Projected Nesterov's Proximal-Gradient Algorithm for Sparse Signal Recovery
Projected Nesterov's Proximal-Gradient Algorithm for Sparse Signal Recovery
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DOI：
10.1109/tsp.2017.2691661
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发表时间：
2015-02
影响因子：
5.4
通讯作者：
Renliang Gu;Aleksandar Dogandzic
中科院分区：
文献类型：
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作者：
Renliang Gu;Aleksandar Dogandzic
我们开发了一种预计的Nesterov近端梯度（PNPG）方法，用于稀疏信号重建，该方法将适应性步长与Nesterov的动量加速相结合。我们希望最小化的目标函数是凸面可区分数据的总和（负模样（NLL））项和凸正则化项的总和。我们应用稀疏的信号正则化，其中信号属于NLL域的闭合内的封闭凸；凸设备约束有助于灵活的NLL域和准确的信号恢复。使用$ \ boldsymbol {\ ell} _1 $ -Norm惩罚对信号线性变换系数施加信号稀疏性。 PNPG方法采用了预测的Nesterov加速步骤，并通过重新启动和基于二重性的内部迭代来计算近端映射。我们提出了一种自适应阶梯尺寸选择方案，以获得NLL的良好局部主要功能并减少所花费的回溯时间。多亏了逐步适应，PNPG收敛的速度比未适应NLL局部曲率的方法更快。我们提出了动量加速度的集成推导和$ \ boldsymbol {\ Mathcal {o}（k^{ - 2}）} $目标函数收敛速率和迭代的融合的证明，该迭代率是适应性步骤大小，不可思议的，迭代近端映射和凸 - 集合约束。 PNPG的调整在很大程度上是独立的。使用Poisson广义线性和高斯线性测量模型进行了断层扫描和压缩感应重建实验，证明了该方法的性能。
We develop a projected Nesterov's proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov's momentum acceleration. The objective function that we wish to minimize is the sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a convex regularization term. We apply sparse signal regularization where the signal belongs to a closed convex set within the closure of the domain of the NLL; the convex-set constraint facilitates flexible NLL domains and accurate signal recovery. Signal sparsity is imposed using the $\boldsymbol{\ell }_1$ -norm penalty on the signal's linear transform coefficients. The PNPG approach employs a projected Nesterov's acceleration step with restart and a duality-based inner iteration to compute the proximal mapping. We propose an adaptive step-size selection scheme to obtain a good local majorizing function of the NLL and reduce the time spent backtracking. Thanks to step-size adaptation, PNPG converges faster than the methods that do not adjust to the local curvature of the NLL. We present an integrated derivation of the momentum acceleration and proofs of $\boldsymbol{\mathcal {O}(k^{-2})}$ objective function convergence rate and convergence of the iterates, which account for adaptive step size, inexactness of the iterative proximal mapping, and the convex-set constraint. The tuning of PNPG is largely application independent. Tomographic and compressed-sensing reconstruction experiments with Poisson generalized linear and Gaussian linear measurement models demonstrate the performance of the proposed approach.