A simple example to showcase autodiff

[chaithyagr]

We could have possibly the following examples:

• A simple U-Net (pulled from fastMRI dataset possibly), trained? @Lenoush can you handle this in your free time?
• A network built with DeepInv library for some already preset reconstruction (PnP possibly?) @matthieutrs can you handle this this in your free time? I think you can also have something basic passed to @Lenoush and she can work on it forward.
• A simple example where we could learn the trajectory possibly? @alineyyy can you handle this in your free time? Have a trajectory learner example and reform the documentation build flow #167
• Add additional support for learning a sampling pattern in 2D with straight line readouts. Perhaps we can do it while supporting stackNUFFT on torch?

[paquiteau]

Beware, there is also autodiff for the image/k-space data (the one that is only currently supported) This could also be show cased.

[chaithyagr]

I really seemed to have clicked open issue too soon. I had written so much more xD. Lemme update

[chaithyagr]

@AsmaTANABEN , can you have a look at the notebook shared in mattermost and see if we can get this on mri-nufft?

[chaithyagr]

Reopening as it got closed by mistake :P

[chaithyagr]

I added that we could have additional support for learning a sampling pattern in 2D with straight line readouts.

Perhaps we can do it while supporting stackNUFFT on torch? @paquiteau is this possible? Can we pass the backprop gradients through the stacked NUFFT from the internal plane NUFFT?

[chaithyagr]

On second thoughts, we would need 176 2D NUFFT then num_samples number of FFTs, I think a simple straightforward 3D NUFFT can be easier. @paquiteau to comment. I think in your usecase for fMRI it is more useful.

[paquiteau]

after rethinking about it, stacked nufft does not have autodiff wrt to trajectory. It does support the autodiff wrt to data however.