  In this paper, we study the problem of recovering two unknown signals from
their convolution, which is commonly referred to as blind deconvolution.
Reformulation of blind deconvolution as a low-rank recovery problem has led to
multiple theoretical recovery guarantees in the past decade due to the success
of the nuclear norm minimization heuristic. In particular, in the absence of
noise, exact recovery has been established for sufficiently incoherent signals
contained in lower-dimensional subspaces. However, if the convolution is
corrupted by additive bounded noise, the stability of the recovery problem
remains much less understood. In particular, existing reconstruction bounds
involve large dimension factors and therefore fail to explain the empirical
evidence for dimension-independent robustness of nuclear norm minimization.
Recently, theoretical evidence has emerged for ill-posed behavior of low-rank
matrix recovery for sufficiently small noise levels. In this work, we develop
improved recovery guarantees for blind deconvolution with adversarial noise
which exhibit square-root scaling in the noise level. Hence, our results are
consistent with existing counterexamples which speak against linear scaling in
the noise level as demonstrated for related low-rank matrix recovery problems.
