  In this paper we analyze the blind deconvolution of an image and an unknown
blur in a coded imaging system. The measurements consist of subsampled
convolution of an unknown blurring kernel with multiple random binary
modulations (coded masks) of the image. To perform the deconvolution, we
consider a standard lifting of the image and the blurring kernel that
transforms the measurements into a set of linear equations of the matrix formed
by their outer product. Any rank-one solution to this system of equation
provides a valid pair of an image and a blur.
  We first express the necessary and sufficient conditions for the uniqueness
of a rank-one solution under some additional assumptions (uniform subsampling
and no limit on the number of coded masks). These conditions are special case
of a previously established result regarding identifiability in the matrix
completion problem. We also characterize a low-dimensional subspace model for
the blur kernel that is sufficient to guarantee identifiability, including the
interesting instance of "bandpass"` blur kernels.
  Next, assuming the bandpass model for the blur kernel, we show that the image
and the blur kernel can be found using nuclear norm minimization. Our main
results show that recovery is achieved (with high probability) when the number
of masks is on the order of
$\mu\log^{2}L\,\log\frac{Le}{\mu}\,\log\log\left(N+1\right)$ where $\mu$ is the
\emph{coherence} of the blur, $L$ is the dimension of the image, and $N$ is the
number of measured samples per mask.
