Quality improvement synthetic aperture radar (SAR) images using compressive sensing (CS) with Moore-Penrose inverse (MPI) and prior from spatial variant apodization (SVA).

When the locations of non-zero samples are known, the Moore-Penrose inverse (MPI) can be used for the data recovery of compressive sensing (CS). First, the prior from the locations is used to shrink the measurement matrix in CS. Then the data can be recovered by using MPI with such shrinking matrix. We can also prove that the results of data recovery from the original CS and our MPI-based method are the same mathematically. Based on such finding, a novel sidelobe-reduction method for synthetic aperture radar (SAR) and Polarimetric SAR (POLSAR) images is studied. The aim of sidelobe reduction is to recover the samples within the mainlobes and suppress the ones within the sidelobes. In our study, prior from spatial variant apodization (SVA) is used to determine the locations of the mainlobes and the sidelobes, respectively. With CS, the mainlobe area can be well recovered. Samples within the sidelobe areas are also recovered using background fusion. Our method is suitable for acquired data with large sizes. The performance of the proposed algorithm is evaluated with acquired spaceborne SAR and air-borne POLSAR data. In our experiments, we use the 1m space-borne SAR data with the size of 10000 (samples) × 10000 (samples) and 0.3m POLSAR data with the size of 10000 (samples) × 26000 (samples) for sidelobe suppression. Furthermore, We also verified that, our method does not affect the polarization signatures. The effectiveness for the sidelobe suppression is qualitatively examined, and results were satisfactory.