where xi∗ > 0 is a is a given constant. The information contained in x relative to xi∗ is the negative of the entropy. If it is required to find x such that only the data Kx = y is used, the information subject to the data needs to be minimized, that is, the entropy has to be maximized. The mathematical justification for the choice L(x) = -ℰ(x) is that it yields the solution which is most 'objective' with respect to missing information. The maximum entropy method has been used with success in image restoration problems where prominent features from noisy data are to be determined.
