Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Frame-constrained Total Variation Regularization for White Noise
  Regression   Despite the popularity and practical success of total variation (TV)
regularization for function estimation, surprisingly little is known about its
theoretical performance in a statistical setting. While TV regularization has
been known for quite some time to be minimax optimal for denoising
one-dimensional signals, for higher dimensions this remains elusive until
today. In this paper we consider frame-constrained TV estimators including many
well-known (overcomplete) frames in a white noise regression model, and prove
their minimax optimality w.r.t. $L^q$-risk ($1\leq q<\infty$) up to a
logarithmic factor in any dimension $d\geq 1$. Overcomplete frames are an
established tool in mathematical imaging and signal recovery, and their
combination with TV regularization has been shown to give excellent results in
practice, which our theory now confirms. Our results rely on a novel connection
between frame-constraints and certain Besov norms, and on an interpolation
inequality to relate them to the risk functional.

9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int