Image-gathering system design for information and fidelity

Image gathering and processing are assessed in terms of information and fidelity, and the relationship between these two figures of merit is examined. It is assumed that the system is linear and isoplanatic and that the signal and noise amplitudes are Gaussian, wide-sense stationary, and statistically independent. Within these constraints, it is found that the combined process of image gathering and reconstruction (which is intended to reproduce the output of the image-gathering system) behaves as optical, or photographic, image formation in that the informationally optimized design of the image-gathering system ordinarily does not maximize the fidelity of the reconstructed image. The combined process of image gathering and restoration (which is intended to reproduce the input of the image-gathering system) behaves more as a communication channel in that the informationally optimized design of the image-gathering system tends to maximize the fidelity of optimally restored representations of the input.