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Blind three dimensional deconvolution via convex optimization
Multidimensional Systems and Signal Processing ( IF 2.5 ) Pub Date : 2020-01-14 , DOI: 10.1007/s11045-019-00696-x
Shayan Shojaei , Farzan Haddadi

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.

中文翻译:

通过凸优化的盲三维反卷积

在本文中,我们讨论从 3 维卷积中恢复两个信号。假设其中一个信号位于已知的子空间中,而另一个信号则假设为稀疏的。在这个框架中可以描述各种应用,例如超分辨率、雷达成像和到达方向估计。我们介绍了一种在低维子空间中估计信号参数的方法,该子空间与另一个由时域中的一些脉冲组成的信号进行卷积。我们使用提升和原子范数以半正定程序的形式将问题转换为凸优化。我们证明了可以通过低通观测来恢复未知参数。数值模拟显示了所提出方法的优异性能。
更新日期:2020-01-14
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