Dear Sheeba,
I've recently read the corresponding papers, so here my two cents for the meantime (don't take it for granted):
In principle it should be possible, but I'm not sure whether it is really that useful, as these toolboxes are dedicated to DTI data and underlying issues. With different diffusion directions/vectors the images have a different contrast and the realignment becomes more difficult ("between-modality registration"), which should not be the case for EPI ("within-modality registration"). Another issue is that during realignment, you can adjust the settings so that the images are oriented onto the first image in an initial step and onto the calculated EPI mean image in the next step (which should improve quality, as a single image might always suffer from particular artefacts and lower SNR). With ECMOCO you seem to need a representative target image, but as you have no mean EPI image you would have to rely on the first or a random EPI image (or maybe the SE-EPI, but this should again reduce the quality due to different contrasts).
Concerning HySCO, the idea is to run sequences with opposite phase encoding direction and also use these data sets for correction, which is easy to accomplish with DTI (several relatively short sequences) but rather uncommon for fMRI. However, I remember a few papers focusing on e.g. amygdala which indeed used opposite phase encoding for different EPI runs. Your data set seems to be diffferent though, as all your GE-EPI are in one phase encoding direction (?) and you've acquired additional SE-EPI sequences. In that case you could also have gone with a fieldmap (as you've increased the scanning time anyway, which HySCO is thought to keep at a minimum by working on the data itself). As far as I understand these SE-EPI sequences can be used to correct the SE-EPI data, but not for other data.
Finally, Fritz et al. have recently presented a poster at HBM, see http://support.brainvoyager.com/documents/Company_Contact/Poster_FritzEtAl_HBM14.pdf , in which they compare different methods to correct EPI data, including ECMOCO and HySCO. Maybe they can provide some more information. As a note, based on the figures the fieldmap & unwarp procedure (which would be the default approach for SPM) seems to be quite close to the raw data = rather not that useful. I'm a little surprised by that finding, but I could imagine that this is related to the fact that the fieldmap has to be reoriented onto the EPI session, which is "between-modality" and thus might be prone to improper registration, leading to incorrect unwarping.
But I'm interested to hear other opinions :-)
Best,
Helmut
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