Algorithm 1:

2-D classification by invariant features

1	Input: Observations $Y_1,\dots ,Y_N$; noise variance ${\sigma }^2$.
2	Expand the observations in the Fourier-Bessel basis, and perform sPCA on the expansion coefficients using the method described in [34].
3	Estimate the mixed invariants of the true images using the sPCA coefficients of the data by (III.5), (III.6) and (III.7).
4	Estimate the sPCA coefficients of the true images and the distribution $\pi$ by solving the optimization problem (III.13).
5	Recover the images ${\widehat{I}}_1,\dots ,{\widehat{I}}_K$ from the sPCA coefficients by (III.16).
6	Output: images ${\widehat{I}}_1,\dots ,{\widehat{I}}_K$ (up to permutation and rotations); distribution $\widehat{\pi }$.