Abstract-Greedy algorithms form an essential tool for compressed sensing. However, their inherent batch mode discourages their use in time-varying environments due to significant complexity and storage requirements. In this paper a powerful greedy scheme developed in [1], [2], is converted into an adaptive algorithm which is applied to estimation of a class of nonlinear communication systems. Performance is assessed via computer simulations on a variety of linear and nonlinear channels; all confirm significant improvements over conventional methods.
Abstract-This paper focuses on the development of novel greedy techniques for distributed learning under sparsity constraints. Greedy techniques have widely been used in centralized systems due to their low computational requirements and at the same time their relatively good performance in estimating sparse parameter vectors/signals. The paper reports two new algorithms in the context of sparsity-aware learning. In both cases, the goal is first to identify the support set of the unknown signal and then to estimate the non-zero values restricted to the active support set. First, an iterative greedy multi-step procedure is developed, based on a neighborhood cooperation strategy, using batch processing on the observed data. Next, an extension of the algorithm to the online setting, based on the diffusion LMS rationale for adaptivity, is derived. Theoretical analysis of the algorithms is provided, where it is shown that the batch algorithm converges to the unknown vector if a Restricted Isometry Property (RIP) holds. Moreover, the online version converges in the mean to the solution vector under some general assumptions. Finally, the proposed schemes are tested against recently developed sparsity-promoting algorithms and their enhanced performance is verified via simulation examples.
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