<title>Image gathering, interpolation, and restoration: a fidelity analysis</title>

Abstract

Many modeling, simulation and performance analysis studies of sampled imaging systems are inherently incomplete because they are conditioned on a discrete-input, discrete-output model which only accounts for blurring during image gathering and additive noise. For those sampled imaging systems where the effects of image gathering, restoration and interpolation are significant the modeling, simulation and performance analysis should be based on a more comprehensive continuous-input, discrete-processing, continuous-output end-to-end model. This more comprehensive model should properly account for the low-pass filtering effects of image gathering prior to sampling, the potentially important noise-like effects of aliasing, additive noise, the high-pass filtering effects of restoration, and the low-pass filtering effects of image reconstruction. Yet this model should not be so complex as to preclude significant mathematical analysis, particularly the mean-square (fidelity) type of analysis so common in linear system theory. In this paper we demonstrate that, although the mathematics of this more comprehensive model is more complex, the increase in complexity is not so great as to prevent a complete fidelity-metric analysis at both the component level and at the end-to-end system level. That is, easily computed, mean-square-based fidelity metrics are developed by which both component-level and system-level performance can be predicted. In particular, it is demonstrated that these fidelity metrics can be used to quantify the combined effects of image gathering, restoration and reconstruction.