Add code for emulated single coil

[mmuckley]

This issue would add code for simulating the single-coil data from multi-coil data described in the following paper:

Tygert M, Zbontar J. Simulating single-coil MRI from the responses of multiple coils. Communications in Applied Mathematics and Computational Science. 2020 Nov 19;15(2):115-27. https://msp.org/camcos/2020/15-2/p01.xhtml

[sriram-1]

Hi, am interested. Please let me know the next steps.

[mmuckley]

Hello @sriram-1, that would be fantastic! I think the first thing would be to read the paper and understand the mathematics of how the single-coil data was simulated. Then you could create a function with a signature like

def simulate_singlecoil_from_multicoil(kspace: Tensor) -> Tensor:
    # write function here

that would return the single-coil k-space based on the paper.

Create a new folder under fastmri_examples called singlecoil_simulation and include a Jupyter notebook using your function and plot the reconstruction. Compare the reconstruction from single-coil to the reconstruction from multi-coil. The single-coil should be noisier.

Once you have all this you can open a pull request and I'll review it. Once everything looks good we can merge it into the repo.