From the strict mathematical viewpoint, it is impossible to fully achieve the goal of digital image processing, which is to determine an unknown function of two dimensions from a finite number of discrete measurements linearly related to it. However, the necessity to display image data in a form that is visually useful to an observer supersedes such mathematically correct admonitions. Engineering defines the technological limits of what kind of image processing can be done and how the resulting image can be displayed. The appeal and usefulness of the final image to the human eye pertains to aesthetics. Effective image processing necessitates unification of mathematical theory, practical implementation, and artistic display.
Keywords: incomplete data, null space, image quality, human observer, image processing requirements, image display
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