The use of transinformation in the design of data sampling schemes for inverse problems

The author analyses the average useful information content of data samples by using the transinformation entropy (rate of transmission) of Shannon's information theory. The author derives a simple expression for the transinformation in linear experiments with Gaussian a priori distributions. The author uses this expression to examine various schemes for sampling the image spaces of a translation invariant (sinc) and a conformally invariant (Laplace) mapping. The optimum sampling scheme is found to be considerably better than the naive sampling scheme (e.g. Nyquist) when the number of samples is small and the a priori knowledge is non-trivial.