CS: Just throw away your lenses .. but not before you perform some calibration.

One of the well established market facts in photography is to make you pay first for the body of your DSLR and then pay more for expensive lenses. This fact of life is based on the assumption that you need lenses and that it provides you with a well established quality of image thanks to Fourier optics and the attendant engineering dedicated to remove artifacts of different kinds.

See in Fourier optics a simplified version of this camera optics can be illustrated as follows (illustration from this page):

or in graphics used in optics class:

Hence, much like the eye, as a first approximation, the lens or the lens body really does an analog inverse Fourier transform. It is good for most cases, and it gets expensive only because you want that transform to be better for certain things. The point being that the limitation of your system depend mainly on the theoretical limitation of this analog Fourier transform. That limitation is pretty much known and if you have ever taken a course in optics, it is the resolving power limited by the Rayleigh criterion. Back in October, it was shown that removing the lenses from a microscope could be used to increase its resolution [1]. The absolutely important point of this experiment and others like it [2], is that the burden is now on you to devise a way to calibrate your system with known objects. In other words, you now have a new transfer function or point spread function, and you need to spend some time showing known objects to it and record its response. Once you have done this long enough, you have a point-to-point mapping between the image space and the focal place space.By inverting this system, you have a transfer function that can provide either superresolution [1] or 3D[2]. The superesolution in [1] comes now from the fact that sampling is performed in the Fourier space not unlike what is being done in MRI. The success of compressed sensing in MRI opens the eye to the fact that computational photography is probably next and points to the need that we collectively need to provide good tools to perform these otherwise lengthy calibration procedures. Another lensfree system can be found here [3].

[1] Far-Field Microscopy of Sparse Subwavelength Objects by Alexander Szameit, Yoav Shechtman, H. Dana, S. Steiner, S. Gazit, T. Cohen-Hyams, E. Bullkich, O. Cohen, Yonina C. Eldar, S. Shoham, E. B. Kley, M. Segev.

[2] Random Lens Imaging, Rob Fergus, Antonio Torralba, and William T. Freeman 
[3] Lensfree Fluorescent On-Chip Imaging Using Compressive Sampling by Ahmet F. Coskun, Ting-wei Su, Ikbal Sencan, and Aydogan Ozca.