Fourier analysis based focusing of synthetic aperture radar (SAR) data collected during circular flight path
is a recent advancement in SAR signal processing. Fast CSAR algorithm uses the Householder transform to
obtain a ground plane circular SAR (CSAR) signal phase history from the slant plane CSAR phase history by
inverting the linear shift-varying system model, thereby circumventing the need for explicitly computing a pseudo-inverse.
The Householder transform has recently been shown to have improved error bounds and stability as an
underdetermined and ill-conditioned system solver, and the Householder transform is computationally efficient.
This paper utilizes the methodology of SAR2 algorithm, a two dimensional variant of the ω-k algorithm, to refocus
out-of-focus images. Refocusing of images may be necessary in machine vision as a preprocessing step before edge
detection or image segmentation in the imaging and manipulation of 3D objects. The SAR2 algorithm generates a
complex amplitude distribution and the corresponding point spread function in a manner similar to Fraunhofer
diffraction distribution model and its point spread function as seen in Fourier optics. The matched filter utilized in the
SAR2 algorithm has a focus-in-altitude interpretation and may be varied to increase or decrease the radius of out-of-focus
blur associated with a particular point spread function of scatterers of various heights. This paper demonstrates
focusing of a line object L={1 : x=y;-≤x≤63; -64≤y≤63}. Although a rectangular aperture is used in the refocusing
process, other apertures may also be used such as circular or Gaussian.
Synthetic Aperture Radar (SAR) is capable of producing high-resolution terrain images from data collected by a relatively small airborne or spaceborne antenna. This data collection is done in cross-range or slow-time along flight trajectory and range or fast-time along direction of electromagnetic wave propagation. The slow-time imaging is what distinguishes SAR from its predecessor imaging radars. The high resolution pulse compression based fast-time imaging in range introduces some visual artifacts into SAR imagery due to range skew and phase information anomaly due to residual video phase (RVP). In this paper, we introduce the concept of SAR 2D aperture synthesis that extends the slow-time imaging concept to range and relies on a single frequency instead of chirp. Moreover, our 2D aperture synthesis implementation does not need computationally expensive Stolt interpolation.
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