A newborn’s brain can be specified by about 10^9 bits of genetic information
While the brain of a new-born baby can be generated by 10^9 bits of genetic information, it’s not true that this is enough to suitably specify a particular new-born’s brain. This is because of the large impact that conditions in the womb have on brain development (e.g. drugs&alcohol) and the limited extent to which brain structure is inherited.
However it’s quite likely that specific sections of the genome contribute to brain development, meaning that your lower bound for how much information it takes to generate a new-born’s brain is (*probably!) much lower than 10^9 bits. Though this still won’t be enough information to specify a particular new-born’s brain, just enough to considerably narrow-down the region of brain-structure-space that the new-born’s brain can occupy.
*Don't take my word for this – I don't know nearly enough to substantiate that claim.
Also, on a tentative note, it might be worth comparing scans of a brain before and after it's been cryogenically preserved in order to see if it's possible to tell the difference (and subsequently if the data from the pre-freezing brain can be approximated from the post freezing brain data).
it’s not true that this is enough to suitably specify a particular new-born’s brain. This is because of the large impact that conditions in the womb have on brain development
The amount of information from a womb to the brain is about zero.
Paul Christiano recently suggested that we can use neuroimaging to form a complete mathematical characterization of a human brain, which a sufficiently powerful superintelligence would be able to reconstruct into a working mind, and the neuroimaging part is already possible today, or close to being possible.
Paul was using this idea as part of an FAI design proposal, but I'm highlighting it here since it seems to have independent value as an alternative or supplement to cryonics. That is, instead of (or in addition to) trying to get your body to be frozen and then preserved in liquid nitrogen after you die, you periodically take neuroimaging scans of your brain and save them to multiple backup locations (1010 bits is only about 1 gigabyte), in the hope that a friendly AI or posthuman will eventually use the scans to reconstruct your mind.
Are there any neuroimaging experts around who can tell us how feasible this really is, and how much such a scan might cost, now or in the near future?
ETA: Given the presence of thermal noise and the fact that a set of neuroimaging data may contain redundant or irrelevant information, 1010 bits ought to be regarded as just a rough lower bound on how much data needs to be collected and stored. Thanks to commenters who pointed this out.