Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sensing Matrix Design and Sparse Recovery on the Sphere and the Rotation
  Group   In this paper, {the goal is to design deterministic sampling patterns on the
sphere and the rotation group} and, thereby, construct sensing matrices for
sparse recovery of band-limited functions. It is first shown that random
sensing matrices, which consists of random samples of Wigner D-functions,
satisfy the Restricted Isometry Property (RIP) with proper preconditioning and
can be used for sparse recovery on the rotation group. The mutual coherence,
however, is used to assess the performance of deterministic and regular sensing
matrices. We show that many of widely used regular sampling patterns yield
sensing matrices with the worst possible mutual coherence, and therefore are
undesirable for sparse recovery. Using tools from angular momentum analysis in
quantum mechanics, we provide a new expression for the mutual coherence, which
encourages the use of regular elevation samples. We construct low coherence
deterministic matrices by fixing the regular samples on the elevation and
minimizing the mutual coherence over the azimuth-polarization choice. It is
shown that once the elevation sampling is fixed, the mutual coherence has a
lower bound that depends only on the elevation samples. This lower bound,
however, can be achieved for spherical harmonics, which leads to new sensing
matrices with better coherence than other representative regular sampling
patterns. This is reflected as well in our numerical experiments where our
proposed sampling patterns perfectly match the phase transition of random
sampling patterns.

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The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg