Ravazzi Chiara, Magli Enrico
1National Research Council of Italy, IEIIT-CNR, c/o Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, 10129 Italy.
2Politecnico di Torino, DET, Corso Duca degli Abruzzi 24, Torino, 10129 Italy.
EURASIP J Adv Signal Process. 2018;2018(1):46. doi: 10.1186/s13634-018-0565-5. Epub 2018 Jul 13.
In this paper, we propose a new method for support detection and estimation of sparse and approximately sparse signals from compressed measurements. Using a double Laplace mixture model as the parametric representation of the signal coefficients, the problem is formulated as a weighted minimization. Then, we introduce a new family of iterative shrinkage-thresholding algorithms based on double Laplace mixture models. They preserve the computational simplicity of classical ones and improve iterative estimation by incorporating soft support detection. In particular, at each iteration, by learning the components that are likely to be nonzero from the current MAP signal estimate, the shrinkage-thresholding step is adaptively tuned and optimized. Unlike other adaptive methods, we are able to prove, under suitable conditions, the convergence of the proposed methods to a local minimum of the weighted minimization. Moreover, we also provide an upper bound on the reconstruction error. Finally, we show through numerical experiments that the proposed methods outperform classical shrinkage-thresholding in terms of rate of convergence, accuracy, and of sparsity-undersampling trade-off.
在本文中，我们提出了一种从压缩测量中检测和估计稀疏及近似稀疏信号的新方法。使用双拉普拉斯混合模型作为信号系数的参数表示，该问题被表述为加权最小化问题。然后，我们引入了基于双拉普拉斯混合模型的一族新的迭代收缩阈值算法。它们保留了经典算法的计算简便性，并通过纳入软支持检测来改进迭代估计。特别是，在每次迭代中，通过从当前的最大后验概率（MAP）信号估计中学习可能非零的分量，收缩阈值步骤被自适应地调整和优化。与其他自适应方法不同，在合适的条件下，我们能够证明所提出的方法收敛到加权最小化问题的一个局部最小值。此外，我们还给出了重构误差的一个上界。最后，我们通过数值实验表明，所提出的方法在收敛速度、准确性和稀疏性与欠采样权衡方面优于经典的收缩阈值算法。
