稀疏信号盲反卷积的稳定性及交替最小化重构

Kiryung Lee, Yanjun Li, M. Junge, Y. Bresler
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引用次数: 19

摘要

盲反卷积是对两个未知信号的卷积恢复。为了克服这一问题的顽固性,在实际应用中开发了针对具体应用的基于先验的解决方案。特别是,稀疏模型提供了有希望的先验。尽管在许多应用中取得了经验上的成功,但现有的分析在两个主要方面相当有限:信号和/或测量模型的理论假设与实际设置之间的差异;或者在信息理论极限所定义的最优范围内,无法证明参数值的成功。特别是,在盲反卷积问题中,单纯稀疏性模型作为可辨识性的先验性不够强。除了稀疏性之外,我们还采用了Ahmed等人的二次约束,该约束在傅里叶域中强制实现平坦谱。在此前提下,我们提供了一种迭代算法,该算法在盲反褶积中实现了有保证的性能,其测量次数与信号的稀疏度水平成正比(最高为对数因子)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stability in blind deconvolution of sparse signals and reconstruction by alternating minimization
Blind deconvolution is the recovery of two unknown signals from their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in practical applications. In particular, sparsity models have provided promising priors. In spite of empirical success in many applications, existing analyses are rather limited in two main ways: by disparity between theoretical assumptions on the signal and/or measurement model versus practical setups; or by failure to demonstrate success for parameter values within the optimal regime defined by the information theoretic limits. In particular, it has been shown that a naive sparsity model is not strong enough as a prior for identifiability in blind deconvolution problem. In addition to sparsity, we adopt a conic constraint by Ahmed et al., which enforces flat spectra in the Fourier domain. Under this prior, we provide an iterative algorithm that achieves guaranteed performance in blind deconvolution with number of measurements proportional (up to a logarithmic factor) to the sparsity level of the signal.
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