The paper proposes a novel signal reconstruction algorithm through substituting the gradient descent method in the iterative hard thresholding algorithm with a faster sparse randomized Kaczmarz method. By designing a ...
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The paper proposes a novel signal reconstruction algorithm through substituting the gradient descent method in the iterative hard thresholding algorithm with a faster sparse randomized Kaczmarz method. By designing a series of gradually attenuated weights for the matrix rows whose indexes lie outside of the support set of the original sparse signal, we can focus the iterations on the effective support rows of the measurement matrix. The experiment results show that the proposed algorithm presents a faster convergence rate and more accurate reconstruction accuracy than the state-of-the-art algorithms. Meanwhile, the successful reconstruction probability of the proposed algorithm is higher than that of other algorithms. Moreover, the characteristics of the proposed signal reconstruction algorithm are also analyzed in detail through numerical experiments.
Based on the iterativehardthresholding (IHT) algorithm, this paper presents the relaxed iterativethresholdingalgorithm which is a modified algorithm of the conventional IHT algorithm. By introducing the relaxed fa...
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ISBN:
(纸本)9783642352102
Based on the iterativehardthresholding (IHT) algorithm, this paper presents the relaxed iterativethresholdingalgorithm which is a modified algorithm of the conventional IHT algorithm. By introducing the relaxed factors, modifying the iterative formulae and proposing the relaxed algorithm correspondingly, we acquired the least number of iterations and error estimate required by the measurement matrices of satisfying the RIP. Compared with the IHT algorithm, the method presented in this paper not only has the advantages of keeping linear stability and clearly delimiting the upper limit of the number of iterations, but also obtains the same computational precision with the less number of iterations which saves the labor of calculation. Finally, taking the Hadamard orthogonal basis as sparse basis, the random Gaussian matrix as measurement matrix, we have verified the validity of the algorithm proposed above by experimental simulation.
Reasonable sparse representation of signals are one of the key factors to ensure the quality of compressed sampling, so a proper sparse representing methods should be selected to make the signals sparse to the greates...
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ISBN:
(纸本)9783642352850
Reasonable sparse representation of signals are one of the key factors to ensure the quality of compressed sampling, so a proper sparse representing methods should be selected to make the signals sparse to the greatest extent in the applications of compressed sensing. In this paper we adopted the framework of block compressed sensing to sample the images, used the iterativehardthresholding(IHT) algorithm to reconstruct the original images, and employed the wavelet-based contourlet transform, an improved contourlet transform, to decompose 2D images in IHT reconstruction process. Numerical experiments indicated that the runtime of the reconstruction algorithm adopting wavelet-based contourlet transform is the shortest compared to that adopting contourlet transform and that adopting wavelet transform;under low compression ratios, the quality of the reconstructed images using wavelet-based contourlet transform is superior to that using contourlet transform and that using traditional wavelet transform.
In this paper, we propose a two-greedy subspace Kaczmarz algorithm to solve the system of linear equations with sparse solution. This algorithm improves the convergence speed compared to randomized Kaczmarz algorithm....
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ISBN:
(纸本)9781728171760
In this paper, we propose a two-greedy subspace Kaczmarz algorithm to solve the system of linear equations with sparse solution. This algorithm improves the convergence speed compared to randomized Kaczmarz algorithm. The speedup is obtained by projecting every iterate onto the solution space generated by greedily selected rows. Our numerical results demonstrate convergence speed for sparse recovery.
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