3D nonlinear inversion by Entropy of Image Contrast optimization

Gennady Ryzhikov and Marina Biryulina

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1: Introduction
2: Strategy
3: Block-scheme
4: Fréchet derivative
5: RT-algorithm
6: Entropy of Image Contrast
7: Regularization
8: Linearization of phase shift
9: Generalized  Karhunen-Loeve basis
10: EnIC
11: REnIC
12: Generalized Ray Tomography
13: some details
14: Conclusions
15: Synthetic experiment
16: Relative Entropy of Image Contrast
17: References
18: RT-algorithm
19: RT-algorithm (continuation)
20: Shannon's Entropy (lemma)
21: Regularized Global Approximation (RGA)

Gennady Ryzhikov and  Marina Biryulina,
3D nonlinear inversion by Entropy of Image Contrast  optimization
SEISMO-series: No. 62 ISEP, UoB,  1995

Clear copies (PDF: 1.7 Mb)  (PostScript.gz: 1. Mb)

"MIRROR (with a slight effect of diffraction)

G. A. Ryzhikov, M. S. Biryulina and A. J. Hanyga, 1995, 
3D nonlinear inversion by entropy of image contrast optimization: 
Nonlinear Processes in Geophysics, v.2, n.3/4, pp 228-240    (PDF:1.1 Mb)

Comments -
a few notions having been introduced:

Diffusion regularization (Sobolev space of infinite order)
Entropy of Image Contrast (EnIC)
Generalized ray tomography
Modified descent method (RT-algorithm)
"Anisotropy" of the Sobolev space  as an a priori information on a medium model
Regularized Global Approximation (RGA)
Analog of  Karhunen-Loeve basis,  induced by Tikhonov regularization
Concave regularizer in minimization problem
Radon transform as a filtering  of  diffused images
Inversion via  EnIC -minimization 
RGA-algorithm for global optimization


Геннадий Рыжиков