BOUNDS ON NULL FUNCTIONS OF LINEAR DIGITAL IMAGING-SYSTEMS

Any linear digital imaging system produces a finite amount of data fro m a continuous object. This means that there are always null functions , so a reconstruction of the object, even without noise in the system, will differ from the actual object. With positivity constraints, the size of a null function is limited, provided that size is measured by the integral of the absolute value of the null function. When smoothin g is used in reconstruction, then smoothed null functions become relev ant. There are bounds on various measures of the size of smoothed null functions, and these bounds can be quite small. Smoothing will decrea se the effects of null functions in object reconstructions, and this e ffect is greater if the smoothing operator is well matched to the syst em operator. (C) 1998 Optical Society of America.