Interrupted SAR imaging with limited persistence scattering models

In this paper, we study the problem of wide-angle SAR imaging in the setting when pulses along the synthetic aperture are randomly subsampled, commonly referred to as interrupted SAR. We propose a regularized inversion method that decomposes the target into a set of scattering centers with limited persistence by utilizing the model based sparsity of scattering coefficients. Based on the prior work on parametric models derived for canonical reflectors, we hypothesize that the scattering coefficient as a function of the viewing angle is embedded in a low-dimensional subspace spanned by a set of functions or dictionary atoms that have a support, which is concentrated in the viewing angle domain. Towards this end, we consider specific choices of dictionary atoms, the first one being copies of piecewise constant functions with a fixed range, the second being Gaussian functions with a fixed variance, which are translated in the mean and finally, a dictionary derived from a series of discrete prolate spheroidal sequences. For these choices, we present preliminary results obtained by solving a regularized optimization problem that enforces the sparsity in spatial as well as in the azimuth domain. We observe that given a small fraction of the pulses, the target locations, and corresponding scattering coefficients are recovered successfully if the signal has a sufficiently sparse representation in the proposed set of dictionary elements.