Non-Common Band SAR Interferometry via Compressive Sensing

To avoid decorrelation, conventional synthetic aperture radar interferometry (InSAR) requires that interferometric images should have a common spectral band and the same resolution after proper preprocessing. For a high-resolution (HR) image and a low-resolution (LR) one, the interferogram quality is limited by the LR one since the non-common band (NCB) between two images is usually discarded. In this article, we try to establish an InSAR method to improve interferogram quality by means of exploiting the NCB. To this end, we first define a new interferogram, which has the same resolution as the HR image. Then we formulate the interferometric relationship between the two images into a compressive sensing (CS) model, which contains the proposed HR interferogram. With the sparsity of interferogram in appropriate domains, we model the interferogram formation as a typical sparse recovery problem. Due to the speckle effect in coherent radar imaging, the sensing matrix of our CS model is inherently random. We theoretically prove that the sensing matrix satisfies restricted isometry property, and thus the interferogram recovery performance is guaranteed. Furthermore, we provide a fast interferogram formation algorithm by exploiting computationally efficient structures of the sensing matrix. Numerical experiments show that the proposed method provides better interferogram quality in the sense of reduced phase noise and obtain extrapolated interferogram spectra with respect to CB processing.