Combination of Correlated Phase Error Correction and Sparsity Models for SAR

Direct image formation in synthetic aperture radar (SAR) involves processing of data modeled as Fourier coefficients that lie on a polar grid. Often in such data acquisition processes, imperfections in the data cannot simply be modeled as additive or even multiplicative noise errors. In the case of SAR, errors in the data can exist due to the imprecise estimation of the round trip wave propagation time, which manifests as linearly varying phase errors in the antenna data across the pulses. To correct for these errors, we propose a phase correction scheme that relies on both the on smoothness characteristics of the image and the phase corrections associated with neighboring pulses, which are possibly highly correlated due to the nature of the data offsetting. Our model takes advantage of these correlations and smoothness characteristics simultaneously for a new autofocusing approach. Our algorithm for the proposed model alternates between approximation of image features and phase error estimates according to the model.