  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.
