Prior
This module implements the prior calculations. Since this is also typically the non-differentiable part of the MCMC algorithms, proximal calculations are also performed here.
- class prior.L1(setting, fwd, adj, T)
Base L1-norm prior. The prox of this prior is soft thresholding.
- Parameters
setting (string) – ‘analysis’ or ‘synthesis’
fwd – function handle for transform operator (e.g.
transforms.Transform.forward())adj – function handle for adjoint transform operator (e.g.
transforms.Transform.forward_adjoint())T (float) – threshold for the soft thresholding function
Todo
fwdandadjare only needed for analysis setting. Make these optional arguments.- prior(X)
Calculates the logprior of mcmc sample
- Parameters
X – MCMC sample
- Returns
log prior
- proxf(X)
Calculates the proximal map of the log prior
- Parameters
X – MCMC sample
- Returns
prox of log prior
- class prior.S2_Wavelets_L1(setting, fwd, adj, T, L, B, J_min, dirs=1, spin=0)
L1 regulariser for wavelets on S2 (MW sampling). Performs some weighting to avoid overemphasizing pixels at the poles.
- Parameters
L (int) – angular bandlimit
B (float) – wavelet scale parameter
J_min (int) – minimum wavelet scale
dirs (int) – azimuthal bandlimit for directional wavelets
spin (int) – spin number of spherical signal
- prior(X)
Calculates the logprior of mcmc sample
- Parameters
X – MCMC sample
- Returns
log prior
- class prior.S2_Wavelets_L1_Power_Weights(setting, fwd, adj, T, L, B, J_min, dirs=1, spin=0, eta=1)
L1 regulariser for wavelets on S2 (MW sampling). Includes weighting for pixel area, wavelet power wavelet decay See eqns 33&34 from Wallis et al 2017
- Parameters
L (int) – angular bandlimit
B (float) – wavelet scale parameter
J_min (int) – minimum wavelet scale
dirs (int) – azimuthal bandlimit for directional wavelets
spin (int) – spin number of spherical signal
eta (float) – wavelet decay tuning parameter
- prior(X)
Calculates the logprior of mcmc sample
- Parameters
X – MCMC sample
- Returns
log prior