绝对值和法重构离散信号
Discrete Signal Reconstruction by Sum of Absolute Values
摘要：
在这封信中，我们考虑一个问题，重建一个未知的离散信号采取的值在一个有限的字母表从不完整的线性测量。这个问题的难点在于重构的计算复杂性实际上是指数级的。为了克服这个困难，我们扩展了压缩感知的思想，并提出解决问题的加权绝对值之和最小化。我们假设定义在字母表上的概率分布是已知的，并将重建问题表示为线性规划。算例表明了该方法的有效性。
英文摘要：
In this letter, we consider a problem of reconstructing an unknown discrete signal taking values in a finite alphabet from incomplete linear measurements. The difficulty of this problem is that the computational complexity of the reconstruction is exponential as it is. To overcome this difficulty, we extend the idea of compressed sensing, and propose to solve the problem by minimizing the sum of weighted absolute values. We assume that the probability distribution defined on an alphabet is known, and formulate the reconstruction problem as linear programming. Examples are shown to illustrate that the proposed method is effective.
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