Least-Square-Based Nonuniform Borehole SAR Imaging for Subsurface Sensing

This paper presents the least-square-based nonuniform borehole synthetic aperture radar (SAR) imaging method with cosine accuracy factor for subsurface sensing. Based on the Stolt migration, the frequency-wavenumber spectrum of nonuniform data is efficiently approximated in the least-square-sense for the target space generation. The nonuniform power exponent basis is interpolated into several uniform power exponent bases with cosine accuracy factors, and then a virtual uniform sample set with a larger scale is generated for frequency-wavenumber spectrum approximation and imaging process. The proposed method can give accurate subsurface image result with nonuniform data at a greatly reduced computational cost. The approximation error and computational cost of the proposed method are analyzed and compared with those of Gaussian nonuniform imaging method. The imaging capabilities of the proposed method are theoretically simulated and experimentally demonstrated for distributed targets. The results show that the normalized mean square error and normalized maximum error of the proposed method are at least 8.07 dB and 4.29 dB, respectively, lower than those of conventional Stolt migration method. The imaging properties of this proposed method are shown to be superior to the conventional Stolt migration method, Gaussian nonuniform imaging method and Kirchhoff migration method, which is suitable for large nonuniform SAR imaging applications.