An implementation of rotated monogenic scattering transform network of 2-D signal $g$.

Let $\theta \in [0, 2 \pi)$. Denote the Riesz kernel $r_l$ and Riesz transform $R_l$ as

$$r_l({\bf x}) = c_l \dfrac{x_l}{\Vert {\bf x} \Vert^3}$$

and

$$R_l g({\bf x}) = \tilde{g}^{(l)}({\bf x}) = (r_l ** g)({\bf x}).$$

Denote the rotated signal as

$$\tilde{g}_{-\theta}({\bf x}) = g({\bf R}_\theta {\bf x}).$$

The Risez tranform of the rotated signal is

$$\tilde{g}^{(l)}_{-\theta}({\bf x}) = R_l \tilde{g}_{-\theta}({\bf x}).$$

The rotated monogenic decomposition is

$$\tilde{g}^{\pm}_{-\theta, \theta}({\bf x}) = g({\bf x}) \pm \bigg( {\bf i} \tilde{g}^{(1)}_{-\theta}({\bf R}_{-\theta} {\bf x}) + {\bf j} \tilde{g}^{(2)}_{-\theta}({\bf R}_{-\theta} {\bf x} ) \bigg).$$

Before running the code, load packages

using CUDA
using ScatteringTransform
using MonogenicFilterFlux

Suppose the feature dimension is (nTrain_x, nTrain_y, 1, nSubsample).

The $l$-th layer monogenic scattering transform network with maximum scale $s$ is

scale = s; 
st = stFlux((nTrain_x, nTrain_y, 1, nSubsample), 2, σ=abs, outputPool = 1, scale = scale); 
st = cu(st);

Suppose input_data is the input of the 2-D signal, and set $\theta$ as ang.

We can find the rotated monogenic decomposition of the scattering output by

img_rot = rotate_image(input_data, ang);
output_rot = st(cu(img_rot))
output_rot = inv_rotate_out(output_rot, img_rot, -ang);