Inverse optical imaging viewed as a backward channel communication problem.
The inverse problem in optics, which is closely related to the classical question of the resolving power, is reconsidered as a communication channel problem. The main result is the evaluation of the maximum number M(epsilon) of epsilon-distinguishable messages (epsilon being a bound on the noise of the image) which can be conveyed back from the image to reconstruct the object. We study the case of coherent illumination. By using the concept of Kolmogorov's epsilon-capacity, we obtain M(epsilon) approximately 2(Slog(1/epsilon))-->infinity, for epsilon-->0 where S is the Shannon number. Moreover, we show that the epsilon-capacity in inverse optical imaging is nearly equal to the amount of information on the object that is contained in the image. We thus compare the results obtained through the classical information theory-which is based on probability theory-with those derived from a form of topological information theory, based on the Kolmogorov epsilon-entropy and epsilon-capacity, which are concepts related to the evaluation of the massiveness of compact sets.
De Micheli
Enrico
E
Istituto di Biofisica, Consiglio Nazionale delle Ricerche, Via De Marini 6, 16149 Genova, Italy. demicheli@ge.cnr.it
Viano
Giovanni Alberto
GA
D001185:Artificial Intelligence; D007091:Image Processing, Computer-Assisted; D007257:Information Theory; D055620:Optical Phenomena; D011336:Probability