论文标题
对数替代模型的统一理论框架，用于稀疏信息恢复及其在多个源位置问题中的应用TDOA
The unified theoretical frame of logarithmic alternative model for sparse information recovery and its application in multiple source location problem by TDOA
论文作者
论文摘要
在稀疏信息恢复中，核心问题是解决NP-HARD的$ L_0 $毫米化。一方面，为了恢复原始的稀疏解决方案，有很多论文设计了$ L_0 $ - 毫米化的替代模型。作为最受欢迎的选择之一，对数替代模型在许多应用中广泛使用。在本文中，我们介绍了针对$ l_0 $ minimization设计的替代模型的统一理论分析。通过理论分析，我们证明了替代模型与原始$ L_0 $ - 毫米化之间的等价关系。此外，本文的主要贡献是给出统一的恢复条件和稳定的结果。通过介绍局部最佳条件，本文还设计了一种统一的算法并呈现相应的收敛结果。最后，我们使用这种新算法来解决多个源位置问题。
In sparse information recovery, the core problem is to solve the $l_0$-minimization which is NP-hard. On one hand, in order to recover the original sparse solution, there are a lot of papers designing alternative model for $l_0$-minimization. As one of the most popular choice, the logarithmic alternative model is widely used in many applications. In this paper, we present an unified theoretical analysis of this alternative model designed for $l_0$-minimization. By the theoretical analysis, we prove the equivalence relationship between the alternative model and the original $l_0$-minimization. Furthermore, the main contribution of this paper is to give an unified recovery condition and stable result of this model. By presenting the local optimal condition, this paper also designs an unified algorithm and presents the corresponding convergence result. Finally, we use this new algorithm to solve the multiple source location problem.
