Theoretically, you could do the same thing with EEG via source localization techniques[0] on the EM spectrum.

In my experience, barely any labs have the know how to implement them in a performative manor to pull something like this off whereas a lot of the fmri software is made from the manufacture (GE, Siemens, etc) that transforms the raw data into the voxels that were used in this setup.

[0] http://www.scholarpedia.org/article/Source_localization

Sounds like you still need too many electrodes !

Depends on which brain regions you want to acquire signals from (usually based on the literature), but generally yes, you need to sample from a "sufficient" number of places (one of my fmr colleges has a lead reduction paper coming out this year that will talk about this).

But keep in mind here, using eeg (and beamforming) is still way cheaper and accessible than any fmri machine, though as far as having the skills to implement such, I think it is out of the reach of most labs who do this sort of research.

Electrodes are even getting better[0] wrt cost and actual ease of real world usage (dry/non gel needed/comfort).

[0] http://doc.ml.tu-berlin.de/bbci/publications/GroVoiFaz11.pdf

Or half as useful as brain implants.