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.

信号驻留在低维子空间的并集中的想法包含了许多低维模型，这些模型在最近十年中已在许多领域和应用中得到广泛使用。直到最近，绝大多数作品还是单独研究了这些模型中的每一个。但是，最近的方法建议使用高斯平均宽度为低维模型提供一般理论，以作为数据固有低维的度量。在这项工作中，我们使用这种新颖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，并在假设测量矩阵为零的前提下，为来自低维线性子空间并集的信号提供一般的恢复保证。高斯。我们讨论了结果对特定模型的影响，并将这种广义算法作为一种新的贪婪方法的灵感来源，该方法用于稀疏合成和稀疏分析相结合的模型中的信号重建。我们进行的实验证明了所提出策略的有用性。