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Generalizing CoSaMP to signals from a union of low dimensional linear subspaces

机译：概率从低维线性子空间的联轴发出舒张

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摘要

The idea that signals reside in a union of low dimensional subspaces subsumes many low dimensional models that have been used extensively in the recent decade in many fields and applications. Until recently, the vast majority of works have studied each one of these models on its own. However, a recent approach suggests providing general theory for low dimensional models using their Gaussian mean width, which serves as a measure for the intrinsic low dimensionality of the data. In this work we use this novel approach to study a generalized version of the popular compressive sampling matching pursuit (CoSaMP) algorithm, and to provide general recovery guarantees for signals from a union of low dimensional linear subspaces, under the assumption that the measurement matrix is Gaussian. We discuss the implications of our results for specific models, and use the generalized algorithm as an inspiration for a new greedy method for signal reconstruction in a combined sparse-synthesis and cosparse-analysis model. We perform experiments that demonstrate the usefulness of the proposed strategy. (C) 2018 Elsevier Inc. All rights reserved.
机译：信号驻留在低维子空间的联合中的想法归入许多低维模型，这些模型已经在许多字段和应用中的最近十年中广泛使用。直到最近，绝大多数作品都自己研究了这些模型中的每一个。然而，最近的方法建议使用其高斯平均宽度为低维模型提供一般理论，其用作数据的内在低维度的度量。在这项工作中，我们使用这种新的方法来研究流行的压缩采样匹配追踪（COSAMP）算法的广义版本，并为来自低维线性子空间的联盟的信号提供一般恢复保证，在测量矩阵是的假设下高斯。我们讨论我们对特定模型的结果的影响，并使用广义算法作为一种新的贪婪方法在组合稀疏合成和Cosparse-Analysis模型中的信号重建方法的启发。我们执行展示拟议策略的有用性的实验。 （c）2018 Elsevier Inc.保留所有权利。

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