标题： 通过特征矩阵在未知噪声水平下的稀疏自由去卷积 显示英文标题

标题： Sparse free deconvolution under unknown noise level via eigenmatrix

摘要： 本文研究了在未知噪声水平下稀疏谱测度的谱估计问题。 主要的技术工具是求解非结构化稀疏恢复问题的特征矩阵方法。当噪声水平确定时，自由去卷积将问题简化为一个可以应用特征矩阵方法的非结构化稀疏恢复问题。为了确定未知的噪声水平，我们基于特征矩阵方法中的中间矩阵的奇异值提出了一个优化问题。 数值结果展示了加性自由去卷积和乘性自由去卷积的效果。 显示英文摘要

摘要： This note considers the spectral estimation problems of sparse spectral measures under unknown noise levels. The main technical tool is the eigenmatrix method for solving unstructured sparse recovery problems. When the noise level is determined, the free deconvolution reduces the problem to an unstructured sparse recovery problem to which the eigenmatrix method can be applied. To determine the unknown noise level, we propose an optimization problem based on the singular values of an intermediate matrix of the eigenmatrix method. Numerical results are provided for both the additive and multiplicative free deconvolutions.