论文标题
$ \ ell_ {0} $的班级解决方案的非唯一性 - 最小化问题
Nonuniqueness of Solutions of a Class of $\ell_{0}$-minimization Problems
论文作者
论文摘要
最近，在许多领域（例如压缩感测，图像处理，统计学习和数据稀疏近似）等许多领域，找到不确定的线性系统的最稀少解决方案已成为重要的请求。在本文中，我们研究了解决方案的一些理论特性，即$ \ ell_ {0} $ - 最小化问题的一般类别，这些问题可用于处理许多实际应用。我们建立了一些必要的条件，使某个问题是解决此类问题的最稀少解决方案，并且我们还表征了对问题的最稀少解决方案的条件。最后，我们讨论了该类别问题的解决方案集界限的某些条件。
Recently, finding the sparsest solution of an underdetermined linear system has become an important request in many areas such as compressed sensing, image processing, statistical learning, and data sparse approximation. In this paper, we study some theoretical properties of the solutions to a general class of $\ell_{0}$-minimization problems, which can be used to deal with many practical applications. We establish some necessary conditions for a point being the sparsest solution to this class of problems, and we also characterize the conditions for the multiplicity of the sparsest solutions to the problem. Finally, we discuss certain conditions for the boundedness of the solution set of this class of problems.
