1. The relationship between the SFR and the sampling passband is chosen to optimize for the available SNR.
2. The relationship between the sampling passband and the PSD of the scene is chosen to optimize . For the PSDs typical of natural scenes, the best match occurs when the sampling intervals are near the mean spatial detail of the scene (i.e., when 1).
These two conditions are consistent with those for which the information rate reaches Shannon's channel capacity . However, blurring and aliasing constrain to values that are smaller than by a factor of nearly two (i.e., /2. Hence, the above conditions replace the role of white and band-limited signals in classical communication theory to establish an upper bound on information rate.
These conditions also appeal intuitively when the problem of image restoration is anticipated:
1. The result that the SFR that optimizes depends on the available SNR is consistent with the observation that, in one extreme, when the SNR is low, substantial blurring should be avoided because the photodetector noise would constrain the enhancement of fine spatial detail even if aliasing were negligible and, in the other extreme, when the SNR is high, substantial aliasing should be avoided so that this enhancement is relieved from any constraints except those that the sampling passband inevitably imposes.
2. The result that reaches its highest value when the sampling intervals are near the mean spatial detail of the scene is consistent with the observation that, ordinarily, it would not be possible to restore spatial details that are finer than the sampling intervals, whereas it would be possible to restore much coarser details from fewer samples.