Invariance considerations in calibration problem of measurement computer systems

Many modern measurement systems, producing a large amounts of data (e.g. image generation system) are invariant with respect to a certain group of transformations. Proper allowance for this invariance offers a way to substantially simplify the development of an optimal measurement computer system. An optimal linear measurement computer system synthesis problem is one of obtaining an optimal processing map (determining processing algorithm) with a specified influence function support. The problem rises to a qualitatively new level if an information about measurement system is not precise enough. In such situations problem of an optimal calibration is stated. It consists in generating of a calibration map, converting calibration data (i.e. results of measurements of known signals) to processing map in an optimal way. It appears that if measurement system possesses high level of invariance the solution of both problems can be significantly simplified. Note that a processing map and the degree of complexity in obtaining it are independent of the amount of data to be processed.