Optimal denoising of rotationally invariant rectangular matrices

Code for reproducing the results in "Optimal denoising of rotationally invariant rectangular matrices"

Dependencies

• Numpy version 1.22.2
• Scipy version 1.7.1
• MPI4PY version 3.0.3
• Matplotlib version 3.5.1
• Pandas version 1.3.2

Note that MPI4PY also requires a MPI implementation. We refer to the MPI4PY documentation for further information.

How to generate the data

We have three kind of data:

• MMSE data: analytical estimate of the MSE of the optimal estimator. It's generated by MSE_int.py and stored in data/MMSE. It requires parameters Delta, R1, R2, NB_points (the number of subdivisions in the integration procedure) and epsilon_imag (we recommend not to change this parameter). All the others parameters have no effect on the data.
• RIE data: empirical MSE of the optimal estimator evaluated on actual matrices. It's generated by MSE_int.py and stored in data/MMSE. It requires parameters Delta, R1, R2, M and epsilon_imag (we recommend not to change this parameter). All the others parameters have no effect on the data.

How to generate figures from the data

The figures in the paper are obtained by running the scripts:

• Figure 1a: plot_low_rank_1.py
• Figure 1b: plot_high_rank.py
• Figure 2: plot_high_rank_approach.py
• Figure 3a: plot_low_rank_2.py
• Figure 3b: plot_low_rank_3.py