12. Four-Dimensional Data Assimilation  11.7 The Maximum-Entropy Approach  11.7.2 Application to spectral

11.7.3 Image reconstruction

Another important application of the maximum-entropy method has been in image reconstruction. Here the quantity

$$s = -\sum p_n \ln p_n \ .$$ (11.52)

 

is maximized, subject to the constraints imposed by the data. The result is to impose a strong preference for uniform images, so that any features in the reconstructed image are required by the data and do not represent noise. A description of the method can be found in Skilling (1989), and for this case also Press et al. (1992) provide a useful computer routine to implement image reconstruction.

SOURCES AND FURTHER READING

Burg, J. P., 1975: Maximum Entropy Spectral Analysis. Ph.D. thesis, Stanford University.

Bury, K.V., 1975: Statistical Models in Applied Science. Wiley and Sons, New York, 625 pp.

Jaynes, E. T., 1985: Where do we go from here? In Maximum-Entropy and Bayesian Methods in Inverse Problems, C. R. Smith and W. T. Grandy, Jr., eds., D. Reidel Publishing Co., Dordrecht, Holland, pp. 21-58.

Levine, R. D., and M. Tribus, 1981: The Maximum Entropy Formalism. The MIT Press, Cambridge, Massachusetts, 498 pp.

Menzel, D. H., 1960: Fundamental Formulas of Physics, Volume One. Dover Publications, New York, 364 pp.

Shannon, 1948:

Skilling, J., 1991: Fundamentals of MaxEnt in data analysis. In Maximum Entropy in Action, B. Buck and V. A. Macaulay, eds., Oxford University Press, Oxford, pp. 19-40.

Press, W. H., Brian P. Flannery, S. A. Teukolsky, and W. T. Vetterling, 1992: Numerical Recipies in C. Second Edition, Cambridge University Press, Cambridge, 735 pp. Cf. pp. XXX-XXX.

Ulrych, T. J., 1985: Spectral analysis and time series models. In Maximum-Entropy and Bayesian Methods in Inverse Problems, C. R. Smith and W. T. Grandy, Jr., editors, D. Reidel Publishing Company, Dordrecht, pp. 243-272.

   
 12. Four-Dimensional Data Assimilation  11.7 The Maximum-Entropy Approach  11.7.2 Application to spectral