On the convergence of the coordinate descent method for convex differentiable minimization
Journal of Optimization Theory and Applications
Convergence of a block coordinate descent method for nondifferentiable minimization
Journal of Optimization Theory and Applications
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
On compressive sensing applied to radar
Signal Processing
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
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Sparse synthetic aperture radar (SAR) imaging has been highlighted in recent studies. As an important sparsity constraint, L"1"/"2 regularizer has been substantiated effectively when applied to SAR imaging. However, L"1"/"2-SAR imaging suffers from a common challenge with other sparse SAR imaging methods: the computational complexity is costly, especially for high dimensional applications. This challenge is mainly due to that L"1"/"2-SAR imaging is a gradient descent based method, of which the convergence is at most linear. Thus, a lot of iterations are often necessary to yield a satisfactory result. In this paper, we propose an accelerated L"1"/"2-SAR imaging method by applying the block coordinate relaxation (BCR) scheme combined with the reduced Newton skill for acceleration. It is numerically shown that the proposed method keeps fast convergence within a very few iterations, and also maintains high reconstruction precision. We provide a series of simulations and two real SAR applications to demonstrate the superiority of the proposed method. Particularly, much faster convergence and higher reconstruction precision in imaging, of the proposed method over the other sparse SAR imaging methods.