Fig. 1: Wavelet decomposition of the AMB+.
From: Effective energy, interactions and out of equilibrium nature of scalar active matter
The iterative wavelet decomposition, or fast wavelet transform, (in green) iteratively decomposes the field φj−1,with length scale 2j−1, into a coarser approximation φj, and 3 wavelet coefficient images \({\overline{\varphi }}_{j}\), with sub-sampled low-pass filtering G and high-pass filtering, along different directions, \(\overline{G}\). It can be inverted (in blue), and φj−1 can be recovered from \(({\varphi }_{j},{\overline{\varphi }}_{j})\), with the transpose operators \(({G}^{{{{\rm{T}}}}}{\overline{G}}^{{{{\rm{T}}}}})\). Illustration is done over a realization of AMB+ at parameters (λ, ξ) = (1, 4), which sets the amount of activity of the model.
