Visual Communication - Information Rate and Robustness of Performance
## Information Rate and Robustness of Performance

The informationally-optimized design of visual communications systems is based inherently on some prescribed statistical properties of natural (random) scenes given by the normalized power spectral density (PSD) _{p}^{-2}_{p} with variance _{p}^{2}, as illustrated below, where _{} is the mean spatial detail of the scene relative to the spacing of the sampling intervals of the image-gathering process are the spatial frequency coordinate system with units of cycles/sample, and *m* controls the fall-off rate with increasing spatial frequencies.
### Robustness of Electro-optical Design

The selection of the spatial frequency response SFR of the image-gathering device relative to its sampling passband , as controlled by the optical-response index , for maximum information rate may be based on the assumption that *m*=3 and _{}=1, as summarized in the table. Similar plots of for various values of *m*, ranging from 1.4 to 4 lead to the selection of for the available SNR, as would plots of for various values of _{}.

### Robustness of Image Restoration

This last figure presents the information rate and the corresponding maximum-realizable fidelity for matched and mismatched Wiener restorations. The matched restorations use the correct values of *m* and _{}. These curves reveal that the informationally optimized designs produce the

highest fidelity and robustness, and that both improve with increasing . Ordinarily, to assure both a high fidelity and robustness, it is necessary for the SNR to be high, above ~64, so that an information rate 3 bits/sample can be attained. Moreover, these curves reveal that, ordinarily, one cannot go far wrong by assuming that the mean spatial detail is equal to the sampling intervals (i.e., _{}=1). This observation appeals intuitively because spatial detail that is much smaller cannot be resolved, and detail that is larger is not degraded substantially by blurring and aliasing.

*Web site curator: Glenn Woodell*