稀疏信息恢复对数替代模型的统一理论框架及TDOA在多信源定位问题中的应用
The unified theoretical frame of logarithmic alternative model for sparse information recovery and its application in multiple source location problem by TDOA
摘要：
稀疏信息恢复的核心问题是求解$l_0$ -极小化问题，该问题是NP难问题。一方面，为了恢复原始稀疏解，有很多文献设计了$l_0$ -极小化的替代模型。对数替代模型作为最常用的选择之一，在许多应用中得到了广泛的应用。在本文中，我们提出了一个统一的理论分析，这个替代模型设计的$l_0$ -最小化。通过理论分析，证明了该模型与原$l_0$ -极小化模型之间的等价关系。此外，本文的主要贡献是给出了该模型的统一恢复条件和稳定性结果。通过给出局部最优条件，设计了一个统一的算法，并给出了相应的收敛性结果。最后，我们用这个新算法解决了多信源定位问题。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
