Echo imaging using synthesized arrays

This thesis addresses signal processing and inversion methods associated with echo imaging using sensor arrays.; A comparison was made analytically and numerically on the signal subspace of the two systems between the physical array and the synthesized array echo imaging system. The analytical result showed equivalence by proving that the physical array data for a point scatterer can be represented via a linear combination, that is invariant of the point scatterer's coordinates, of the synthetic aperture data for the point scatterer. We then used the Gram-Schmidt procedure to establish this equivalence numerically in simulated echo imaging systems. This empirical study indicates that the physical array data and synthetic aperture data span the same signal subspace.; We then developed a compression technique in the echo imaging system with the synthesized array, i.e., SAR (Synthetic Aperture radar) imaging system via a demodulation technique. The processing time and size of data collected in the synthetic aperture domain can be reduced by compressing the SAR signal with a known demodulation function. We also compressed support bands of the reconstructed image by proper shifting of the support bands for each target via an approximated interpolation kernel without sacrificing the resolution of the image.; Phase uncertainties in SAR imaging result in the presence of speckle and/or severe degradation in the reconstructed image. We use SAR's system model to develop a non-iterative solution for the complex phase error from the measured corrupted SAR data. This is achieved via combining the two differential equations governing the echoed signal having linear phase after Fresnel approximation at two temporal frequencies of the radar signal. The added white noise itself does not give severe degradation in the reconstructed image but disturb the speckle processing. We studied how the speckle processing method proposed above could be disturbed by the added white noise and how to remove the disturbance for a good phase error estimation.