Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adapting to unknown noise level in sparse deconvolution   In this paper, we study sparse spike deconvolution over the space of
complex-valued measures when the input measure is a finite sum of Dirac masses.
We introduce a modified version of the Beurling Lasso (BLasso), a semi-definite
program that we refer to as the Concomitant Beurling Lasso (CBLasso). This new
procedure estimates the target measure and the unknown noise level
simultaneously. Contrary to previous estimators in the literature, theory holds
for a tuning parameter that depends only on the sample size, so that it can be
used for unknown noise level problems. Consistent noise level estimation is
standardly proved. As for Radon measure estimation, theoretical guarantees
match the previous state-of-the-art results in Super-Resolution regarding
minimax prediction and localization. The proofs are based on a bound on the
noise level given by a new tail estimate of the supremum of a stationary
non-Gaussian process through the Rice method.

13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an