We Don't Know
Consciousness is not something we've puzzled out yet. The brain operates both via synaptic connections and neurochemical interactions, there may even be quantum effects, it's incredibly plastic (damage to one section might do, as far as the owner and observers can tell, nothing, while a different section might destroy their personality, and that isn't the same between any two people).
Rather than just tomography, you would probably need an advanced fMRI, and probably sensors placed surgically inside the brain - this all assuming that you can capture all the necessary information nondestructively. It is much, much more likely that what you could arrive at is something that convincingly simulates the consciousness you're attempting to copy, but which cannot be demonstrated to be the same person.
(On the other hand, that is both an interesting ethical question and potentially a subject that would keep people from wanting to use your brain scan, which is an interesting worldbuilding concept.)
As for just "how much data would I need"? We have an early example, in a Google brain mapping experiment: here.
The brain map, which is freely available online, includes 50,000 cells, all rendered in three dimensions. They are joined together by hundreds of millions of spidery tendrils, forming 130 million connections called synapses. The data set measures 1.4 petabytes, roughly 700 times the storage capacity of an average modern computer.
Assuming that knowledge of the cell locations and synaptic connections is enough (and you don't need the quantum/chemical data), you could scale this up. There are approximately eighty-six billion neurons in the brain, so you'd just need 2.58 zettabytes of storage. There are currently estimated to be about 40 zettabytes of digital data on all media in the entire world, so you could store about 30 brains - again, assuming no other data is needed to accurately simulate the behaviour of the brain. Also, this assumes that the scaling-up is linear (it's probably not exponential as synapses only stretch so far, but it's probably not strictly linear).