Compressed Counting Meets Compressed Sensing
published: July 15, 2014, recorded: June 2014, views: 3193
Slides
Related content
Report a problem or upload files
If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Description
Compressed sensing (sparse signal recovery) has been a popular and important research topic in recent years. By observing that natural signals (e.g., images or network data) are often nonnegative, we propose a framework for nonnegative signal recovery using Compressed Counting (CC). CC is a technique built on maximally-skewed α-stable random projections originally developed for data stream computations (e.g., entropy estimations). Our recovery procedure is computationally efficient in that it requires only one linear scan of the coordinates.
In our settings, the signal x∈RN is assumed to be nonnegative, i.e., xi≥0,∀ i. We prove that, when α∈(0, 0.5], it suffices to use M=(Cα+o(1))ϵ−α(∑Ni=1xαi)logN/δ measurements so that, with probability 1−δ, all coordinates will be recovered within ϵ additive precision, in one scan of the coordinates. The constant Cα=1 when α→0 and Cα=π/2 when α=0.5. In particular, when α→0, the required number of measurements is essentially M=KlogN/δ, where K=∑Ni=11{xi≠0} is the number of nonzero coordinates of the signal.
Link this page
Would you like to put a link to this lecture on your homepage?Go ahead! Copy the HTML snippet !
Write your own review or comment: