Reconstruction of jointly sparse vectors via manifold optimization
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In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This result reveals a reduction in the computational complexity of the original problem and enables a simple implementation of joint sparse recovery algorithms for full rank setting. Secondly, we propose a new method for joint sparse recovery in the form of a nonconvex optimization problem on a non-compact Steifel manifold. Numerical experiments are provided showing that our method outperforms the commonly used l_2,1 minimization in the sense that much fewer measurements are required for accurate sparse reconstructions.
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