Stagewise Weak Gradient Pursuits
Stagewise Weak Gradient Pursuits
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DOI：
10.1109/tsp.2009.2025088
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发表时间：
2009-11-01
影响因子：
5.4
通讯作者：
Davies, Mike E.
中科院分区：
文献类型：
--
作者：
Blumensath, Thomas;Davies, Mike E.
在从信号采集到源分离的广泛信号处理应用中，寻找欠定逆问题的稀疏解是一个基本的挑战。本文着眼于贪婪算法，适用于非常大的问题。主要的贡献是一个新的选择策略（称为stagewise弱选择），有效地选择在每次迭代中的几个元素的发展。新的选择策略是基于实现，许多经典的证明稀疏信号的恢复可以平凡地扩展到新的设置。仿真结果表明了该方法的计算效率和良好的性能。这种策略可以用于几个贪婪算法，我们认为在梯度追踪框架内使用，其中所选系数使用共轭更新方向进行更新。对于此更新，我们提出了一个快速实现和新颖的收敛结果。
Finding sparse solutions to underdetermined inverse problems is a fundamental challenge encountered in a wide range of signal processing applications, from signal acquisition to source separation. This paper looks at greedy algorithms that are applicable to very large problems. The main contribution is the development of a new selection strategy (called stagewise weak selection) that effectively selects several elements in each iteration. The new selection strategy is based on the realization that many classical proofs for recovery of sparse signals can be trivially extended to the new setting. What is more, simulation studies show the computational benefits and good performance of the approach. This strategy can be used in several greedy algorithms, and we argue for the use within the gradient pursuit framework in which selected coefficients are updated using a conjugate update direction. For this update, we present a fast implementation and novel convergence result.