The problem of computing exact finite impulse response (FIR) inverses for multivariate multiple-input multiple-output (MIMO) FIR systems is considered. Necessary and sufficient conditions for invertibility are given, along with computation techniques. Random systems and structured systems are defined. Necessary and sufficient conditions for the almost sure invertibility of structured random systems are derived. Bounds on the orders of the inverse filters are computed.
A necessary and sufficient condition is given for the existence of a polynomial left inverse for a polynomial (FIR) system. Additionally, random systems are defined, and a sufficient condition is given for almost sure existence of a polynomial inverse. The two results extend previous work in single-input, multiple-output systems to the case of multiple input systems and to functions of several variables. An algorithm to compute minimal order equalizers is also presented. Corollaries describe calibration of polarimetric, wide-band radar imagery.
Ultra wideband (UWB) radar is an emerging technology with potential for all-weather, remote sensing of objects obscured by foliage or buried underground. Multiple octaves of frequency coverage and 90 degrees or more of viewing angle across a synthesized aperture are used to obtain high spatial resolution mapping of scattering behavior. Additionally, fully polarimetric responses can be measured, providing a multichannel characterization of objects in a scene. However, the diversity in wavelength and viewing angle presents significant challenges for system engineering and data interpretation. In particular, the multichannel UWB system poses unique imaging challenges arising from the variation of the UWB antenna response.We present an overview of calibration techniques for polarimetric wideband imagery, and introduce an image domain calibration technique using calibration targets.
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