Gabor decon in dispersive media CREWES Research Report — Volume 27 (2015) 1 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 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 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. INTRODUCTION Various inverse Q filtering techniques have been developed in the field of Seismology to compensate for energy loss, to correct for wavelet distortion in terms of shape and timing, and to produce an image with high resolution. Among these, the Gabor deconvolution method developed by (Margrave et al., 2011) has been successfully tested with industrial seismic data (Margrave et al., 2003, and Perz et al., 2005). The results indicate that, compared to the industry standard approach, Gabor deconvolution provides improved amplitude and phase content of certain seismic events. It is the purpose of this study to extend these findings to radar data, which necessitates a good understanding of the differences in the application conditions between the seismic waves and the EM waves, as well as the media being studied. In particular, our study focuses on the tissue sensing adaptive radar (TSAR) system developed by (Fear et al., 2013) at the University of Calgary. The TSAR system uses low power microwave frequency electromagnetic (EM) waves to image the breast interior for tumor detection. Encouraging results have been obtained with simulation and phantom data, as well as some preliminary clinical exams. Those results indicate that TSAR images are able to detect the dielectric property changes in breast tissues. However, limited success