





















In the problem of one-bit compressed sensing, the goal is to find a $δ$-close estimation of a $k$-sparse vector $x \in \mathbb{R}^n$ given the signs of the entries of $y = Φx$, where $Φ$ is called the measurement matrix. For the one-bit compressed sensing problem, previous work \cite{Plan-robust,support} achieved $Θ(δ^{-2} k \log(n/k))$ and $\tilde{ \Oh} ( \frac{1}{ δ} k \log (n/k))$ measurements, respectively, but the decoding time was $Ω( n k \log (n / k ))$. \ In this paper, using tools and techniques developed in the context of two-stage group testing and streaming algorithms, we contribute towards the direction of very fast decoding time. We give a variety of schemes for the different versions of one-bit compressed sensing, such as the for-each and for-all version, support recovery; all these have $poly(k, \log n)$ decoding time, which is an exponential improvement over previous work, in terms of the dependence of $n$.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。