Statistical Maxwell's Electromagnetic Theories have been developed over many years and applied to a wide range of practical problems in remote sensing of geographical media, imaging in biological media, medical optics, ultrasound imaging, and object detection and imaging and communications in clutter environment. This paper gives a review of recent advances, development and applications of statistical wave theory. Many important problems on imaging in geophysical and biological media have been treated often as separate problems. This paper attempts to present unified theoretical work and viewpoints under the statistical theories which may help further advance and understanding of theories and applications. The statistical electromagnetic theories encompass most advanced mathematical and theoretical work and most practical applications. This includes time-reversal imaging through multiple scattering media, super resolution, communication channel capacity in clutter, space-time vector radiative transfer, bio-electromagnetics and ultrasound in tissues, coherence in multiple scattering, memory effects, the use of transformation electromagnetics, seismic coda, and the fundamental multiple scattering theories. Statistical Electromagnetics Theories are one of the most challenging theoretical problems today involving many applications in geographical and biological media.
2. Ishimaru, A., Electromagnetic Wave Propagation, Radiation, and Scattering, 637, Prentice Hall, Englewood Cliffs, NJ, 1991.
3. Tatarskii, V. I., "The effects of the turbulent atmosphere on wave propagation,", TT-68-50464, US Department of Commerce, Springerfield, Virginia, 1971.
4. Tatarskii, V. I., A. Ishimaru, and V. U. Zavorotny, Wave Propagation in Random Media (Scintillation), SPIE Press and Bristol, Institute of Physics Publishing, Bellingham, WA, England, 1993.
5. Tsang, L. and J. A. Kong, Scattering of Electromagnetic Waves, Advanced Topics, Vol. 26, John Wiley & Sons, 2004.
6. Ulaby, F. T., R. K. Moore, and A. K. Fung, Microwave Remote Sensing: Microwave Remote Sensing Fundamentals and Radiometry, Vol. I, Advanced Book Program/World Science Division, Addison-Wesley Publishing Company, 1981.
7. Lin, J. C., Ed., Electromagnetic Fields in Biological Systems, CRC Press, 2011.
8. Devaney, J., Mathematical Foundations of Imaging, Tomography and Wavefield Inversion, Cambridge University Press, 2012.
9. Ishimaru, S. J. and Y. Kuga, "Imaging through random multiple scattering media using integration of propagation and array signal processing," Waves in Random Media, Vol. 22, No. 1, 29-39, Feb. 2012.
10. Prada, C. and M. Fink, "Eigenmodes of the time reversal operator: A solution to selective focusing in multiple-target media," Wave Motion, Vol. 20, No. 2, 151-163, 1994.
11. Paulraj, A., R. Nabar, and D. Gore, Introduction to Space-time Wireless Communications, Cambridge University Press, 2003.
12. Ishimaru, A., et al., "A MIMO propagation channel model in a random medium," IEEE Transactions on Antennas and Propagation, Vol. 58, No. 1, 178-186, 2010.
13. Khaled, A.-R. A. and K. Vafai, "The role of porous media in modeling flow and heat transfer in biological tissues," International Journal of Heat and Mass Transfer, Vol. 46, No. 26, 4989-5003, 2003.
14. Shung, K. K. and G. A. Thieme, Ultrasonic Scattering in Biological Tissues, CRC Press, Boca Raton, 1992.
15. Tsang, L., J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing, John Wiley and Sons, 1985.
16. Ulaby, F. T., R. K. Moore, and A. K. Fung, Microwave Remote Sensing Active and Passive, Vol. III, Advanced Book Program/World Science Division, Addison-Wesley Publishing Company, 1981.
17. Lagendijk, A. and B. A. Van Tiggelen, "Resonant multiple scattering of light," Physics Reports, Vol. 270, No. 3, 143-215, 1996.
18. Ishimaru, A., "Backscattering enhancement — From radar cross sections to electron and light localizations to rough surface scattering," IEEE Antennas Propagation Magazine, Vol. 33, 7-11, 1991.
19. Ishimaru, A., C. Zhang, M. Stoneback, and Y. Kuga, "Time-reversal imaging of objects near rough surfaces based on surface flattening transform," Waves in Random and Complex Media, Vol. 23, No. 3, 306-317, 2013.
20. Leonhardt, U. and T. Philbin, Geometry and Light: The Science of Invisibility, Courier Dover Publications, 2012.
21. Sato, H. and M. C. Fehler, Seismic Wave Propagation and Scattering in the Heterogeneous Earth, Springer, New York, 1998.
22. Johnson, D. H. and D. E. Dudgeon, Array Signal Processing: Concepts and Techniques, Prentice Hall, Englewood Cliffs, NJ, 1993.