unbinned vs. Fourier-binned refinement

We have a ribosomal data set that goes down to ~3Å resolution, with which we’ve been conducting numerous tests. The data was collected in super-resolution mode, and an unbinned stack (pixel size 0.6565) was assembled. Additionally, the stack was Fourier binned by 2 using resample_mp.exe to a pixel size 1.315 and refined in an identical manner. Both stacks were normalized to mean 0 and std 1.

While the FSC curves for the two are very similar in shape / features, the super-resolution reconstruction is systematically improved at higher spatial frequencies. Of note, the final resolution of the reconstruction for the binned stack is very close to, but still below Nyquist (~0.8-0.9 Nyquist).

The Figure below shows the result:

1) red curve: unbinned super-resolution stack, orientations refined with unbinned data
2) blue curve: identical orientations as above (obtained from unbinned data), except that the stack was Fourier binned by 2
3) green curve: all orientations & final reconstruction obtained using binned by 2 stack

My understanding is that Fourier binning should be lossless, and thus an FSC curve for a reconstruction with Fourier-binned data that is still below Nyquist should match the FSC curve for the unbinned data. However, this is not the case in our result.

Some additional notes:

- different Fourier binning algorithms. Both resample_mp.exe and relion Fourier binnign provide virtually identical results
- using latest v9.11 version of Frealign
- the FSCs are not masked, apart from the soft spherical mask in Frealign. The curves are from the direct 1/2 maps output by Frealign

Any thoughts would be greatly appreciated.

Dmitry