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

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Abstract
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.

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