An Improvement on the Maximum or Minimum Cross Entropy Method in the Crosswell Ray Tomography

Abstract

In the ray tomography and diffraction tomography, the methods of maximum entropy (ME) and minimum cross entropy (MICE) are widely used to improve the quality of the reconstruction image. 1, 2There are two kinds of ME or MICE methods: the gradient algorithm and dual algorithm. The gradient algorithm of ME or MICE method can be formulated into different forms according to different tomography types and inversion methods. 1The dual algorithm2 of ME or MICE method, however, has united form for ray tomography and diffraction tomography. This is because the only difference between different tomographies is the estimated region in the wave-number domain of image function. The dual algorithm proposed by Lo2 has two shortcomings. Firstly, because the algorithm reconstructs the wave-number spectrum directly from observation data according to Fourier slice theorem, the interpolation in the spectrum domain are needed, which may reduce the computing efficiency. Secondly, when the estimated region in the wave-number domain is an angle region as in the straight ray tomography, the improvement of reconstruction image by the ME or MICE method is not significant. This paper will work on those two aspects.