Add functionality for dependency between echoes

[handwerkerd]

Summary

EPITI sequences may be very useful for multi-echo denoising. They generate many more echoes and have significantly less spatial distortions. One issue is that neighboring echoes use overlapping k-space data (similar to a sliding window). That means one might get a new echo every few milliseconds, but echoes that are independent and don't use any of the same underlying k-space data may be approximately 10ms apart. When using these data for denoising, we may want to include all the echoes, but this dependence would be required to be accounted for whenever a fit threshold is used.

Additional Detail

There are several publications on the EPITI sequences, but the original and this video on it might be good starting points: Wang F, Dong Z, Reese TG, et al. Echo planar time-resolved imaging (EPTI). Magn Reson Med. 2019;81(6):3599-3615. doi:10.1002/mrm.27673 Fuyixue Wang and Kawin Setsompop: Echo Planar Time-resolved Imaging (EPTI) YouTube summary

Next Steps

• There's a good chance I'll be collecting some EPITI data soonish (months?). Once I/we have the data we might might have a better idea what's necessary to change & how much work it will be. I'm not sure when anyone will focus on this issue, but I wanted to open it now to let others know & potentially spark discussion.
• Add an input option to mark dependence between echoes
• Identify where statistical thresholds matter. Is it just DICE or are there other places where the thresholds and not just the fits are used?
• Check if a large increase in the number of echoes causes non-trivial memory/processing/visualization issues

[tsalo]

@handwerkerd Have you had a chance to acquire any EPTI data?

[handwerkerd]

Not yet. I'm working on another acquisition project now, but I should follow up on at least getting some EPITI data.