Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational Convergence Analysis With Smoothed-TV Interpretation   The problem of minimizing the least squares functional with a Fr\'echet
differentiable, lower semi-continuous, convex penalizer $J$ is considered to be
solved. The penalizer maps the functions of Banach space $\mathcal{V}$ into
$\mathbb{R}_{+},$ $ J : \mathcal{V} \rightarrow \mathbb{R}_{+}.$ It is assumed
that some given data $f^{\delta}$ is defined on a compact domain $\mathcal{G}
\subset \mathbb{R}_{+}$ and in the class of Hilbert space, $f^{\delta} \in
\mathcal{L}^{2}(\mathcal{G}).$ Then general Tikhonov functional associated with
some given linear, compact and injective forward operator $\mathcal{T} :
\mathcal{V} \rightarrow \mathcal{L}^{2}(\mathcal{G})$ is formulated as
\begin{eqnarray} F_{\alpha}(\varphi, f^{\delta}) : & \mathcal{V} \times
\mathcal{L}^{2}(\mathcal{G}) & \rightarrow \mathbb{R}_{+} \nonumber\\ &
(\varphi, f^{\delta}) & \mapsto F_{\alpha}(\varphi, f^{\delta}) :=
\frac{1}{2}\Vert\mathcal{T}\varphi -
f^{\delta}\Vert_{\mathcal{L}^{2}(\mathcal{G})}^2 + \alpha J(\varphi) .
\nonumber \end{eqnarray} Convergence of the regularized solution
$\varphi_{\alpha(\delta)} \in \mathrm{argmin}_{\varphi \in \mathcal{V}}
F_{\alpha}(\varphi, f^{\delta})$ to the true solution $\varphi^{\dagger}$ is
analysed by means of Bregman divergence. First part of this aims to provide
some general convergence analysis for generally strongly convex functional $J$
in the cost functional $F_{\alpha}$. In this part the key observation is that
strong convexity of the penalty term $J$ with its convexity modulus implies
norm convergence in the Bregman metric sense. In the second part, this general
analysis will be interepreted for the smoothed-TV functional. The result of
this work is applicable for any strongly convex functional.

25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
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The categories of this paper are: stat
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc