Bayesian approach with the maximum entropy principle in image reconstruction from microwave scattered field data

Microwave imaging is of great interest in medical applications owing to its high sensitivity with respect to dielectric properties. It allows detection of very small inhomogeneities. The image reconstruction employing the microwave inverse scattering consists of reconstructing the image of an object from the scattered field measured behind the object. This reconstruction runs up against the nonuniqueness of the solution of the inverse scattering problem. The authors propose to solve the ill-posed inverse problem by a statistical regularization method based on the Bayesian maximum a posteriori estimation where the principle of maximum entropy is used for assigning the a priori laws. The results obtained demonstrate the power and potential of this method in image reconstruction.

[1]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[2]  G. Demoment,et al.  Maximum entropy Fourier synthesis with application to diffraction tomography. , 1987, Applied optics.

[3]  W. J. Tompkins,et al.  Iterative reconstruction methods using regularization and optimal current patterns in electrical impedance tomography. , 1991, IEEE transactions on medical imaging.

[4]  Weng Cho Chew,et al.  Nonlinear two-dimensional velocity profile inversion using time domain data , 1992, IEEE Trans. Geosci. Remote. Sens..

[5]  T M Cannon,et al.  Comparison of image restoration methods. , 1978, Applied optics.

[6]  W. Chew,et al.  Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method. , 1990, IEEE transactions on medical imaging.

[7]  M Baribaud,et al.  Microwave imagery: analytical method and maximum entropy method , 1990 .

[8]  Ali Mohammad-Djafari,et al.  Maximum Entropy Prior Laws of Images and Estimation of their Parameters , 1991 .

[9]  Y. Censor.  Finite series-expansion reconstruction methods , 1983, Proceedings of the IEEE.

[10]  A. Devaney,et al.  Nonuniqueness in inverse source and scattering problems , 1982 .

[11]  Bobby R. Hunt,et al.  Bayesian Methods in Nonlinear Digital Image Restoration , 1977, IEEE Transactions on Computers.

[12]  Y. Censor,et al.  Optimization of “log x entropy over linear equality constraints , 1987 .

[13]  John Skilling,et al.  Maximum entropy method in image processing , 1984 .

[14]  B. Frieden.  Restoring with maximum likelihood and maximum entropy. , 1972, Journal of the Optical Society of America.

[15]  H. Trussell,et al.  Notes on linear image restoration by maximizing the a posteriori probability , 1978 .

[16]  K. Langenberg,et al.  Limitations and defects of certain inverse scattering theories , 1984 .

[17]  H. Trussell.  The relationship between image restoration by the maximum a posteriori method and a maximum entropy method , 1980 .

[18]  Ali Mohammad-Djafari,et al.  On the estimation of hyperparameters in Bayesian approach of solving inverse problems , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[19]  S. Gull,et al.  Maximum entropy algorithm applied to image enhancement , 1980 .

[20]  Anthony J. Devaney,et al.  Maximum likelihood estimation of object location in diffraction tomography. II. Strongly scattering objects , 1991, IEEE Trans. Signal Process..

[21]  S. Twomey,et al.  On the Numerical Solution of Fredholm Integral Equations of the First Kind by the Inversion of the Linear System Produced by Quadrature , 1963, JACM.

[22]  G Demoment,et al.  Maximum entropy image reconstruction in X-ray and diffraction tomography. , 1988, IEEE transactions on medical imaging.

[23]  Guy Demoment,et al.  Image reconstruction and restoration: overview of common estimation structures and problems , 1989, IEEE Trans. Acoust. Speech Signal Process..

[24]  B. Roy Frieden,et al.  Restoring with maximum entropy. III. Poisson sources and backgrounds , 1978 .

[25]  E. Jaynes.  On the rationale of maximum-entropy methods , 1982, Proceedings of the IEEE.

[26]  B. Frieden.  Statistical models for the image restoration problem , 1980 .

[27]  Tianhu Lei,et al.  Statistical approach to X-ray CT imaging and its applications in image analysis. I. Statistical analysis of X-ray CT imaging , 1992, IEEE Trans. Medical Imaging.

[28]  Stephen J. Wernecke,et al.  Maximum Entropy Image Reconstruction , 1977, IEEE Transactions on Computers.

[29]  A. Mohammad-Djafari,et al.  Maximum Entropy and Bayesian Methods , 1993 .