Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Manifold Gradient Descent Solves Multi-Channel Sparse Blind
  Deconvolution Provably and Efficiently   Multi-channel sparse blind deconvolution, or convolutional sparse coding,
refers to the problem of learning an unknown filter by observing its circulant
convolutions with multiple input signals that are sparse. This problem finds
numerous applications in signal processing, computer vision, and inverse
problems. However, it is challenging to learn the filter efficiently due to the
bilinear structure of the observations with the respect to the unknown filter
and inputs, as well as the sparsity constraint. In this paper, we propose a
novel approach based on nonconvex optimization over the sphere manifold by
minimizing a smooth surrogate of the sparsity-promoting loss function. It is
demonstrated that manifold gradient descent with random initializations will
provably recover the filter, up to scaling and shift ambiguity, as soon as the
number of observations is sufficiently large under an appropriate random data
model. Numerical experiments are provided to illustrate the performance of the
proposed method with comparisons to existing ones.

22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin