Abstract
In this paper we discuss recovering two signals from their convolution in 3 dimensions. One of the signals is assumed to lie in a known subspace and the other one is assumed to be sparse. Various applications such as super resolution, radar imaging, and direction of arrival estimation can be described in this framework. We introduce a method to estimate parameters of a signal in a low-dimensional subspace which is convolved with another signal comprised of some impulses in time domain. We transform the problem to a convex optimization in the form of a positive semi-definite program using lifting and the atomic norm. We demonstrate that unknown parameters can be recovered by lowpass observations. Numerical simulations show excellent performance of the proposed method.
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