Wavelet transform (Numpy)

# Install s2wav
!pip install s2wav &> /dev/null

Lets start by importing some packages which we’ll be using in this notebook

import s2wav       # Wavelet transforms on the sphere and rotation group
import s2fft       # Spherical harmonic and Wigner transforms
import numpy as np

Now we’ll define the constraints of the problem and generated some random data just for this example

L = 16            # Spherical harmonic bandlimit
N = 3             # Azimuthal (directional) bandlimit
sampling = "mw"   # Sampling scheme

# Generate a random bandlimited signal to work with
rng = np.random.default_rng(12346161)
flm = s2fft.utils.signal_generator.generate_flm(rng, L)
f = s2fft.inverse(flm, L)

We can calculate the wavelet and scaling coefficients by running

wavelet_coeffs, scaling_coeffs = s2wav.analysis_base(f, L, N)

when an exact sampling theorem is chosen we can recover the original signal to machine precision by running

f_check = s2wav.synthesis_base(wavelet_coeffs, scaling_coeffs, L, N)

Lets double check that we actually got machine precision!

print(f"Mean absolute error = {np.nanmean(np.abs(f_check - f))}")

Mean absolute error = 2.056856753687673e-14