Maximum entropy diffraction tomography

In diffraction tomography, the generalized Radon theorem relates the Fourier Transform (FT) of the diffracted field to the two-dimensional FT of the diffracting object. The relation stands on algebraic contours, which are semi-circles in the case of Born or Rytov first order linear approximations. We propose a Maximum Entropy method to reconstruct the object from either the Fourier domain data or directly from the original diffracted field measurements. To do this, we give a new definition for the entropy of an object considered as a function of R²to C. To take into account the presence of noise, a χ²statistics is added to the entropy measure. The objective function thus obtained is minimized using variational techniques and a conjugate-gradient iterative method. The computational cost and practical implementation of the algorithm are discussed. Some simulated results are given which compare this new method with the classical ones.