Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact Dimensionality Reduction for Partial Line Spectra Estimation
  Problems   Line spectral estimation theory aims to estimate the off-the-grid spectral
components of a time signal with optimal precision. Recent results have shown
that it is possible to recover signals having sparse line spectra from few
temporal observations via the use of convex programming. However, the
computational cost of such approaches remains the major flaw to their
application to practical systems. This work investigates the recovery of
spectrally sparse signal from low-dimensional partial measurements. It is shown
in the first part of this paper that, under a light assumption on the
sub-sampling matrix, the partial line spectral estimation problems can be
relaxed into a low-dimensional semidefinite program. The proof technique relies
on a novel extension of the Gram parametrization to subspaces of trigonometric
polynomials.
  The second part of this work focuses on the analysis of two particular
sub-sampling patterns: multirate sampling and random selection sampling. It is
shown that those sampling patterns guarantee perfect recovery of the line
spectra, and that the reconstruction can be achieved in a poly-logarithmic time
with respect to the full observation case. Moreover, the sub-Nyquist recovery
capabilities of such sampling patterns are highlighted. The atomic soft
thresholding method is adapted in the presented framework to estimate sparse
spectra in noisy environments, and a scalable algorithm for its resolution is
proposed.

5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph