This paper proposes an algorithm combining classic CS algorithm with Dechirp technique for the process of imaging
with big range cell migrations and partial aperture data. A great deal of interpolation will be needed if the azimuth pulse
compression is accomplished by using a matched filter with only partial aperture data. So the CS algorithm is used to
correct the range cell migration and complete the range pulse compression, while the Dechirp technique to accomplish
the azimuth pulse compression. In addition, motion compensation is added because of the instability of the airborne SAR
that leads to a debasement of the image. A curve of displacements in the LOS direction and phases of azimuth errors can
be fitted by estimating the data, Thus it is easy to compensate them.
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