Linear Inversion by the Maximum Entropy Method with Specific Non-Trivial Prior Information

  • V. A. Macaulay
  • B. Buck
Part of the Fundamental Theories of Physics book series (FTPH, volume 39)


Here we present the MaxEnt solution of an inverse problem in scattering physics, the recovery of a nuclear charge density from noisy and incomplete measurements of its Fourier transform. Prior information on the charge density is used to motivate a Fourier-Bessel expansion and in addition to restrict the space of feasible reconstructions sufficiently to produce a convergent error estimate.


Form Factor Charge Density Maximum Entropy Error Band Linear Inversion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Frosch R F et al. 1967 Structure of the 4He Nucleus from Elastic Electron Scattering Phys. Rev. 160 874–879.CrossRefGoogle Scholar
  2. [2]
    McCarthy J S et al. 1977 Electromagnetic Structure of the Helium Isotopes Phys. Rev. C 15 1396–1414.CrossRefGoogle Scholar
  3. [3]
    Jaynes E T 1988 The Relation of Bayesian and Maximum Entropy Methods Maximum-Entropy and Bayesian Methods in Science and Engineering (Volume 1) Erickson G J and Smith C R (eds.) (Dordrecht: Kluwer) 25–29Google Scholar
  4. [4]
    Macaulay V A and Buck B 1989 Linear Inversion by the Method of Maximum Entropy Inverse Problems (in press)Google Scholar
  5. Borysowicz J and Hetherington J H 1973 Errors on Charge Densities Determined from Electron Scattering Phys. Rev. C 7 2293–2303CrossRefGoogle Scholar
  6. [6]
    Dreher B et al. 1974 The Determination of the Nuclear Ground State and Transition Charge Density from Measured Electron Scattering Data Nucl. Phys. A 235 219–248CrossRefGoogle Scholar
  7. [7]
    Slepian D 1983 Some Comments on Fourier Analysis, Uncertainty and Modeling SIAM Review 25 379–393MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    Watson G 1944 A Treatise on the Theory of Bessel Functions (second edition) (Cambridge: Cambridge University Press) 595.zbMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • V. A. Macaulay
    • 1
  • B. Buck
    • 1
  1. 1.Department of Theoretical PhysicsOxfordUK

Personalised recommendations