There is a good reason why DSLR camera lenses are so expensive; in order to perfectly focus an image many lens elements are required making the whole system expensive to both to design and manufacture. But with the following research it seems like there is a high quality future for cheap lenses too. The research paper describes a way to post-process images, shot through a cheap single element lens and bring out the lost sharpness of the original image. The process works by calculating the way the image is distorted when passed through the lens and then reversing its effects. To do this they first shoot calibration targets and mathematically extract the distortion pattern for the particular lens. You can view the video below for more details:
I can see this having a good practical application in mobile phone imaging where due to the size of the optics its nearly impossible to include a multi-element lens.
Source: Project Home Page