论文标题
压缩感中的一个奇妙的三角形
A wonderful triangle in compressed sensing
论文作者
论文摘要
为了确定与$ \ ell_ {0} $ quasi-norm具有直接度量关系的稀疏近似函数，我们介绍了一个奇妙的三角形，其侧面由$ \ vert \ vert \ vert \ mathbf {x} \ vert_ {0} \ Mathbf {X} \ Vert _ {\ infty} $用于任何非零的Vector $ \ Mathbf {X} \ in \ Mathbb {r}^{n} $，通过探究本文中的迭代软售货操作员。基于此三角形，我们推断出比率$ \ ell_ {1} $和$ \ ell _ {\ infty} $ norms作为稀疏信号重建的稀疏目标函数，并尝试给出信号的稀疏间隔。考虑$ \ ell_ {1}/\ ell _ {\ infty} $从三角形的角度$β$最小化，与该侧相对应，其长度为$ \ vert \ vert \ mathbf {x} \ vert _ {\ vert _ {\ infty} - {\ infty} - \ Mathbf {X} \ Vert_ {0} $，我们最终演示了现有$ \ ell_ {1}/\ ell _ {\ infty} $ algorithm的性能，通过将其与$ \ ell_ {1}/\ ell_ ell_ {2} $ algorithm进行比较。
In order to determine the sparse approximation function which has a direct metric relationship with the $\ell_{0}$ quasi-norm, we introduce a wonderful triangle whose sides are composed of $\Vert \mathbf{x} \Vert_{0}$, $\Vert \mathbf{x} \Vert_{1}$ and $\Vert \mathbf{x} \Vert_{\infty}$ for any non-zero vector $\mathbf{x} \in \mathbb{R}^{n}$ by delving into the iterative soft-thresholding operator in this paper. Based on this triangle, we deduce the ratio $\ell_{1}$ and $\ell_{\infty}$ norms as a sparsity-promoting objective function for sparse signal reconstruction and also try to give the sparsity interval of the signal. Considering the $\ell_{1}/\ell_{\infty}$ minimization from a angle $β$ of the triangle corresponding to the side whose length is $\Vert \mathbf{x} \Vert_{\infty} - \Vert \mathbf{x} \Vert_{1}/\Vert \mathbf{x} \Vert_{0}$, we finally demonstrate the performance of existing $\ell_{1}/\ell_{\infty}$ algorithm by comparing it with $\ell_{1}/\ell_{2}$ algorithm.
