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Sparsity-Based Recovery of Finite Alphabet Solutions to Underdetermined Linear Systems

机译:欠定线性系统基于稀疏性的有限字母解的恢复

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摘要

We consider the problem of estimating a deterministic finite alphabet vector from underdetermined measurements , where is a given (random) matrix. Two new convex optimization methods are introduced for the recovery of finite alphabet signals via -norm minimization. The first method is based on regularization. In the second approach, the problem is formulated as the recovery of sparse signals after a suitable sparse transform. The regularization-based method is less complex than the transform-based one. When the alphabet size equals 2 and grows proportionally, the conditions under which the signal will be recovered with high probability are the same for the two methods. When , the behavior of the transform-based method is established. Experimental results support this theoretical result and show that the transform method outperforms the regularization-based one.
机译:我们考虑了从欠定的度量估计确定性有限字母向量的问题,其中给定(随机)矩阵。引入了两种新的凸优化方法,用于通过-norm最小化恢复有限字母信号。第一种方法基于正则化。在第二种方法中,问题被表述为在进行适当的稀疏变换之后恢复稀疏信号。基于正则化的方法不如基于变换的方法复杂。当字母大小等于2并成比例增长时,这两种方法将以高概率恢复信号的条件相同。当为时,将建立基于变换的方法的行为。实验结果支持了这一理论结果,并表明该变换方法优于基于正则化的变换方法。

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