Despite major hardware drawbacks such as much smaller sensors and cheap lenses, I think computational photography will play a big role in shrinking the gap with current gen DSLR's too, over the next decade. We are slowly managing to put bigger and bigger sensor sizes in phones, too, without any compromises in design, as Sony has shown with its 1/2.3" sensors in the Xperia Z series [1].
Maybe in 2-3 years a 2/3" sensor will fit just as well, too. Again, I'm talking about no compromises in design. I know there are already 1" sensors in some smartphones such as the Panasonic Lumix DMC-CM1 [2], but despite myself being fine with buying such a phone, I assume most OEMs or smartphone customers have no interest in those.
Not sure if it's what you meant by computational, but some pocket cameras already apply software correction to known lens distortions. The Sony RX100, for instance, which is presumably how they can have a 1" sensor and very bright lens in a really small camera.
> We are slowly managing to put bigger and bigger sensor sizes in phones, too, without any compromises in design
It helps that the phones are getting bigger. The camera in my Nexus 5 is a ton better than in my old Blackberry Pearl, but the phone is also twice the horizontal size.
Maybe in 2-3 years a 2/3" sensor will fit just as well, too. Again, I'm talking about no compromises in design. I know there are already 1" sensors in some smartphones such as the Panasonic Lumix DMC-CM1 [2], but despite myself being fine with buying such a phone, I assume most OEMs or smartphone customers have no interest in those.
[1] - http://www.sonymobile.com/global-en/products/phones/xperia-z...
[2] - http://www.panasonic.com/de/consumer/foto-video/lumix-kompak...