That seems to be what the scientists are doing for the MRI, but the author seems to think this would be useful in that it would allow people to throw away a lot of data. I think it would be much better for extrapolating even farther from the data we have.
One application he mentions is sensor networks that can withstand a loss of a large number of nodes.
As soon as I saw the article my first thought was: "real-time raytracing?"
The reason is that MRI sampling is prohibitively time-expensive: you need to keep the sample still for a long time to sample many points. In the article's case, that would require the patient to end up dead. ;) Sparsely sampling the volume takes much less time and allows for a reasonable reconstruction.
I'm not intimately familiar with MRI processing, but there may also be some intricacy of the imaging process (possibly related to the time-to-spatial-frequency conversion?) that makes the lower-res sampling especially suited for this algorithm.
I could be wrong, though -- I only did this back-of-the-envelope a few months ago. I never really tried that hard to make it work.
This is most likely true. Additionally, raytracing just might produce samples that are too regular for this to work well. I haven't really thought about it :)