Gabor nonstationary deconvolution for attenuation compensation in highly lossy dispersive media

Kay Y. Liu, Elise C. Fear, and Mike E. Potter

ABSTRACT

Gabor nonstationary deconvolution was developed in the field of Seismology to compensate for attenuation loss, correct phase dispersion, and produce images with high resolution. Compared to seismic waves, a stronger attenuation and dispersion effect is observed in microwave frequency electromagnetic (EM) waves, especially with the propagating medium that has high loss and high dispersion, such as human body tissues. In the microwave image, it is displayed as a characteristic blurriness or lack of resolution that increases with time/distance. To produce microwave images with high resolution, there is a strong need for a technique that is able to compensate for the energy loss and correct for the wavelet distortion. Therefore, the Gabor algorithm is proposed to deal with the nonstationarity in EM wave propagation and attenuation. Gabor deconvolution is essentially based on the assumption that the anelastic attenuation of seismic waves can be described by a constant Q theory. Our study reveals that the same definition of Q as in seismic can also be used to characterize EM wave propagation and attenuation. Even though the Q for EM waves is not constant over the microwave frequency of interest; however, a new parameter Q*, which is closely related to Q, can be approximated as constant for highly lossy dispersive human body tissues. Q and Q* might be different in the order of magnitude; however, these quantities describe the attenuation and dispersion in the same manner. Our test results indicate that the Gabor nonstationary deconvolution is able to sufficiently compensate for attenuation loss and correct phase dispersion for EM waves that propagate through high lossy dispersive media. It can work effectively where a constant Q* approximation is achieved.

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