Compression

s2scat.compression.C01_C11_to_isotropic(C01: List[float64], C11: List[float64], J_min: int, J_max: int) → Tuple[Array]

Convert the fourth (C01) and sixth (C11) order covariances to isotropic coefficients.

Parameters:

• C01 (List[jnp.float64]) – Fourth order covariance statistic \(\text{Cov}\big [ \Psi^{\lambda_1} f, \Psi^{\lambda_1} | \Psi^{\lambda_2} f | \big ]\).

• C11 (List[jnp.float64]) – Sixth order covariance statistic \(\text{Cov}\big [ \Psi^{\lambda_1} | \Psi^{\lambda_3} f |, \Psi^{\lambda_1} | \Psi^{\lambda_2} f | \big ]\).

• J_min (int) – Minimum dyadic wavelet scale to consider.

• J_max (int) – Maximum dyadic wavelet scale to consider.

Returns:

Isotropic fourth and sixth order scattering covariance statistics.

Return type:

Tuple[jnp.ndarray]

Notes

For isotropic coefficients the statistics will be contracted across \(n\). This will dramatically compress the covariance representation, but will be somewhat less sensitive to directional structure.