Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recovering H\"older smooth functions from noisy modulo samples   In signal processing, several applications involve the recovery of a function
given noisy modulo samples. The setting considered in this paper is that the
samples corrupted by an additive Gaussian noise are wrapped due to the modulo
operation. Typical examples of this problem arise in phase unwrapping problems
or in the context of self-reset analog to digital converters. We consider a
fixed design setting where the modulo samples are given on a regular grid.
Then, a three stage recovery strategy is proposed to recover the ground truth
signal up to a global integer shift. The first stage denoises the modulo
samples by using local polynomial estimators. In the second stage, an
unwrapping algorithm is applied to the denoised modulo samples on the grid.
Finally, a spline based quasi-interpolant operator is used to yield an estimate
of the ground truth function up to a global integer shift. For a function in
H\"older class, uniform error rates are given for recovery performance with
high probability. This extends recent results obtained by Fanuel and Tyagi for
Lipschitz smooth functions wherein $k$NN regression was used in the denoising
step.

9
The categories of this paper are: nlin
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th