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Distributed Sampling of Signals Linked by Sparse Filtering: Theory and Applications

机译:稀疏滤波链接的信号的分布式采样:理论与应用

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摘要

We study the distributed sampling and centralized reconstruction of two correlated signals, modeled as the input and output of an unknown sparse filtering operation. This is akin to a Slepian-Wolf setup, but in the sampling rather than the lossless compression case. Two different scenarios are considered: In the case of universal reconstruction, we look for a sensing and recovery mechanism that works for all possible signals, whereas in what we call almost sure reconstruction, we allow to have a small set (with measure zero) of unrecoverable signals. We derive achievability bounds on the number of samples needed for both scenarios. Our results show that, only in the almost sure setup can we effectively exploit the signal correlations to achieve effective gains in sampling efficiency. In addition to the above theoretical analysis, we propose an efficient and robust distributed sampling and reconstruction algorithm based on annihilating filters. We evaluate the performance of our method in one synthetic scenario, and two practical applications, including the distributed audio sampling in binaural hearing aids and the efficient estimation of room impulse responses. The numerical results confirm the effectiveness and robustness of the proposed algorithm in both synthetic and practical setups.
机译:我们研究了两个相关信号的分布式采样和集中重建,它们被建模为未知稀疏滤波操作的输入和输出。这类似于Slepian-Wolf设置,但是在采样而非无损压缩情况下。考虑了两种不同的情况:在通用重建的情况下,我们寻找一种适用于所有可能信号的感知和恢复机制,而在我们几乎可以肯定的重建中,我们允许使用一小部分(度量为零)不可恢复的信号。我们得出两种情况所需的样本数量的可实现性界限。我们的结果表明,只有在几乎确定的设置中,我们才能有效地利用信号相关性,以实现采样效率的有效提高。除上述理论分析外,我们还提出了一种基于an灭滤波器的高效鲁棒的分布式采样和重构算法。我们在一个综合场景和两个实际应用中评估了该方法的性能,包括双耳助听器中的分布式音频采样以及对室内冲激响应的有效估计。数值结果证实了该算法在合成和实际设置中的有效性和鲁棒性。

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