. the original signal can be synthesised from its wavelet coefficients exactly since the wavelet coefficients capture all the information content of band-limited signals.
It is primarily intended to work with the SSHT code built on our novel sampling theorem on the sphere to perform exact spherical harmonic transforms on the sphere.
SSHT provides functionality to perform fast and exact spin spherical harmonic transforms based on the sampling theorem on the sphere derived in our paper: A novel sampling theorem on the sphere.
In some applications adjoint forward and inverse spherical harmonic transforms are also required (for example, when solving convex optimisation problems). Functionality to perform fast and exact adjoint transforms is also included, based on the fast algorithms derived in our paper: Sparse image reconstruction on the sphere: implications of a new sampling theorem.