Most lenses tend to be expensive because the lens needs to be very complicated in order to correct for various optical effects (aberration, etc). Is it possible to build a sensor and processor combination which would fix defects produced by cheap lenses? I'm assuming the processor knows exactly the parameters of the len's defects.
Answer
Not only is it possible, but it's becoming commonplace. The micro-four-thirds system makes extensive use of it, and some compact cameras now do too. (I imagine that if they don't yet, most super-zooms will within a few years.) Digital Photography Review has a good article on this at http://www.dpreview.com/articles/5653763779/a-distorted-view-in-camera-distortion-correction , and it's worth reading even if you don't like that site's reviews in general.
Correcting distortion and lateral chromatic aberration is an option in my Pentax K-7, but although it doesn't impact shot-to-shot time (unless you fill the buffer), it takes a few extra seconds per image.
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