Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smoothing for signals with discontinuities using higher order
  Mumford-Shah models   Minimizing the Mumford-Shah functional is frequently used for smoothing
signals or time series with discontinuities. A significant limitation of the
standard Mumford-Shah model is that linear trends -- and in general polynomial
trends -- in the data are not well preserved. This can be improved by building
on splines of higher order which leads to higher order Mumford-Shah models. In
this work, we study these models in the univariate situation: we discuss
important differences to the first order Mumford-Shah model, and we obtain
uniqueness results for their solutions. As a main contribution, we derive fast
minimization algorithms for Mumford-Shah models of arbitrary orders. We show
that the worst case complexity of all proposed schemes is quadratic in the
length of the signal. Remarkably, they thus achieve the worst case complexity
of the fastest solver for the piecewise constant Mumford-Shah model (which is
the simplest model of the class). Further, we obtain stability results for the
proposed algorithms. We complement these results with a numerical study. Our
reference implementation processes signals with more than 10,000 elements in
less than one second.

33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas