Blind deconvolution and compressed sensing

In this paper we consider the classical problem of blind deconvolution of multiple signals from its superposition, also called blind demixing and deconvolution. One is given a signal Σ
^r
_i=1
w
_i
× x
_i
= y ϵ R
^L
which is the superposition of r unknown source signals {x
_i
}
^r
_i=1
and convolution kernels {w
_i
}
^r
_i=1
The goal is to reconstruct the vectors w
_i
and x
_i
, which are elements of known but random subspaces. The problem can be lifted into a low rank matrix recovery problem. We will discuss uniform as well as non-uniform recovery guarantees.