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Consistent Dictionary Learning for Signal Declipping

机译:一致的字典学习用于信号衰减

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摘要

Clipping, or saturation, is a common nonlinear distortion in signal processing. Recently, declipping techniques have been proposed based on sparse decomposition of the clipped signals on a fixed dictionary, with additional constraints on the amplitude of the clipped samples. Here we propose a dictionary learning approach, where the dictionary is directly learned from the clipped measurements. We propose a soft-consistency metric that minimizes the distance to a convex feasibility set, and takes into account our knowledge about the clipping process. We then propose a gradient descent-based dictionary learning algorithm that minimizes the proposed metric, and is thus consistent with the clipping measurement. Experiments show that the proposed algorithm outperforms other dictionary learning algorithms applied to clipped signals. We also show that learning the dictionary directly from the clipped signals outperforms consistent sparse coding with a fixed dictionary.
机译:削波或饱和是信号处理中常见的非线性失真。近来,已经提出了基于固定字典上的削波信号的稀疏分解的削波技术,并且对削波样本的幅度具有附加约束。在这里,我们提出了一种字典学习方法,其中从裁剪后的测量结果中直接学习字典。我们提出了一种软一致性度量,该度量将到凸可行集的距离最小化,并考虑了我们对裁剪过程的了解。然后,我们提出了一种基于梯度下降的字典学习算法,该算法可最大程度地减少所提出的指标,从而与限幅测量保持一致。实验表明,该算法优于其他应用于限幅信号的字典学习算法。我们还表明,直接从裁剪后的信号中学习字典的效果优于使用固定字典的一致稀疏编码。

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