Implement Projector in Fourier Space (Slicing)

[ninamiolane]

What?

• Implement the projection operation of the cryo-EM image formation model on a 3D array in Fourier space, which is a slicing operation.
• Add details about the structure of the config input to the docstrings of the simSPI/linear_simulator/projector.py module.
• Add corresponding unit-tests.
• Use pre-commit (see README) to make sure that your code follows style guidelines.

Why?

Cryo-EM image formation model has different characteristics depending on whether it is formulated in image space (real space) or Fourier space (reciprocal space).

The community needs to be able to experiment with both formulations of the image formation model.

Where?

• The Projector class is located in the simSPI/linear_simulator/projector.py module.
• The unit-tests are here.

How?

• Allow the config input to the Projector class to have a space key, where the value will be either image or fourier.
• Rename current forward method into a private _forward_image method.
• Create a _forward_fourier method, with the projection operation in fourier space.
• Create a forward method that calls either _forward_image or _forward_fourier depending on the value in the self.config attribute.
• [ ]
  Details on the cryo-EM image formation models can be found in Donnat et al 2022.

[mbrubake]

This is close to being complete but some additional features are suggested and likely to be needed:

• Fourier space slicing with a specified resolution/radius in Fourier space, particularly in a circular region.
• Handling of the Hermitian nature of this Fourier transform, i.e., with a real signal, only half of the Fourier coefficients are needed. The other half are complex conjugates of the original.
• Need to specify conventions on FT for all of compSPI. For best interpolation performance when slicing assuming the volume is approximately centered in real space, DFT[I] = fft3(fftshift(I)). Also, the scaling factor of Fourier transform is important to identify clearly.
• Support different interpolation methods in the Projector API. At a minimum nearest neighbour and trilinear. Also need to specify and document the defaults.

Can try to put these into issues at some point but wanted to do a brain dump here