TL;DR本文探讨了如何利用 L_p-norm 等方法在限制非零元素个数的条件下,通过线性转换的约束来重构出一个 N 维向量 x.
Abstract
We consider the problem of reconstructing an $N$-dimensional continuous
vector $\bx$ from $P$ constraints which are generated by its linear
transformation under the assumption that the number of non-zero elements of
$\bx$ is typically limited to $\rho N$ ($0\le \rho \le 1$). Problems of this
type can be solved by minimizing a cost function with respect to th
本文主要研究了基于生成模型的压缩感知问题,通过下界分析表明基于 L-Lipschitz 生成模型的压缩感知需要线性测量数至少是 k 乘以对数级别的,同时指出生成模型可以作为一种结构表示方法进行推广。作者还构造了一个具有 ReLU 激活的神经网络模型,其层数为 O (1),每层的激活函数个数为 O (kn),且该模型可以表示所有 k 稀疏向量。