Complex-valued sparse reconstruction via arctangent regularization

doi:10.1016/j.sigpro.2014.04.037

Complex-valued sparse reconstruction via arctangent regularization

2014-11-01

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DOI：10.1016/j.sigpro.2014.04.037

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Complex-valued sparse reconstruction is conventionally solved by transforming it into real-valued problems. However, this method might not work efficiently and correctly, especially when the size of the problem is large, or the mutual coherence is high. In this paper, we present a novel algorithm called the arctangent regularization (ATANR), which can handle the complex-valued problems of large size and high mutual coherence directly. The ATANR is implemented with the iterative least squares (IRLS) framework, and accelerated by the dimension reduction and active set selection steps. Further, we summarize and analyze the common properties of a penalty kernel which is suitable for sparse reconstruction. The analyses show that the key difference, between the arctangent kernel and the l(l) norm, is that the first order derivative of ATANR is close to zero for a nonzero variable. This will make ATANR less sensitive to the regularization parameter lambda than l(1) regularization methods. Finally, lots of numerical experiments validate that ATANR usually has better performance than the conventional l(1) regularization methods, not only for the random signs ensemble, but also for the sensing matrix with high mutual coherence, such as the resolution enhancement case. (C) 2014 Elsevier B.V. All rights reserved.

Keywords:

Arctangent regularization

Complex-valued problem

Active set projection

Penalty functions

Sparse reconstruction

Resolution enhancement

Complex-valued sparse reconstruction via arctangent regularization

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