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The proposed NUFFT-based SPGL1 algorithm to solve group sparse BPDN problem for polarimetric TWRI system is described in Section 3.
To solve this problem, the proposed imaging algorithm adopts SPGL1 algorithm to solve the group sparse BPDN problem of (7).
In order to improve the performance of BPDN algorithm, iteratively reweighted basis pursuit algorithm  has been proposed.
Theoretical results have proved that, by iteratively utilizing the prior information obtained in the last iteration, the iteratively reweighted basis pursuit algorithm improves the performance than that of BPDN algorithm.
and consider the BPDN optimization problem (16) with [lambda] = [square root of (16[[sigma].sup.2] log M:)]
Given the standard model in compressed sensing y = [PHI]x + e and given the sensing matrix [PHI]' defined above, the K-sparse signal could be reconstructed from the new measurement vector y' = [PHI]'x + e perfectly using the BPDN optimization method with probability on the order of 1 - 1/[M.sup.2].
In the simulation, we use the BPDN algorithm to estimate the sparse vector [[??].sup.n].
Later on, the Coherence-Based Guarantee for BPDN has been found by Ben-Haim et al.
On different conditions, the performances of the two modified-BMP estimators (AMMSE and MAP) are clearly superior to those of BPDN and OMP.
In this paper, we use the BPDN model to sparsely representing the [[??].sub.k]'s for DOA estimation, and the fitting-error constrained objective function for each eigenvector is
In the case when there are noisy measurements, Basis Pursuit De-Noising (BPDN) techniques can be used to reconstruct the original signals .
The proposed SMP method is compared to several popular greedy algorithms, for example, the OMP, ROMP, StOMP, SP, CoSaMP and BAOMP algorithms, and the convex optimization algorithm, BPDN method.
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